id	sid	tid	token	lemma	pos
cord-326631-7gd3hjc3	1	1	key	key	ADJ
cord-326631-7gd3hjc3	1	2	:	:	PUNCT
cord-326631-7gd3hjc3	1	3	cord-326631	cord-326631	PROPN
cord-326631-7gd3hjc3	1	4	-	-	PUNCT
cord-326631-7gd3hjc3	1	5	7gd3hjc3	7gd3hjc3	PROPN
cord-326631-7gd3hjc3	1	6	authors	author	NOUN
cord-326631-7gd3hjc3	1	7	:	:	PUNCT
cord-326631-7gd3hjc3	1	8	ma	ma	PROPN
cord-326631-7gd3hjc3	1	9	,	,	PUNCT
cord-326631-7gd3hjc3	1	10	junling	junling	NOUN
cord-326631-7gd3hjc3	1	11	;	;	PUNCT
cord-326631-7gd3hjc3	1	12	earn	earn	VERB
cord-326631-7gd3hjc3	1	13	,	,	PUNCT
cord-326631-7gd3hjc3	1	14	david	david	PROPN
cord-326631-7gd3hjc3	1	15	j.	j.	PROPN
cord-326631-7gd3hjc3	1	16	d.	d.	PROPN
cord-326631-7gd3hjc3	1	17	title	title	PROPN
cord-326631-7gd3hjc3	1	18	:	:	PUNCT
cord-326631-7gd3hjc3	1	19	generality	generality	NOUN
cord-326631-7gd3hjc3	1	20	of	of	ADP
cord-326631-7gd3hjc3	1	21	the	the	DET
cord-326631-7gd3hjc3	1	22	final	final	ADJ
cord-326631-7gd3hjc3	1	23	size	size	NOUN
cord-326631-7gd3hjc3	1	24	formula	formula	NOUN
cord-326631-7gd3hjc3	1	25	for	for	ADP
cord-326631-7gd3hjc3	1	26	an	an	DET
cord-326631-7gd3hjc3	1	27	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	1	28	of	of	ADP
cord-326631-7gd3hjc3	1	29	a	a	DET
cord-326631-7gd3hjc3	1	30	newly	newly	ADV
cord-326631-7gd3hjc3	1	31	invading	invade	VERB
cord-326631-7gd3hjc3	1	32	infectious	infectious	ADJ
cord-326631-7gd3hjc3	1	33	disease	disease	NOUN
cord-326631-7gd3hjc3	1	34	date	date	NOUN
cord-326631-7gd3hjc3	1	35	:	:	PUNCT
cord-326631-7gd3hjc3	1	36	2006	2006	NUM
cord-326631-7gd3hjc3	1	37	-	-	SYM
cord-326631-7gd3hjc3	1	38	04	04	NUM
cord-326631-7gd3hjc3	1	39	-	-	PUNCT
cord-326631-7gd3hjc3	1	40	08	08	NUM
cord-326631-7gd3hjc3	1	41	journal	journal	NOUN
cord-326631-7gd3hjc3	1	42	:	:	PUNCT
cord-326631-7gd3hjc3	1	43	bull	bull	NOUN
cord-326631-7gd3hjc3	1	44	math	math	NOUN
cord-326631-7gd3hjc3	1	45	biol	biol	NOUN
cord-326631-7gd3hjc3	1	46	doi	doi	PROPN
cord-326631-7gd3hjc3	1	47	:	:	PUNCT
cord-326631-7gd3hjc3	1	48	10.1007	10.1007	NUM
cord-326631-7gd3hjc3	1	49	/	/	SYM
cord-326631-7gd3hjc3	1	50	s11538	s11538	NOUN
cord-326631-7gd3hjc3	1	51	-	-	PUNCT
cord-326631-7gd3hjc3	1	52	005	005	NUM
cord-326631-7gd3hjc3	1	53	-	-	PUNCT
cord-326631-7gd3hjc3	1	54	9047	9047	NUM
cord-326631-7gd3hjc3	1	55	-	-	SYM
cord-326631-7gd3hjc3	1	56	7	7	NUM
cord-326631-7gd3hjc3	1	57	sha	sha	NOUN
cord-326631-7gd3hjc3	1	58	:	:	PUNCT
cord-326631-7gd3hjc3	1	59	doc_id	doc_id	X
cord-326631-7gd3hjc3	1	60	:	:	PUNCT
cord-326631-7gd3hjc3	1	61	326631	326631	NUM
cord-326631-7gd3hjc3	1	62	cord_uid	cord_uid	ADJ
cord-326631-7gd3hjc3	1	63	:	:	PUNCT
cord-326631-7gd3hjc3	1	64	7gd3hjc3	7gd3hjc3	NUM
cord-326631-7gd3hjc3	1	65	the	the	DET
cord-326631-7gd3hjc3	1	66	well	well	ADV
cord-326631-7gd3hjc3	1	67	-	-	PUNCT
cord-326631-7gd3hjc3	1	68	known	know	VERB
cord-326631-7gd3hjc3	1	69	formula	formula	NOUN
cord-326631-7gd3hjc3	1	70	for	for	ADP
cord-326631-7gd3hjc3	1	71	the	the	DET
cord-326631-7gd3hjc3	1	72	final	final	ADJ
cord-326631-7gd3hjc3	1	73	size	size	NOUN
cord-326631-7gd3hjc3	1	74	of	of	ADP
cord-326631-7gd3hjc3	1	75	an	an	DET
cord-326631-7gd3hjc3	1	76	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	1	77	was	be	AUX
cord-326631-7gd3hjc3	1	78	published	publish	VERB
cord-326631-7gd3hjc3	1	79	by	by	ADP
cord-326631-7gd3hjc3	1	80	kermack	kermack	PROPN
cord-326631-7gd3hjc3	1	81	and	and	CCONJ
cord-326631-7gd3hjc3	1	82	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	1	83	in	in	ADP
cord-326631-7gd3hjc3	1	84	1927	1927	NUM
cord-326631-7gd3hjc3	1	85	.	.	PUNCT
cord-326631-7gd3hjc3	2	1	their	their	PRON
cord-326631-7gd3hjc3	2	2	analysis	analysis	NOUN
cord-326631-7gd3hjc3	2	3	was	be	AUX
cord-326631-7gd3hjc3	2	4	based	base	VERB
cord-326631-7gd3hjc3	2	5	on	on	ADP
cord-326631-7gd3hjc3	2	6	a	a	DET
cord-326631-7gd3hjc3	2	7	simple	simple	ADJ
cord-326631-7gd3hjc3	2	8	susceptible	susceptible	ADV
cord-326631-7gd3hjc3	2	9	-	-	PUNCT
cord-326631-7gd3hjc3	2	10	infected	infect	VERB
cord-326631-7gd3hjc3	2	11	-	-	PUNCT
cord-326631-7gd3hjc3	2	12	recovered	recover	VERB
cord-326631-7gd3hjc3	2	13	(	(	PUNCT
cord-326631-7gd3hjc3	2	14	sir	sir	PROPN
cord-326631-7gd3hjc3	2	15	)	)	PUNCT
cord-326631-7gd3hjc3	2	16	model	model	NOUN
cord-326631-7gd3hjc3	2	17	that	that	PRON
cord-326631-7gd3hjc3	2	18	assumes	assume	VERB
cord-326631-7gd3hjc3	2	19	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	2	20	distributed	distribute	VERB
cord-326631-7gd3hjc3	2	21	infectious	infectious	ADJ
cord-326631-7gd3hjc3	2	22	periods	period	NOUN
cord-326631-7gd3hjc3	2	23	.	.	PUNCT
cord-326631-7gd3hjc3	3	1	more	more	ADV
cord-326631-7gd3hjc3	3	2	recent	recent	ADJ
cord-326631-7gd3hjc3	3	3	analyses	analysis	NOUN
cord-326631-7gd3hjc3	3	4	have	have	AUX
cord-326631-7gd3hjc3	3	5	established	establish	VERB
cord-326631-7gd3hjc3	3	6	that	that	SCONJ
cord-326631-7gd3hjc3	3	7	the	the	DET
cord-326631-7gd3hjc3	3	8	standard	standard	ADJ
cord-326631-7gd3hjc3	3	9	final	final	ADJ
cord-326631-7gd3hjc3	3	10	size	size	NOUN
cord-326631-7gd3hjc3	3	11	formula	formula	NOUN
cord-326631-7gd3hjc3	3	12	is	be	AUX
cord-326631-7gd3hjc3	3	13	valid	valid	ADJ
cord-326631-7gd3hjc3	3	14	regardless	regardless	ADV
cord-326631-7gd3hjc3	3	15	of	of	ADP
cord-326631-7gd3hjc3	3	16	the	the	DET
cord-326631-7gd3hjc3	3	17	distribution	distribution	NOUN
cord-326631-7gd3hjc3	3	18	of	of	ADP
cord-326631-7gd3hjc3	3	19	infectious	infectious	ADJ
cord-326631-7gd3hjc3	3	20	periods	period	NOUN
cord-326631-7gd3hjc3	3	21	,	,	PUNCT
cord-326631-7gd3hjc3	3	22	but	but	CCONJ
cord-326631-7gd3hjc3	3	23	that	that	SCONJ
cord-326631-7gd3hjc3	3	24	it	it	PRON
cord-326631-7gd3hjc3	3	25	fails	fail	VERB
cord-326631-7gd3hjc3	3	26	to	to	PART
cord-326631-7gd3hjc3	3	27	be	be	AUX
cord-326631-7gd3hjc3	3	28	correct	correct	ADJ
cord-326631-7gd3hjc3	3	29	in	in	ADP
cord-326631-7gd3hjc3	3	30	the	the	DET
cord-326631-7gd3hjc3	3	31	presence	presence	NOUN
cord-326631-7gd3hjc3	3	32	of	of	ADP
cord-326631-7gd3hjc3	3	33	certain	certain	ADJ
cord-326631-7gd3hjc3	3	34	kinds	kind	NOUN
cord-326631-7gd3hjc3	3	35	of	of	ADP
cord-326631-7gd3hjc3	3	36	heterogeneous	heterogeneous	ADJ
cord-326631-7gd3hjc3	3	37	mixing	mixing	NOUN
cord-326631-7gd3hjc3	3	38	(	(	PUNCT
cord-326631-7gd3hjc3	3	39	e.g.	e.g.	ADV
cord-326631-7gd3hjc3	3	40	,	,	PUNCT
cord-326631-7gd3hjc3	3	41	if	if	SCONJ
cord-326631-7gd3hjc3	3	42	there	there	PRON
cord-326631-7gd3hjc3	3	43	is	be	VERB
cord-326631-7gd3hjc3	3	44	a	a	DET
cord-326631-7gd3hjc3	3	45	core	core	NOUN
cord-326631-7gd3hjc3	3	46	group	group	NOUN
cord-326631-7gd3hjc3	3	47	,	,	PUNCT
cord-326631-7gd3hjc3	3	48	as	as	ADP
cord-326631-7gd3hjc3	3	49	for	for	ADP
cord-326631-7gd3hjc3	3	50	sexually	sexually	ADV
cord-326631-7gd3hjc3	3	51	transmitted	transmit	VERB
cord-326631-7gd3hjc3	3	52	diseases	disease	NOUN
cord-326631-7gd3hjc3	3	53	)	)	PUNCT
cord-326631-7gd3hjc3	3	54	.	.	PUNCT
cord-326631-7gd3hjc3	4	1	we	we	PRON
cord-326631-7gd3hjc3	4	2	review	review	VERB
cord-326631-7gd3hjc3	4	3	previous	previous	ADJ
cord-326631-7gd3hjc3	4	4	work	work	NOUN
cord-326631-7gd3hjc3	4	5	and	and	CCONJ
cord-326631-7gd3hjc3	4	6	establish	establish	VERB
cord-326631-7gd3hjc3	4	7	more	more	ADJ
cord-326631-7gd3hjc3	4	8	general	general	ADJ
cord-326631-7gd3hjc3	4	9	conditions	condition	NOUN
cord-326631-7gd3hjc3	4	10	under	under	ADP
cord-326631-7gd3hjc3	4	11	which	which	PRON
cord-326631-7gd3hjc3	4	12	kermack	kermack	NOUN
cord-326631-7gd3hjc3	4	13	and	and	CCONJ
cord-326631-7gd3hjc3	4	14	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	4	15	's	's	PART
cord-326631-7gd3hjc3	4	16	formula	formula	NOUN
cord-326631-7gd3hjc3	4	17	is	be	AUX
cord-326631-7gd3hjc3	4	18	valid	valid	ADJ
cord-326631-7gd3hjc3	4	19	.	.	PUNCT
cord-326631-7gd3hjc3	5	1	we	we	PRON
cord-326631-7gd3hjc3	5	2	show	show	VERB
cord-326631-7gd3hjc3	5	3	that	that	SCONJ
cord-326631-7gd3hjc3	5	4	the	the	DET
cord-326631-7gd3hjc3	5	5	final	final	ADJ
cord-326631-7gd3hjc3	5	6	size	size	NOUN
cord-326631-7gd3hjc3	5	7	formula	formula	NOUN
cord-326631-7gd3hjc3	5	8	is	be	AUX
cord-326631-7gd3hjc3	5	9	unchanged	unchanged	ADJ
cord-326631-7gd3hjc3	5	10	if	if	SCONJ
cord-326631-7gd3hjc3	5	11	there	there	PRON
cord-326631-7gd3hjc3	5	12	is	be	VERB
cord-326631-7gd3hjc3	5	13	a	a	DET
cord-326631-7gd3hjc3	5	14	latent	latent	ADJ
cord-326631-7gd3hjc3	5	15	stage	stage	NOUN
cord-326631-7gd3hjc3	5	16	,	,	PUNCT
cord-326631-7gd3hjc3	5	17	any	any	DET
cord-326631-7gd3hjc3	5	18	number	number	NOUN
cord-326631-7gd3hjc3	5	19	of	of	ADP
cord-326631-7gd3hjc3	5	20	distinct	distinct	ADJ
cord-326631-7gd3hjc3	5	21	infectious	infectious	ADJ
cord-326631-7gd3hjc3	5	22	stages	stage	NOUN
cord-326631-7gd3hjc3	5	23	and/or	and/or	CCONJ
cord-326631-7gd3hjc3	5	24	a	a	DET
cord-326631-7gd3hjc3	5	25	stage	stage	NOUN
cord-326631-7gd3hjc3	5	26	during	during	ADP
cord-326631-7gd3hjc3	5	27	which	which	PRON
cord-326631-7gd3hjc3	5	28	infectives	infective	NOUN
cord-326631-7gd3hjc3	5	29	are	be	AUX
cord-326631-7gd3hjc3	5	30	isolated	isolate	VERB
cord-326631-7gd3hjc3	5	31	(	(	PUNCT
cord-326631-7gd3hjc3	5	32	the	the	DET
cord-326631-7gd3hjc3	5	33	durations	duration	NOUN
cord-326631-7gd3hjc3	5	34	of	of	ADP
cord-326631-7gd3hjc3	5	35	each	each	DET
cord-326631-7gd3hjc3	5	36	stage	stage	NOUN
cord-326631-7gd3hjc3	5	37	can	can	AUX
cord-326631-7gd3hjc3	5	38	be	be	AUX
cord-326631-7gd3hjc3	5	39	drawn	draw	VERB
cord-326631-7gd3hjc3	5	40	from	from	ADP
cord-326631-7gd3hjc3	5	41	any	any	DET
cord-326631-7gd3hjc3	5	42	integrable	integrable	ADJ
cord-326631-7gd3hjc3	5	43	distribution	distribution	NOUN
cord-326631-7gd3hjc3	5	44	)	)	PUNCT
cord-326631-7gd3hjc3	5	45	.	.	PUNCT
cord-326631-7gd3hjc3	6	1	we	we	PRON
cord-326631-7gd3hjc3	6	2	also	also	ADV
cord-326631-7gd3hjc3	6	3	consider	consider	VERB
cord-326631-7gd3hjc3	6	4	the	the	DET
cord-326631-7gd3hjc3	6	5	possibility	possibility	NOUN
cord-326631-7gd3hjc3	6	6	that	that	SCONJ
cord-326631-7gd3hjc3	6	7	the	the	DET
cord-326631-7gd3hjc3	6	8	transmission	transmission	NOUN
cord-326631-7gd3hjc3	6	9	rates	rate	NOUN
cord-326631-7gd3hjc3	6	10	of	of	ADP
cord-326631-7gd3hjc3	6	11	infectious	infectious	ADJ
cord-326631-7gd3hjc3	6	12	individuals	individual	NOUN
cord-326631-7gd3hjc3	6	13	are	be	AUX
cord-326631-7gd3hjc3	6	14	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	6	15	distributed	distribute	VERB
cord-326631-7gd3hjc3	6	16	—	—	PUNCT
cord-326631-7gd3hjc3	6	17	allowing	allow	VERB
cord-326631-7gd3hjc3	6	18	,	,	PUNCT
cord-326631-7gd3hjc3	6	19	in	in	ADP
cord-326631-7gd3hjc3	6	20	particular	particular	ADJ
cord-326631-7gd3hjc3	6	21	,	,	PUNCT
cord-326631-7gd3hjc3	6	22	for	for	ADP
cord-326631-7gd3hjc3	6	23	the	the	DET
cord-326631-7gd3hjc3	6	24	existence	existence	NOUN
cord-326631-7gd3hjc3	6	25	of	of	ADP
cord-326631-7gd3hjc3	6	26	super	super	NOUN
cord-326631-7gd3hjc3	6	27	-	-	NOUN
cord-326631-7gd3hjc3	6	28	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	6	29	—	—	PUNCT
cord-326631-7gd3hjc3	6	30	and	and	CCONJ
cord-326631-7gd3hjc3	6	31	prove	prove	VERB
cord-326631-7gd3hjc3	6	32	that	that	SCONJ
cord-326631-7gd3hjc3	6	33	this	this	DET
cord-326631-7gd3hjc3	6	34	potential	potential	ADJ
cord-326631-7gd3hjc3	6	35	complexity	complexity	NOUN
cord-326631-7gd3hjc3	6	36	has	have	VERB
cord-326631-7gd3hjc3	6	37	no	no	DET
cord-326631-7gd3hjc3	6	38	impact	impact	NOUN
cord-326631-7gd3hjc3	6	39	on	on	ADP
cord-326631-7gd3hjc3	6	40	the	the	DET
cord-326631-7gd3hjc3	6	41	final	final	ADJ
cord-326631-7gd3hjc3	6	42	size	size	NOUN
cord-326631-7gd3hjc3	6	43	formula	formula	NOUN
cord-326631-7gd3hjc3	6	44	.	.	PUNCT
cord-326631-7gd3hjc3	7	1	finally	finally	ADV
cord-326631-7gd3hjc3	7	2	,	,	PUNCT
cord-326631-7gd3hjc3	7	3	we	we	PRON
cord-326631-7gd3hjc3	7	4	show	show	VERB
cord-326631-7gd3hjc3	7	5	that	that	SCONJ
cord-326631-7gd3hjc3	7	6	the	the	DET
cord-326631-7gd3hjc3	7	7	final	final	ADJ
cord-326631-7gd3hjc3	7	8	size	size	NOUN
cord-326631-7gd3hjc3	7	9	formula	formula	NOUN
cord-326631-7gd3hjc3	7	10	is	be	AUX
cord-326631-7gd3hjc3	7	11	unchanged	unchanged	ADJ
cord-326631-7gd3hjc3	7	12	even	even	ADV
cord-326631-7gd3hjc3	7	13	for	for	ADP
cord-326631-7gd3hjc3	7	14	a	a	DET
cord-326631-7gd3hjc3	7	15	general	general	ADJ
cord-326631-7gd3hjc3	7	16	class	class	NOUN
cord-326631-7gd3hjc3	7	17	of	of	ADP
cord-326631-7gd3hjc3	7	18	spatial	spatial	ADJ
cord-326631-7gd3hjc3	7	19	contact	contact	NOUN
cord-326631-7gd3hjc3	7	20	structures	structure	NOUN
cord-326631-7gd3hjc3	7	21	.	.	PUNCT
cord-326631-7gd3hjc3	8	1	we	we	PRON
cord-326631-7gd3hjc3	8	2	conclude	conclude	VERB
cord-326631-7gd3hjc3	8	3	that	that	SCONJ
cord-326631-7gd3hjc3	8	4	whenever	whenever	SCONJ
cord-326631-7gd3hjc3	8	5	a	a	DET
cord-326631-7gd3hjc3	8	6	new	new	ADJ
cord-326631-7gd3hjc3	8	7	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	8	8	pathogen	pathogen	PROPN
cord-326631-7gd3hjc3	8	9	emerges	emerge	VERB
cord-326631-7gd3hjc3	8	10	,	,	PUNCT
cord-326631-7gd3hjc3	8	11	an	an	DET
cord-326631-7gd3hjc3	8	12	estimate	estimate	NOUN
cord-326631-7gd3hjc3	8	13	of	of	ADP
cord-326631-7gd3hjc3	8	14	the	the	DET
cord-326631-7gd3hjc3	8	15	expected	expect	VERB
cord-326631-7gd3hjc3	8	16	magnitude	magnitude	NOUN
cord-326631-7gd3hjc3	8	17	of	of	ADP
cord-326631-7gd3hjc3	8	18	the	the	DET
cord-326631-7gd3hjc3	8	19	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	8	20	can	can	AUX
cord-326631-7gd3hjc3	8	21	be	be	AUX
cord-326631-7gd3hjc3	8	22	made	make	VERB
cord-326631-7gd3hjc3	8	23	as	as	ADV
cord-326631-7gd3hjc3	8	24	soon	soon	ADV
cord-326631-7gd3hjc3	8	25	the	the	DET
cord-326631-7gd3hjc3	8	26	basic	basic	ADJ
cord-326631-7gd3hjc3	8	27	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	8	28	number	number	NOUN
cord-326631-7gd3hjc3	8	29	ℝ(0	ℝ(0	PUNCT
cord-326631-7gd3hjc3	8	30	)	)	PUNCT
cord-326631-7gd3hjc3	8	31	can	can	AUX
cord-326631-7gd3hjc3	8	32	be	be	AUX
cord-326631-7gd3hjc3	8	33	approximated	approximate	VERB
cord-326631-7gd3hjc3	8	34	,	,	PUNCT
cord-326631-7gd3hjc3	8	35	and	and	CCONJ
cord-326631-7gd3hjc3	8	36	this	this	DET
cord-326631-7gd3hjc3	8	37	estimate	estimate	NOUN
cord-326631-7gd3hjc3	8	38	is	be	AUX
cord-326631-7gd3hjc3	8	39	likely	likely	ADJ
cord-326631-7gd3hjc3	8	40	to	to	PART
cord-326631-7gd3hjc3	8	41	be	be	AUX
cord-326631-7gd3hjc3	8	42	improved	improve	VERB
cord-326631-7gd3hjc3	8	43	only	only	ADV
cord-326631-7gd3hjc3	8	44	by	by	ADP
cord-326631-7gd3hjc3	8	45	more	more	ADV
cord-326631-7gd3hjc3	8	46	accurate	accurate	ADJ
cord-326631-7gd3hjc3	8	47	estimates	estimate	NOUN
cord-326631-7gd3hjc3	8	48	of	of	ADP
cord-326631-7gd3hjc3	8	49	ℝ(0	ℝ(0	NUM
cord-326631-7gd3hjc3	8	50	)	)	PUNCT
cord-326631-7gd3hjc3	8	51	,	,	PUNCT
cord-326631-7gd3hjc3	8	52	not	not	PART
cord-326631-7gd3hjc3	8	53	by	by	ADP
cord-326631-7gd3hjc3	8	54	knowledge	knowledge	NOUN
cord-326631-7gd3hjc3	8	55	of	of	ADP
cord-326631-7gd3hjc3	8	56	any	any	DET
cord-326631-7gd3hjc3	8	57	other	other	ADJ
cord-326631-7gd3hjc3	8	58	epidemiological	epidemiological	ADJ
cord-326631-7gd3hjc3	8	59	details	detail	NOUN
cord-326631-7gd3hjc3	8	60	.	.	PUNCT
cord-326631-7gd3hjc3	9	1	whenever	whenever	SCONJ
cord-326631-7gd3hjc3	9	2	a	a	DET
cord-326631-7gd3hjc3	9	3	serious	serious	ADJ
cord-326631-7gd3hjc3	9	4	infectious	infectious	ADJ
cord-326631-7gd3hjc3	9	5	disease	disease	NOUN
cord-326631-7gd3hjc3	9	6	emerges	emerge	VERB
cord-326631-7gd3hjc3	9	7	or	or	CCONJ
cord-326631-7gd3hjc3	9	8	re	re	VERB
cord-326631-7gd3hjc3	9	9	-	-	NOUN
cord-326631-7gd3hjc3	9	10	emerges	emerge	VERB
cord-326631-7gd3hjc3	9	11	in	in	ADP
cord-326631-7gd3hjc3	9	12	a	a	DET
cord-326631-7gd3hjc3	9	13	human	human	ADJ
cord-326631-7gd3hjc3	9	14	population	population	NOUN
cord-326631-7gd3hjc3	9	15	,	,	PUNCT
cord-326631-7gd3hjc3	9	16	a	a	DET
cord-326631-7gd3hjc3	9	17	matter	matter	NOUN
cord-326631-7gd3hjc3	9	18	of	of	ADP
cord-326631-7gd3hjc3	9	19	immediate	immediate	ADJ
cord-326631-7gd3hjc3	9	20	interest	interest	NOUN
cord-326631-7gd3hjc3	9	21	is	be	AUX
cord-326631-7gd3hjc3	9	22	the	the	DET
cord-326631-7gd3hjc3	9	23	likely	likely	ADJ
cord-326631-7gd3hjc3	9	24	magnitude	magnitude	NOUN
cord-326631-7gd3hjc3	9	25	of	of	ADP
cord-326631-7gd3hjc3	9	26	the	the	DET
cord-326631-7gd3hjc3	9	27	outbreak	outbreak	NOUN
cord-326631-7gd3hjc3	9	28	.	.	PUNCT
cord-326631-7gd3hjc3	10	1	this	this	PRON
cord-326631-7gd3hjc3	10	2	is	be	AUX
cord-326631-7gd3hjc3	10	3	often	often	ADV
cord-326631-7gd3hjc3	10	4	called	call	VERB
cord-326631-7gd3hjc3	10	5	the	the	DET
cord-326631-7gd3hjc3	10	6	expected	expect	VERB
cord-326631-7gd3hjc3	10	7	final	final	ADJ
cord-326631-7gd3hjc3	10	8	size	size	NOUN
cord-326631-7gd3hjc3	10	9	of	of	ADP
cord-326631-7gd3hjc3	10	10	the	the	DET
cord-326631-7gd3hjc3	10	11	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	10	12	(	(	PUNCT
cord-326631-7gd3hjc3	10	13	bailey	bailey	NOUN
cord-326631-7gd3hjc3	10	14	,	,	PUNCT
cord-326631-7gd3hjc3	10	15	1975	1975	NUM
cord-326631-7gd3hjc3	10	16	;	;	PUNCT
cord-326631-7gd3hjc3	10	17	anderson	anderson	PROPN
cord-326631-7gd3hjc3	10	18	and	and	CCONJ
cord-326631-7gd3hjc3	10	19	watsons	watson	NOUN
cord-326631-7gd3hjc3	10	20	,	,	PUNCT
cord-326631-7gd3hjc3	10	21	1980	1980	NUM
cord-326631-7gd3hjc3	10	22	;	;	PUNCT
cord-326631-7gd3hjc3	10	23	anderson	anderson	PROPN
cord-326631-7gd3hjc3	10	24	and	and	CCONJ
cord-326631-7gd3hjc3	10	25	may	may	AUX
cord-326631-7gd3hjc3	10	26	,	,	PUNCT
cord-326631-7gd3hjc3	10	27	1991	1991	NUM
cord-326631-7gd3hjc3	10	28	;	;	PUNCT
cord-326631-7gd3hjc3	10	29	andersson	andersson	PROPN
cord-326631-7gd3hjc3	10	30	and	and	CCONJ
cord-326631-7gd3hjc3	10	31	britton	britton	PROPN
cord-326631-7gd3hjc3	10	32	,	,	PUNCT
cord-326631-7gd3hjc3	10	33	2000	2000	NUM
cord-326631-7gd3hjc3	10	34	;	;	PUNCT
cord-326631-7gd3hjc3	10	35	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	10	36	and	and	CCONJ
cord-326631-7gd3hjc3	10	37	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	10	38	,	,	PUNCT
cord-326631-7gd3hjc3	10	39	2000	2000	NUM
cord-326631-7gd3hjc3	10	40	)	)	PUNCT
cord-326631-7gd3hjc3	10	41	,	,	PUNCT
cord-326631-7gd3hjc3	10	42	which	which	PRON
cord-326631-7gd3hjc3	10	43	we	we	PRON
cord-326631-7gd3hjc3	10	44	denote	denote	VERB
cord-326631-7gd3hjc3	10	45	z.	z.	PROPN
cord-326631-7gd3hjc3	10	46	of	of	ADP
cord-326631-7gd3hjc3	10	47	course	course	NOUN
cord-326631-7gd3hjc3	10	48	,	,	PUNCT
cord-326631-7gd3hjc3	10	49	if	if	SCONJ
cord-326631-7gd3hjc3	10	50	the	the	DET
cord-326631-7gd3hjc3	10	51	emergent	emergent	PROPN
cord-326631-7gd3hjc3	10	52	pathogen	pathogen	PROPN
cord-326631-7gd3hjc3	10	53	becomes	become	VERB
cord-326631-7gd3hjc3	10	54	endemic	endemic	ADJ
cord-326631-7gd3hjc3	10	55	in	in	ADP
cord-326631-7gd3hjc3	10	56	the	the	DET
cord-326631-7gd3hjc3	10	57	population	population	NOUN
cord-326631-7gd3hjc3	10	58	then	then	ADV
cord-326631-7gd3hjc3	10	59	there	there	PRON
cord-326631-7gd3hjc3	10	60	will	will	AUX
cord-326631-7gd3hjc3	10	61	never	never	ADV
cord-326631-7gd3hjc3	10	62	really	really	ADV
cord-326631-7gd3hjc3	10	63	be	be	AUX
cord-326631-7gd3hjc3	10	64	a	a	DET
cord-326631-7gd3hjc3	10	65	"	"	PUNCT
cord-326631-7gd3hjc3	10	66	final	final	ADJ
cord-326631-7gd3hjc3	10	67	"	"	PUNCT
cord-326631-7gd3hjc3	10	68	size	size	NOUN
cord-326631-7gd3hjc3	10	69	,	,	PUNCT
cord-326631-7gd3hjc3	10	70	but	but	CCONJ
cord-326631-7gd3hjc3	10	71	in	in	ADP
cord-326631-7gd3hjc3	10	72	that	that	DET
cord-326631-7gd3hjc3	10	73	case	case	NOUN
cord-326631-7gd3hjc3	10	74	the	the	DET
cord-326631-7gd3hjc3	10	75	matter	matter	NOUN
cord-326631-7gd3hjc3	10	76	at	at	ADP
cord-326631-7gd3hjc3	10	77	issue	issue	NOUN
cord-326631-7gd3hjc3	10	78	is	be	AUX
cord-326631-7gd3hjc3	10	79	the	the	DET
cord-326631-7gd3hjc3	10	80	likely	likely	ADJ
cord-326631-7gd3hjc3	10	81	magnitude	magnitude	NOUN
cord-326631-7gd3hjc3	10	82	of	of	ADP
cord-326631-7gd3hjc3	10	83	the	the	DET
cord-326631-7gd3hjc3	10	84	first	first	ADJ
cord-326631-7gd3hjc3	10	85	major	major	ADJ
cord-326631-7gd3hjc3	10	86	wave	wave	NOUN
cord-326631-7gd3hjc3	10	87	of	of	ADP
cord-326631-7gd3hjc3	10	88	cases	case	NOUN
cord-326631-7gd3hjc3	10	89	.	.	PUNCT
cord-326631-7gd3hjc3	11	1	to	to	ADP
cord-326631-7gd3hjc3	11	2	our	our	PRON
cord-326631-7gd3hjc3	11	3	knowledge	knowledge	NOUN
cord-326631-7gd3hjc3	11	4	,	,	PUNCT
cord-326631-7gd3hjc3	11	5	a	a	DET
cord-326631-7gd3hjc3	11	6	formal	formal	ADJ
cord-326631-7gd3hjc3	11	7	,	,	PUNCT
cord-326631-7gd3hjc3	11	8	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	11	9	argument	argument	NOUN
cord-326631-7gd3hjc3	11	10	leading	lead	VERB
cord-326631-7gd3hjc3	11	11	to	to	ADP
cord-326631-7gd3hjc3	11	12	an	an	DET
cord-326631-7gd3hjc3	11	13	estimate	estimate	NOUN
cord-326631-7gd3hjc3	11	14	of	of	ADP
cord-326631-7gd3hjc3	11	15	an	an	DET
cord-326631-7gd3hjc3	11	16	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	11	17	's	's	PART
cord-326631-7gd3hjc3	11	18	expected	expect	VERB
cord-326631-7gd3hjc3	11	19	final	final	ADJ
cord-326631-7gd3hjc3	11	20	size	size	NOUN
cord-326631-7gd3hjc3	11	21	z	z	PROPN
cord-326631-7gd3hjc3	11	22	was	be	AUX
cord-326631-7gd3hjc3	11	23	first	first	ADV
cord-326631-7gd3hjc3	11	24	published	publish	VERB
cord-326631-7gd3hjc3	11	25	in	in	ADP
cord-326631-7gd3hjc3	11	26	the	the	DET
cord-326631-7gd3hjc3	11	27	landmark	landmark	NOUN
cord-326631-7gd3hjc3	11	28	1927	1927	NUM
cord-326631-7gd3hjc3	11	29	paper	paper	NOUN
cord-326631-7gd3hjc3	11	30	by	by	ADP
cord-326631-7gd3hjc3	11	31	kermack	kermack	PROPN
cord-326631-7gd3hjc3	11	32	and	and	CCONJ
cord-326631-7gd3hjc3	11	33	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	11	34	(	(	PUNCT
cord-326631-7gd3hjc3	11	35	1927	1927	NUM
cord-326631-7gd3hjc3	11	36	)	)	PUNCT
cord-326631-7gd3hjc3	11	37	.	.	PUNCT
cord-326631-7gd3hjc3	12	1	the	the	DET
cord-326631-7gd3hjc3	12	2	formula	formula	NOUN
cord-326631-7gd3hjc3	12	3	for	for	ADP
cord-326631-7gd3hjc3	12	4	z	z	NOUN
cord-326631-7gd3hjc3	12	5	that	that	DET
cord-326631-7gd3hjc3	12	6	kermack	kermack	PROPN
cord-326631-7gd3hjc3	12	7	and	and	CCONJ
cord-326631-7gd3hjc3	12	8	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	12	9	obtained	obtain	VERB
cord-326631-7gd3hjc3	12	10	[	[	PROPN
cord-326631-7gd3hjc3	12	11	eq	eq	X
cord-326631-7gd3hjc3	12	12	.	.	PUNCT
cord-326631-7gd3hjc3	12	13	(	(	PUNCT
cord-326631-7gd3hjc3	12	14	5	5	NUM
cord-326631-7gd3hjc3	12	15	)	)	PUNCT
cord-326631-7gd3hjc3	12	16	below	below	ADP
cord-326631-7gd3hjc3	12	17	]	]	PUNCT
cord-326631-7gd3hjc3	12	18	depends	depend	VERB
cord-326631-7gd3hjc3	12	19	only	only	ADV
cord-326631-7gd3hjc3	12	20	on	on	ADP
cord-326631-7gd3hjc3	12	21	the	the	DET
cord-326631-7gd3hjc3	12	22	basic	basic	ADJ
cord-326631-7gd3hjc3	12	23	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	12	24	number	number	NOUN
cord-326631-7gd3hjc3	12	25	,	,	PUNCT
cord-326631-7gd3hjc3	12	26	r	r	NOUN
cord-326631-7gd3hjc3	12	27	0	0	NUM
cord-326631-7gd3hjc3	12	28	(	(	PUNCT
cord-326631-7gd3hjc3	12	29	the	the	DET
cord-326631-7gd3hjc3	12	30	expected	expect	VERB
cord-326631-7gd3hjc3	12	31	number	number	NOUN
cord-326631-7gd3hjc3	12	32	of	of	ADP
cord-326631-7gd3hjc3	12	33	secondary	secondary	ADJ
cord-326631-7gd3hjc3	12	34	cases	case	NOUN
cord-326631-7gd3hjc3	12	35	caused	cause	VERB
cord-326631-7gd3hjc3	12	36	by	by	ADP
cord-326631-7gd3hjc3	12	37	a	a	DET
cord-326631-7gd3hjc3	12	38	typical	typical	ADJ
cord-326631-7gd3hjc3	12	39	primary	primary	ADJ
cord-326631-7gd3hjc3	12	40	case	case	NOUN
cord-326631-7gd3hjc3	12	41	in	in	ADP
cord-326631-7gd3hjc3	12	42	a	a	DET
cord-326631-7gd3hjc3	12	43	fully	fully	ADV
cord-326631-7gd3hjc3	12	44	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	12	45	population	population	NOUN
cord-326631-7gd3hjc3	12	46	)	)	PUNCT
cord-326631-7gd3hjc3	12	47	.	.	PUNCT
cord-326631-7gd3hjc3	13	1	however	however	ADV
cord-326631-7gd3hjc3	13	2	,	,	PUNCT
cord-326631-7gd3hjc3	13	3	without	without	ADP
cord-326631-7gd3hjc3	13	4	further	further	ADJ
cord-326631-7gd3hjc3	13	5	analysis	analysis	NOUN
cord-326631-7gd3hjc3	13	6	,	,	PUNCT
cord-326631-7gd3hjc3	13	7	it	it	PRON
cord-326631-7gd3hjc3	13	8	is	be	AUX
cord-326631-7gd3hjc3	13	9	unclear	unclear	ADJ
cord-326631-7gd3hjc3	13	10	to	to	PART
cord-326631-7gd3hjc3	13	11	what	what	DET
cord-326631-7gd3hjc3	13	12	extent	extent	NOUN
cord-326631-7gd3hjc3	13	13	this	this	DET
cord-326631-7gd3hjc3	13	14	formula	formula	NOUN
cord-326631-7gd3hjc3	13	15	depends	depend	VERB
cord-326631-7gd3hjc3	13	16	on	on	ADP
cord-326631-7gd3hjc3	13	17	the	the	DET
cord-326631-7gd3hjc3	13	18	particular	particular	ADJ
cord-326631-7gd3hjc3	13	19	assumptions	assumption	NOUN
cord-326631-7gd3hjc3	13	20	that	that	PRON
cord-326631-7gd3hjc3	13	21	kermack	kermack	NOUN
cord-326631-7gd3hjc3	13	22	and	and	CCONJ
cord-326631-7gd3hjc3	13	23	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	13	24	made	make	VERB
cord-326631-7gd3hjc3	13	25	in	in	ADP
cord-326631-7gd3hjc3	13	26	constructing	construct	VERB
cord-326631-7gd3hjc3	13	27	their	their	PRON
cord-326631-7gd3hjc3	13	28	model	model	NOUN
cord-326631-7gd3hjc3	13	29	,	,	PUNCT
cord-326631-7gd3hjc3	13	30	and	and	CCONJ
cord-326631-7gd3hjc3	13	31	hence	hence	ADV
cord-326631-7gd3hjc3	13	32	whether	whether	SCONJ
cord-326631-7gd3hjc3	13	33	it	it	PRON
cord-326631-7gd3hjc3	13	34	bears	bear	VERB
cord-326631-7gd3hjc3	13	35	a	a	DET
cord-326631-7gd3hjc3	13	36	strong	strong	ADJ
cord-326631-7gd3hjc3	13	37	relationship	relationship	NOUN
cord-326631-7gd3hjc3	13	38	to	to	ADP
cord-326631-7gd3hjc3	13	39	the	the	DET
cord-326631-7gd3hjc3	13	40	final	final	ADJ
cord-326631-7gd3hjc3	13	41	size	size	NOUN
cord-326631-7gd3hjc3	13	42	in	in	ADP
cord-326631-7gd3hjc3	13	43	realistic	realistic	ADJ
cord-326631-7gd3hjc3	13	44	situations	situation	NOUN
cord-326631-7gd3hjc3	13	45	.	.	PUNCT
cord-326631-7gd3hjc3	14	1	one	one	NUM
cord-326631-7gd3hjc3	14	2	implicit	implicit	ADJ
cord-326631-7gd3hjc3	14	3	assumption	assumption	NOUN
cord-326631-7gd3hjc3	14	4	of	of	ADP
cord-326631-7gd3hjc3	14	5	the	the	DET
cord-326631-7gd3hjc3	14	6	kermack	kermack	NOUN
cord-326631-7gd3hjc3	14	7	and	and	CCONJ
cord-326631-7gd3hjc3	14	8	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	14	9	(	(	PUNCT
cord-326631-7gd3hjc3	14	10	1927	1927	NUM
cord-326631-7gd3hjc3	14	11	)	)	PUNCT
cord-326631-7gd3hjc3	14	12	analysis	analysis	NOUN
cord-326631-7gd3hjc3	14	13	is	be	AUX
cord-326631-7gd3hjc3	14	14	that	that	SCONJ
cord-326631-7gd3hjc3	14	15	infectious	infectious	ADJ
cord-326631-7gd3hjc3	14	16	periods	period	NOUN
cord-326631-7gd3hjc3	14	17	are	be	AUX
cord-326631-7gd3hjc3	14	18	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	14	19	distributed	distribute	VERB
cord-326631-7gd3hjc3	14	20	.	.	PUNCT
cord-326631-7gd3hjc3	15	1	anderson	anderson	PROPN
cord-326631-7gd3hjc3	15	2	and	and	CCONJ
cord-326631-7gd3hjc3	15	3	watsons	watson	NOUN
cord-326631-7gd3hjc3	15	4	(	(	PUNCT
cord-326631-7gd3hjc3	15	5	1980	1980	NUM
cord-326631-7gd3hjc3	15	6	)	)	PUNCT
cord-326631-7gd3hjc3	15	7	showed	show	VERB
cord-326631-7gd3hjc3	15	8	that	that	SCONJ
cord-326631-7gd3hjc3	15	9	the	the	DET
cord-326631-7gd3hjc3	15	10	final	final	ADJ
cord-326631-7gd3hjc3	15	11	size	size	NOUN
cord-326631-7gd3hjc3	15	12	formula	formula	NOUN
cord-326631-7gd3hjc3	15	13	remains	remain	VERB
cord-326631-7gd3hjc3	15	14	valid	valid	ADJ
cord-326631-7gd3hjc3	15	15	if	if	SCONJ
cord-326631-7gd3hjc3	15	16	infectious	infectious	ADJ
cord-326631-7gd3hjc3	15	17	periods	period	NOUN
cord-326631-7gd3hjc3	15	18	follow	follow	VERB
cord-326631-7gd3hjc3	15	19	a	a	DET
cord-326631-7gd3hjc3	15	20	gamma	gamma	NOUN
cord-326631-7gd3hjc3	15	21	distribution	distribution	NOUN
cord-326631-7gd3hjc3	15	22	.	.	PUNCT
cord-326631-7gd3hjc3	16	1	in	in	ADP
cord-326631-7gd3hjc3	16	2	section	section	NOUN
cord-326631-7gd3hjc3	16	3	1.3	1.3	NUM
cord-326631-7gd3hjc3	16	4	of	of	ADP
cord-326631-7gd3hjc3	16	5	their	their	PRON
cord-326631-7gd3hjc3	16	6	book	book	NOUN
cord-326631-7gd3hjc3	16	7	,	,	PUNCT
cord-326631-7gd3hjc3	16	8	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	16	9	and	and	CCONJ
cord-326631-7gd3hjc3	16	10	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	16	11	(	(	PUNCT
cord-326631-7gd3hjc3	16	12	2000	2000	NUM
cord-326631-7gd3hjc3	16	13	)	)	PUNCT
cord-326631-7gd3hjc3	16	14	generalized	generalize	VERB
cord-326631-7gd3hjc3	16	15	this	this	DET
cord-326631-7gd3hjc3	16	16	statement	statement	NOUN
cord-326631-7gd3hjc3	16	17	to	to	PART
cord-326631-7gd3hjc3	16	18	cover	cover	VERB
cord-326631-7gd3hjc3	16	19	an	an	DET
cord-326631-7gd3hjc3	16	20	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	16	21	distribution	distribution	NOUN
cord-326631-7gd3hjc3	16	22	of	of	ADP
cord-326631-7gd3hjc3	16	23	infectious	infectious	ADJ
cord-326631-7gd3hjc3	16	24	periods	period	NOUN
cord-326631-7gd3hjc3	16	25	.	.	PUNCT
cord-326631-7gd3hjc3	17	1	another	another	DET
cord-326631-7gd3hjc3	17	2	key	key	ADJ
cord-326631-7gd3hjc3	17	3	assumption	assumption	NOUN
cord-326631-7gd3hjc3	17	4	of	of	ADP
cord-326631-7gd3hjc3	17	5	the	the	DET
cord-326631-7gd3hjc3	17	6	kermack	kermack	NOUN
cord-326631-7gd3hjc3	17	7	and	and	CCONJ
cord-326631-7gd3hjc3	17	8	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	17	9	(	(	PUNCT
cord-326631-7gd3hjc3	17	10	1927	1927	NUM
cord-326631-7gd3hjc3	17	11	)	)	PUNCT
cord-326631-7gd3hjc3	17	12	analysis	analysis	NOUN
cord-326631-7gd3hjc3	17	13	is	be	AUX
cord-326631-7gd3hjc3	17	14	that	that	SCONJ
cord-326631-7gd3hjc3	17	15	the	the	DET
cord-326631-7gd3hjc3	17	16	host	host	NOUN
cord-326631-7gd3hjc3	17	17	population	population	NOUN
cord-326631-7gd3hjc3	17	18	is	be	AUX
cord-326631-7gd3hjc3	17	19	homogeneously	homogeneously	ADV
cord-326631-7gd3hjc3	17	20	mixed	mixed	ADJ
cord-326631-7gd3hjc3	17	21	.	.	PUNCT
cord-326631-7gd3hjc3	18	1	it	it	PRON
cord-326631-7gd3hjc3	18	2	is	be	AUX
cord-326631-7gd3hjc3	18	3	well	well	ADV
cord-326631-7gd3hjc3	18	4	known	know	VERB
cord-326631-7gd3hjc3	18	5	that	that	SCONJ
cord-326631-7gd3hjc3	18	6	if	if	SCONJ
cord-326631-7gd3hjc3	18	7	this	this	DET
cord-326631-7gd3hjc3	18	8	assumption	assumption	NOUN
cord-326631-7gd3hjc3	18	9	is	be	AUX
cord-326631-7gd3hjc3	18	10	dropped	drop	VERB
cord-326631-7gd3hjc3	18	11	then	then	ADV
cord-326631-7gd3hjc3	18	12	the	the	DET
cord-326631-7gd3hjc3	18	13	final	final	ADJ
cord-326631-7gd3hjc3	18	14	size	size	NOUN
cord-326631-7gd3hjc3	18	15	will	will	AUX
cord-326631-7gd3hjc3	18	16	not	not	PART
cord-326631-7gd3hjc3	18	17	necessarily	necessarily	ADV
cord-326631-7gd3hjc3	18	18	be	be	AUX
cord-326631-7gd3hjc3	18	19	given	give	VERB
cord-326631-7gd3hjc3	18	20	by	by	ADP
cord-326631-7gd3hjc3	18	21	the	the	DET
cord-326631-7gd3hjc3	18	22	standard	standard	ADJ
cord-326631-7gd3hjc3	18	23	formula	formula	NOUN
cord-326631-7gd3hjc3	18	24	.	.	PUNCT
cord-326631-7gd3hjc3	19	1	in	in	ADP
cord-326631-7gd3hjc3	19	2	particular	particular	ADJ
cord-326631-7gd3hjc3	19	3	,	,	PUNCT
cord-326631-7gd3hjc3	19	4	the	the	DET
cord-326631-7gd3hjc3	19	5	existence	existence	NOUN
cord-326631-7gd3hjc3	19	6	of	of	ADP
cord-326631-7gd3hjc3	19	7	a	a	DET
cord-326631-7gd3hjc3	19	8	core	core	NOUN
cord-326631-7gd3hjc3	19	9	group	group	NOUN
cord-326631-7gd3hjc3	19	10	,	,	PUNCT
cord-326631-7gd3hjc3	19	11	as	as	ADP
cord-326631-7gd3hjc3	19	12	for	for	ADP
cord-326631-7gd3hjc3	19	13	sexually	sexually	ADV
cord-326631-7gd3hjc3	19	14	transmitted	transmit	VERB
cord-326631-7gd3hjc3	19	15	diseases	disease	NOUN
cord-326631-7gd3hjc3	19	16	,	,	PUNCT
cord-326631-7gd3hjc3	19	17	gives	give	VERB
cord-326631-7gd3hjc3	19	18	rise	rise	NOUN
cord-326631-7gd3hjc3	19	19	to	to	ADP
cord-326631-7gd3hjc3	19	20	a	a	DET
cord-326631-7gd3hjc3	19	21	different	different	ADJ
cord-326631-7gd3hjc3	19	22	formula	formula	NOUN
cord-326631-7gd3hjc3	19	23	for	for	ADP
cord-326631-7gd3hjc3	19	24	the	the	DET
cord-326631-7gd3hjc3	19	25	final	final	ADJ
cord-326631-7gd3hjc3	19	26	size	size	NOUN
cord-326631-7gd3hjc3	19	27	(	(	PUNCT
cord-326631-7gd3hjc3	19	28	anderson	anderson	PROPN
cord-326631-7gd3hjc3	19	29	and	and	CCONJ
cord-326631-7gd3hjc3	19	30	may	may	PROPN
cord-326631-7gd3hjc3	19	31	,	,	PUNCT
cord-326631-7gd3hjc3	19	32	1991	1991	NUM
cord-326631-7gd3hjc3	19	33	;	;	PUNCT
cord-326631-7gd3hjc3	19	34	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	19	35	and	and	CCONJ
cord-326631-7gd3hjc3	19	36	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	19	37	,	,	PUNCT
cord-326631-7gd3hjc3	19	38	2000	2000	NUM
cord-326631-7gd3hjc3	19	39	)	)	PUNCT
cord-326631-7gd3hjc3	19	40	.	.	PUNCT
cord-326631-7gd3hjc3	20	1	in	in	ADP
cord-326631-7gd3hjc3	20	2	this	this	DET
cord-326631-7gd3hjc3	20	3	paper	paper	NOUN
cord-326631-7gd3hjc3	20	4	,	,	PUNCT
cord-326631-7gd3hjc3	20	5	we	we	PRON
cord-326631-7gd3hjc3	20	6	explore	explore	VERB
cord-326631-7gd3hjc3	20	7	the	the	DET
cord-326631-7gd3hjc3	20	8	generality	generality	NOUN
cord-326631-7gd3hjc3	20	9	of	of	ADP
cord-326631-7gd3hjc3	20	10	the	the	DET
cord-326631-7gd3hjc3	20	11	standard	standard	ADJ
cord-326631-7gd3hjc3	20	12	kermack	kermack	PROPN
cord-326631-7gd3hjc3	20	13	-	-	PUNCT
cord-326631-7gd3hjc3	20	14	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	20	15	final	final	ADJ
cord-326631-7gd3hjc3	20	16	size	size	NOUN
cord-326631-7gd3hjc3	20	17	formula	formula	NOUN
cord-326631-7gd3hjc3	20	18	(	(	PUNCT
cord-326631-7gd3hjc3	20	19	5	5	NUM
cord-326631-7gd3hjc3	20	20	)	)	PUNCT
cord-326631-7gd3hjc3	20	21	.	.	PUNCT
cord-326631-7gd3hjc3	21	1	we	we	PRON
cord-326631-7gd3hjc3	21	2	begin	begin	VERB
cord-326631-7gd3hjc3	21	3	with	with	ADP
cord-326631-7gd3hjc3	21	4	a	a	DET
cord-326631-7gd3hjc3	21	5	pedagogical	pedagogical	ADJ
cord-326631-7gd3hjc3	21	6	review	review	NOUN
cord-326631-7gd3hjc3	21	7	of	of	ADP
cord-326631-7gd3hjc3	21	8	the	the	DET
cord-326631-7gd3hjc3	21	9	main	main	ADJ
cord-326631-7gd3hjc3	21	10	results	result	NOUN
cord-326631-7gd3hjc3	21	11	that	that	PRON
cord-326631-7gd3hjc3	21	12	have	have	AUX
cord-326631-7gd3hjc3	21	13	been	be	AUX
cord-326631-7gd3hjc3	21	14	obtained	obtain	VERB
cord-326631-7gd3hjc3	21	15	previously	previously	ADV
cord-326631-7gd3hjc3	21	16	,	,	PUNCT
cord-326631-7gd3hjc3	21	17	adding	add	VERB
cord-326631-7gd3hjc3	21	18	model	model	NOUN
cord-326631-7gd3hjc3	21	19	structure	structure	NOUN
cord-326631-7gd3hjc3	21	20	in	in	ADP
cord-326631-7gd3hjc3	21	21	steps	step	NOUN
cord-326631-7gd3hjc3	21	22	.	.	PUNCT
cord-326631-7gd3hjc3	22	1	we	we	PRON
cord-326631-7gd3hjc3	22	2	then	then	ADV
cord-326631-7gd3hjc3	22	3	proceed	proceed	VERB
cord-326631-7gd3hjc3	22	4	to	to	PART
cord-326631-7gd3hjc3	22	5	generalize	generalize	VERB
cord-326631-7gd3hjc3	22	6	these	these	DET
cord-326631-7gd3hjc3	22	7	results	result	NOUN
cord-326631-7gd3hjc3	22	8	in	in	ADP
cord-326631-7gd3hjc3	22	9	three	three	NUM
cord-326631-7gd3hjc3	22	10	new	new	ADJ
cord-326631-7gd3hjc3	22	11	directions	direction	NOUN
cord-326631-7gd3hjc3	22	12	,	,	PUNCT
cord-326631-7gd3hjc3	22	13	showing	show	VERB
cord-326631-7gd3hjc3	22	14	that	that	SCONJ
cord-326631-7gd3hjc3	22	15	the	the	DET
cord-326631-7gd3hjc3	22	16	standard	standard	ADJ
cord-326631-7gd3hjc3	22	17	formula	formula	NOUN
cord-326631-7gd3hjc3	22	18	remains	remain	VERB
cord-326631-7gd3hjc3	22	19	valid	valid	ADJ
cord-326631-7gd3hjc3	22	20	(	(	PUNCT
cord-326631-7gd3hjc3	22	21	i	i	NOUN
cord-326631-7gd3hjc3	22	22	)	)	PUNCT
cord-326631-7gd3hjc3	22	23	regardless	regardless	ADV
cord-326631-7gd3hjc3	22	24	of	of	ADP
cord-326631-7gd3hjc3	22	25	the	the	DET
cord-326631-7gd3hjc3	22	26	number	number	NOUN
cord-326631-7gd3hjc3	22	27	of	of	ADP
cord-326631-7gd3hjc3	22	28	distinct	distinct	ADJ
cord-326631-7gd3hjc3	22	29	infectious	infectious	ADJ
cord-326631-7gd3hjc3	22	30	stages	stage	NOUN
cord-326631-7gd3hjc3	22	31	,	,	PUNCT
cord-326631-7gd3hjc3	22	32	(	(	PUNCT
cord-326631-7gd3hjc3	22	33	ii	ii	PROPN
cord-326631-7gd3hjc3	22	34	)	)	PUNCT
cord-326631-7gd3hjc3	22	35	if	if	SCONJ
cord-326631-7gd3hjc3	22	36	the	the	DET
cord-326631-7gd3hjc3	22	37	mean	mean	ADJ
cord-326631-7gd3hjc3	22	38	contact	contact	NOUN
cord-326631-7gd3hjc3	22	39	rate	rate	NOUN
cord-326631-7gd3hjc3	22	40	is	be	AUX
cord-326631-7gd3hjc3	22	41	itself	itself	PRON
cord-326631-7gd3hjc3	22	42	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	22	43	distributed	distribute	VERB
cord-326631-7gd3hjc3	22	44	and	and	CCONJ
cord-326631-7gd3hjc3	22	45	(	(	PUNCT
cord-326631-7gd3hjc3	22	46	iii	iii	NUM
cord-326631-7gd3hjc3	22	47	)	)	PUNCT
cord-326631-7gd3hjc3	22	48	for	for	ADP
cord-326631-7gd3hjc3	22	49	a	a	DET
cord-326631-7gd3hjc3	22	50	large	large	ADJ
cord-326631-7gd3hjc3	22	51	class	class	NOUN
cord-326631-7gd3hjc3	22	52	of	of	ADP
cord-326631-7gd3hjc3	22	53	spatially	spatially	ADV
cord-326631-7gd3hjc3	22	54	heterogeneous	heterogeneous	ADJ
cord-326631-7gd3hjc3	22	55	contact	contact	NOUN
cord-326631-7gd3hjc3	22	56	structures	structure	NOUN
cord-326631-7gd3hjc3	22	57	.	.	PUNCT
cord-326631-7gd3hjc3	23	1	we	we	PRON
cord-326631-7gd3hjc3	23	2	conclude	conclude	VERB
cord-326631-7gd3hjc3	23	3	that	that	SCONJ
cord-326631-7gd3hjc3	23	4	the	the	DET
cord-326631-7gd3hjc3	23	5	kermack	kermack	NOUN
cord-326631-7gd3hjc3	23	6	-	-	PUNCT
cord-326631-7gd3hjc3	23	7	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	23	8	formula	formula	NOUN
cord-326631-7gd3hjc3	23	9	(	(	PUNCT
cord-326631-7gd3hjc3	23	10	5	5	NUM
cord-326631-7gd3hjc3	23	11	)	)	PUNCT
cord-326631-7gd3hjc3	23	12	applies	apply	VERB
cord-326631-7gd3hjc3	23	13	in	in	ADP
cord-326631-7gd3hjc3	23	14	great	great	ADJ
cord-326631-7gd3hjc3	23	15	generality	generality	NOUN
cord-326631-7gd3hjc3	23	16	,	,	PUNCT
cord-326631-7gd3hjc3	23	17	making	make	VERB
cord-326631-7gd3hjc3	23	18	it	it	PRON
cord-326631-7gd3hjc3	23	19	an	an	DET
cord-326631-7gd3hjc3	23	20	extremely	extremely	ADV
cord-326631-7gd3hjc3	23	21	useful	useful	ADJ
cord-326631-7gd3hjc3	23	22	relationship	relationship	NOUN
cord-326631-7gd3hjc3	23	23	in	in	ADP
cord-326631-7gd3hjc3	23	24	practice	practice	NOUN
cord-326631-7gd3hjc3	23	25	.	.	PUNCT
cord-326631-7gd3hjc3	24	1	the	the	DET
cord-326631-7gd3hjc3	24	2	standard	standard	ADJ
cord-326631-7gd3hjc3	24	3	sir	sir	PROPN
cord-326631-7gd3hjc3	24	4	model	model	NOUN
cord-326631-7gd3hjc3	24	5	(	(	PUNCT
cord-326631-7gd3hjc3	24	6	anderson	anderson	PROPN
cord-326631-7gd3hjc3	24	7	and	and	CCONJ
cord-326631-7gd3hjc3	24	8	may	may	PROPN
cord-326631-7gd3hjc3	24	9	,	,	PUNCT
cord-326631-7gd3hjc3	24	10	1991	1991	NUM
cord-326631-7gd3hjc3	24	11	;	;	PUNCT
cord-326631-7gd3hjc3	24	12	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	24	13	and	and	CCONJ
cord-326631-7gd3hjc3	24	14	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	24	15	,	,	PUNCT
cord-326631-7gd3hjc3	24	16	2000	2000	NUM
cord-326631-7gd3hjc3	24	17	;	;	PUNCT
cord-326631-7gd3hjc3	24	18	brauer	brauer	PROPN
cord-326631-7gd3hjc3	24	19	and	and	CCONJ
cord-326631-7gd3hjc3	24	20	castillo	castillo	PROPN
cord-326631-7gd3hjc3	24	21	-	-	PUNCT
cord-326631-7gd3hjc3	24	22	chavez	chavez	PROPN
cord-326631-7gd3hjc3	24	23	,	,	PUNCT
cord-326631-7gd3hjc3	24	24	2001	2001	NUM
cord-326631-7gd3hjc3	24	25	)	)	PUNCT
cord-326631-7gd3hjc3	24	26	is	be	AUX
cord-326631-7gd3hjc3	24	27	represented	represent	VERB
cord-326631-7gd3hjc3	24	28	by	by	ADP
cord-326631-7gd3hjc3	24	29	a	a	DET
cord-326631-7gd3hjc3	24	30	system	system	NOUN
cord-326631-7gd3hjc3	24	31	of	of	ADP
cord-326631-7gd3hjc3	24	32	three	three	NUM
cord-326631-7gd3hjc3	24	33	ordinary	ordinary	ADJ
cord-326631-7gd3hjc3	24	34	differential	differential	ADJ
cord-326631-7gd3hjc3	24	35	equations	equation	NOUN
cord-326631-7gd3hjc3	24	36	,	,	PUNCT
cord-326631-7gd3hjc3	24	37	here	here	ADV
cord-326631-7gd3hjc3	24	38	,	,	PUNCT
cord-326631-7gd3hjc3	24	39	s	s	PROPN
cord-326631-7gd3hjc3	24	40	,	,	PUNCT
cord-326631-7gd3hjc3	24	41	i	i	PROPN
cord-326631-7gd3hjc3	24	42	,	,	PUNCT
cord-326631-7gd3hjc3	24	43	and	and	CCONJ
cord-326631-7gd3hjc3	24	44	r	r	NOUN
cord-326631-7gd3hjc3	24	45	denote	denote	NOUN
cord-326631-7gd3hjc3	24	46	the	the	DET
cord-326631-7gd3hjc3	24	47	proportions	proportion	NOUN
cord-326631-7gd3hjc3	24	48	of	of	ADP
cord-326631-7gd3hjc3	24	49	the	the	DET
cord-326631-7gd3hjc3	24	50	population	population	NOUN
cord-326631-7gd3hjc3	24	51	that	that	PRON
cord-326631-7gd3hjc3	24	52	are	be	AUX
cord-326631-7gd3hjc3	24	53	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	24	54	,	,	PUNCT
cord-326631-7gd3hjc3	24	55	infectious	infectious	ADJ
cord-326631-7gd3hjc3	24	56	and	and	CCONJ
cord-326631-7gd3hjc3	24	57	recovered	recover	VERB
cord-326631-7gd3hjc3	24	58	,	,	PUNCT
cord-326631-7gd3hjc3	24	59	respectively	respectively	ADV
cord-326631-7gd3hjc3	24	60	.	.	PUNCT
cord-326631-7gd3hjc3	25	1	recovered	recover	VERB
cord-326631-7gd3hjc3	25	2	individuals	individual	NOUN
cord-326631-7gd3hjc3	25	3	are	be	AUX
cord-326631-7gd3hjc3	25	4	assumed	assume	VERB
cord-326631-7gd3hjc3	25	5	to	to	PART
cord-326631-7gd3hjc3	25	6	be	be	AUX
cord-326631-7gd3hjc3	25	7	immune	immune	ADJ
cord-326631-7gd3hjc3	25	8	to	to	ADP
cord-326631-7gd3hjc3	25	9	reinfection	reinfection	NOUN
cord-326631-7gd3hjc3	25	10	.	.	PUNCT
cord-326631-7gd3hjc3	26	1	since	since	SCONJ
cord-326631-7gd3hjc3	26	2	s	s	PROPN
cord-326631-7gd3hjc3	26	3	+	+	CCONJ
cord-326631-7gd3hjc3	26	4	i	i	PRON
cord-326631-7gd3hjc3	26	5	+	+	CCONJ
cord-326631-7gd3hjc3	26	6	r	r	NOUN
cord-326631-7gd3hjc3	26	7	=	=	SYM
cord-326631-7gd3hjc3	26	8	1	1	NUM
cord-326631-7gd3hjc3	26	9	,	,	PUNCT
cord-326631-7gd3hjc3	26	10	one	one	NUM
cord-326631-7gd3hjc3	26	11	of	of	ADP
cord-326631-7gd3hjc3	26	12	the	the	DET
cord-326631-7gd3hjc3	26	13	three	three	NUM
cord-326631-7gd3hjc3	26	14	equations	equation	NOUN
cord-326631-7gd3hjc3	26	15	is	be	AUX
cord-326631-7gd3hjc3	26	16	redundant	redundant	ADJ
cord-326631-7gd3hjc3	26	17	.	.	PUNCT
cord-326631-7gd3hjc3	27	1	the	the	DET
cord-326631-7gd3hjc3	27	2	two	two	NUM
cord-326631-7gd3hjc3	27	3	parameters	parameter	NOUN
cord-326631-7gd3hjc3	27	4	in	in	ADP
cord-326631-7gd3hjc3	27	5	the	the	DET
cord-326631-7gd3hjc3	27	6	model	model	NOUN
cord-326631-7gd3hjc3	27	7	are	be	AUX
cord-326631-7gd3hjc3	27	8	the	the	DET
cord-326631-7gd3hjc3	27	9	transmission	transmission	NOUN
cord-326631-7gd3hjc3	27	10	rate	rate	NOUN
cord-326631-7gd3hjc3	27	11	(	(	PUNCT
cord-326631-7gd3hjc3	27	12	β	β	NOUN
cord-326631-7gd3hjc3	27	13	)	)	PUNCT
cord-326631-7gd3hjc3	27	14	and	and	CCONJ
cord-326631-7gd3hjc3	27	15	the	the	DET
cord-326631-7gd3hjc3	27	16	recovery	recovery	NOUN
cord-326631-7gd3hjc3	27	17	rate	rate	NOUN
cord-326631-7gd3hjc3	27	18	(	(	PUNCT
cord-326631-7gd3hjc3	27	19	γ	γ	NOUN
cord-326631-7gd3hjc3	27	20	)	)	PUNCT
cord-326631-7gd3hjc3	27	21	.	.	PUNCT
cord-326631-7gd3hjc3	28	1	the	the	DET
cord-326631-7gd3hjc3	28	2	mean	mean	ADJ
cord-326631-7gd3hjc3	28	3	infectious	infectious	ADJ
cord-326631-7gd3hjc3	28	4	period	period	NOUN
cord-326631-7gd3hjc3	28	5	is	be	AUX
cord-326631-7gd3hjc3	28	6	t	t	NOUN
cord-326631-7gd3hjc3	28	7	=	=	SYM
cord-326631-7gd3hjc3	28	8	1	1	NUM
cord-326631-7gd3hjc3	28	9	/	/	SYM
cord-326631-7gd3hjc3	28	10	γ	γ	NOUN
cord-326631-7gd3hjc3	28	11	.	.	PUNCT
cord-326631-7gd3hjc3	29	1	the	the	DET
cord-326631-7gd3hjc3	29	2	basic	basic	ADJ
cord-326631-7gd3hjc3	29	3	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	29	4	number	number	NOUN
cord-326631-7gd3hjc3	29	5	is	be	AUX
cord-326631-7gd3hjc3	29	6	r	r	NOUN
cord-326631-7gd3hjc3	29	7	0	0	NUM
cord-326631-7gd3hjc3	29	8	=	=	NOUN
cord-326631-7gd3hjc3	29	9	βt	βt	NOUN
cord-326631-7gd3hjc3	29	10	.	.	PUNCT
cord-326631-7gd3hjc3	30	1	the	the	DET
cord-326631-7gd3hjc3	30	2	proportion	proportion	NOUN
cord-326631-7gd3hjc3	30	3	of	of	ADP
cord-326631-7gd3hjc3	30	4	the	the	DET
cord-326631-7gd3hjc3	30	5	population	population	NOUN
cord-326631-7gd3hjc3	30	6	that	that	PRON
cord-326631-7gd3hjc3	30	7	is	be	AUX
cord-326631-7gd3hjc3	30	8	infected	infect	VERB
cord-326631-7gd3hjc3	30	9	can	can	AUX
cord-326631-7gd3hjc3	30	10	increase	increase	VERB
cord-326631-7gd3hjc3	30	11	,	,	PUNCT
cord-326631-7gd3hjc3	30	12	and	and	CCONJ
cord-326631-7gd3hjc3	30	13	hence	hence	ADV
cord-326631-7gd3hjc3	30	14	an	an	DET
cord-326631-7gd3hjc3	30	15	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	30	16	can	can	AUX
cord-326631-7gd3hjc3	30	17	occur	occur	VERB
cord-326631-7gd3hjc3	30	18	,	,	PUNCT
cord-326631-7gd3hjc3	30	19	if	if	SCONJ
cord-326631-7gd3hjc3	30	20	and	and	CCONJ
cord-326631-7gd3hjc3	30	21	only	only	ADV
cord-326631-7gd3hjc3	30	22	if	if	SCONJ
cord-326631-7gd3hjc3	30	23	r	r	NOUN
cord-326631-7gd3hjc3	30	24	0	0	PUNCT
cord-326631-7gd3hjc3	30	25	>	>	SYM
cord-326631-7gd3hjc3	30	26	1	1	NUM
cord-326631-7gd3hjc3	30	27	.	.	PUNCT
cord-326631-7gd3hjc3	30	28	in	in	ADP
cord-326631-7gd3hjc3	30	29	eqs	eqs	PROPN
cord-326631-7gd3hjc3	30	30	.	.	PUNCT
cord-326631-7gd3hjc3	31	1	(	(	PUNCT
cord-326631-7gd3hjc3	31	2	1	1	NUM
cord-326631-7gd3hjc3	31	3	)	)	PUNCT
cord-326631-7gd3hjc3	31	4	,	,	PUNCT
cord-326631-7gd3hjc3	31	5	recruitment	recruitment	NOUN
cord-326631-7gd3hjc3	31	6	of	of	ADP
cord-326631-7gd3hjc3	31	7	new	new	ADJ
cord-326631-7gd3hjc3	31	8	susceptibles	susceptible	NOUN
cord-326631-7gd3hjc3	31	9	through	through	ADP
cord-326631-7gd3hjc3	31	10	birth	birth	NOUN
cord-326631-7gd3hjc3	31	11	or	or	CCONJ
cord-326631-7gd3hjc3	31	12	immigration	immigration	NOUN
cord-326631-7gd3hjc3	31	13	is	be	AUX
cord-326631-7gd3hjc3	31	14	ignored	ignore	VERB
cord-326631-7gd3hjc3	31	15	,	,	PUNCT
cord-326631-7gd3hjc3	31	16	as	as	SCONJ
cord-326631-7gd3hjc3	31	17	is	be	AUX
cord-326631-7gd3hjc3	31	18	loss	loss	NOUN
cord-326631-7gd3hjc3	31	19	of	of	ADP
cord-326631-7gd3hjc3	31	20	individuals	individual	NOUN
cord-326631-7gd3hjc3	31	21	through	through	ADP
cord-326631-7gd3hjc3	31	22	mortality	mortality	NOUN
cord-326631-7gd3hjc3	31	23	or	or	CCONJ
cord-326631-7gd3hjc3	31	24	emmigration	emmigration	NOUN
cord-326631-7gd3hjc3	31	25	.	.	PUNCT
cord-326631-7gd3hjc3	32	1	this	this	DET
cord-326631-7gd3hjc3	32	2	approximation	approximation	NOUN
cord-326631-7gd3hjc3	32	3	is	be	AUX
cord-326631-7gd3hjc3	32	4	reasonable	reasonable	ADJ
cord-326631-7gd3hjc3	32	5	provided	provide	VERB
cord-326631-7gd3hjc3	32	6	the	the	DET
cord-326631-7gd3hjc3	32	7	timescale	timescale	NOUN
cord-326631-7gd3hjc3	32	8	of	of	ADP
cord-326631-7gd3hjc3	32	9	the	the	DET
cord-326631-7gd3hjc3	32	10	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	32	11	is	be	AUX
cord-326631-7gd3hjc3	32	12	much	much	ADV
cord-326631-7gd3hjc3	32	13	shorter	short	ADJ
cord-326631-7gd3hjc3	32	14	than	than	ADP
cord-326631-7gd3hjc3	32	15	the	the	DET
cord-326631-7gd3hjc3	32	16	timescale	timescale	NOUN
cord-326631-7gd3hjc3	32	17	over	over	ADP
cord-326631-7gd3hjc3	32	18	which	which	PRON
cord-326631-7gd3hjc3	32	19	demographic	demographic	ADJ
cord-326631-7gd3hjc3	32	20	turnover	turnover	NOUN
cord-326631-7gd3hjc3	32	21	occurs	occur	VERB
cord-326631-7gd3hjc3	32	22	.	.	PUNCT
cord-326631-7gd3hjc3	33	1	no	no	DET
cord-326631-7gd3hjc3	33	2	recruitment	recruitment	NOUN
cord-326631-7gd3hjc3	33	3	ensures	ensure	VERB
cord-326631-7gd3hjc3	33	4	that	that	SCONJ
cord-326631-7gd3hjc3	33	5	the	the	DET
cord-326631-7gd3hjc3	33	6	disease	disease	NOUN
cord-326631-7gd3hjc3	33	7	will	will	AUX
cord-326631-7gd3hjc3	33	8	eventually	eventually	ADV
cord-326631-7gd3hjc3	33	9	burn	burn	VERB
cord-326631-7gd3hjc3	33	10	out	out	ADP
cord-326631-7gd3hjc3	33	11	,	,	PUNCT
cord-326631-7gd3hjc3	33	12	i.e.	i.e.	X
cord-326631-7gd3hjc3	33	13	,	,	PUNCT
cord-326631-7gd3hjc3	33	14	i(∞	i(∞	PROPN
cord-326631-7gd3hjc3	33	15	)	)	PUNCT
cord-326631-7gd3hjc3	33	16	=	=	NOUN
cord-326631-7gd3hjc3	33	17	0	0	NUM
cord-326631-7gd3hjc3	33	18	.	.	PUNCT
cord-326631-7gd3hjc3	34	1	to	to	PART
cord-326631-7gd3hjc3	34	2	see	see	VERB
cord-326631-7gd3hjc3	34	3	formally	formally	ADV
cord-326631-7gd3hjc3	34	4	that	that	SCONJ
cord-326631-7gd3hjc3	34	5	we	we	PRON
cord-326631-7gd3hjc3	34	6	must	must	AUX
cord-326631-7gd3hjc3	34	7	have	have	VERB
cord-326631-7gd3hjc3	34	8	i(∞	i(∞	PROPN
cord-326631-7gd3hjc3	34	9	)	)	PUNCT
cord-326631-7gd3hjc3	34	10	=	=	NOUN
cord-326631-7gd3hjc3	34	11	0	0	NUM
cord-326631-7gd3hjc3	34	12	,	,	PUNCT
cord-326631-7gd3hjc3	34	13	note	note	VERB
cord-326631-7gd3hjc3	34	14	that	that	SCONJ
cord-326631-7gd3hjc3	34	15	the	the	DET
cord-326631-7gd3hjc3	34	16	positive	positive	ADJ
cord-326631-7gd3hjc3	34	17	orthant	orthant	NOUN
cord-326631-7gd3hjc3	34	18	is	be	AUX
cord-326631-7gd3hjc3	34	19	invariant	invariant	ADJ
cord-326631-7gd3hjc3	34	20	so	so	ADV
cord-326631-7gd3hjc3	34	21	all	all	DET
cord-326631-7gd3hjc3	34	22	solutions	solution	NOUN
cord-326631-7gd3hjc3	34	23	of	of	ADP
cord-326631-7gd3hjc3	34	24	eqs	eqs	PROPN
cord-326631-7gd3hjc3	34	25	.	.	PUNCT
cord-326631-7gd3hjc3	35	1	(	(	PUNCT
cord-326631-7gd3hjc3	35	2	1	1	X
cord-326631-7gd3hjc3	35	3	)	)	PUNCT
cord-326631-7gd3hjc3	35	4	lie	lie	NOUN
cord-326631-7gd3hjc3	35	5	in	in	ADP
cord-326631-7gd3hjc3	35	6	the	the	DET
cord-326631-7gd3hjc3	35	7	non	non	ADJ
cord-326631-7gd3hjc3	35	8	-	-	ADJ
cord-326631-7gd3hjc3	35	9	negative	negative	ADJ
cord-326631-7gd3hjc3	35	10	,	,	PUNCT
cord-326631-7gd3hjc3	35	11	bounded	bound	VERB
cord-326631-7gd3hjc3	35	12	set	set	NOUN
cord-326631-7gd3hjc3	35	13	defined	define	VERB
cord-326631-7gd3hjc3	35	14	by	by	ADP
cord-326631-7gd3hjc3	35	15	s	s	NOUN
cord-326631-7gd3hjc3	35	16	,	,	PUNCT
cord-326631-7gd3hjc3	35	17	i	i	NOUN
cord-326631-7gd3hjc3	35	18	,	,	PUNCT
cord-326631-7gd3hjc3	35	19	r	r	NOUN
cord-326631-7gd3hjc3	35	20	≥	≥	NOUN
cord-326631-7gd3hjc3	35	21	0	0	NUM
cord-326631-7gd3hjc3	35	22	and	and	CCONJ
cord-326631-7gd3hjc3	35	23	s	s	NOUN
cord-326631-7gd3hjc3	36	1	+	+	X
cord-326631-7gd3hjc3	36	2	i	i	PRON
cord-326631-7gd3hjc3	36	3	+	+	CCONJ
cord-326631-7gd3hjc3	37	1	r	r	NOUN
cord-326631-7gd3hjc3	37	2	=	=	SYM
cord-326631-7gd3hjc3	37	3	1	1	X
cord-326631-7gd3hjc3	37	4	.	.	PUNCT
cord-326631-7gd3hjc3	37	5	observing	observe	VERB
cord-326631-7gd3hjc3	37	6	that	that	SCONJ
cord-326631-7gd3hjc3	37	7	we	we	PRON
cord-326631-7gd3hjc3	37	8	see	see	VERB
cord-326631-7gd3hjc3	37	9	that	that	PRON
cord-326631-7gd3hjc3	37	10	s	s	X
cord-326631-7gd3hjc3	38	1	+	+	CCONJ
cord-326631-7gd3hjc3	38	2	i	i	PRON
cord-326631-7gd3hjc3	38	3	is	be	AUX
cord-326631-7gd3hjc3	38	4	decreasing	decrease	VERB
cord-326631-7gd3hjc3	38	5	whenever	whenever	SCONJ
cord-326631-7gd3hjc3	38	6	i	i	PRON
cord-326631-7gd3hjc3	38	7	>	>	X
cord-326631-7gd3hjc3	38	8	0	0	NUM
cord-326631-7gd3hjc3	38	9	.	.	PUNCT
cord-326631-7gd3hjc3	39	1	however	however	ADV
cord-326631-7gd3hjc3	39	2	,	,	PUNCT
cord-326631-7gd3hjc3	39	3	s	s	PROPN
cord-326631-7gd3hjc3	40	1	+	+	CCONJ
cord-326631-7gd3hjc3	40	2	i	i	PRON
cord-326631-7gd3hjc3	40	3	is	be	AUX
cord-326631-7gd3hjc3	40	4	bounded	bound	VERB
cord-326631-7gd3hjc3	40	5	below	below	ADV
cord-326631-7gd3hjc3	40	6	by	by	ADP
cord-326631-7gd3hjc3	40	7	0	0	NUM
cord-326631-7gd3hjc3	40	8	;	;	PUNCT
cord-326631-7gd3hjc3	40	9	hence	hence	ADV
cord-326631-7gd3hjc3	40	10	it	it	PRON
cord-326631-7gd3hjc3	40	11	has	have	VERB
cord-326631-7gd3hjc3	40	12	a	a	DET
cord-326631-7gd3hjc3	40	13	limit	limit	NOUN
cord-326631-7gd3hjc3	40	14	.	.	PUNCT
cord-326631-7gd3hjc3	41	1	moreover	moreover	ADV
cord-326631-7gd3hjc3	41	2	,	,	PUNCT
cord-326631-7gd3hjc3	41	3	eq	eq	PROPN
cord-326631-7gd3hjc3	41	4	.	.	PUNCT
cord-326631-7gd3hjc3	41	5	(	(	PUNCT
cord-326631-7gd3hjc3	41	6	2	2	X
cord-326631-7gd3hjc3	41	7	)	)	PUNCT
cord-326631-7gd3hjc3	41	8	implies	imply	VERB
cord-326631-7gd3hjc3	41	9	that	that	SCONJ
cord-326631-7gd3hjc3	41	10	d	d	PROPN
cord-326631-7gd3hjc3	41	11	dt	dt	PROPN
cord-326631-7gd3hjc3	41	12	(	(	PUNCT
cord-326631-7gd3hjc3	41	13	s	s	PROPN
cord-326631-7gd3hjc3	41	14	+	+	X
cord-326631-7gd3hjc3	41	15	i	i	NOUN
cord-326631-7gd3hjc3	41	16	)	)	PUNCT
cord-326631-7gd3hjc3	41	17	is	be	AUX
cord-326631-7gd3hjc3	41	18	bounded	bound	VERB
cord-326631-7gd3hjc3	41	19	because	because	SCONJ
cord-326631-7gd3hjc3	41	20	i	i	PRON
cord-326631-7gd3hjc3	41	21	is	be	AUX
cord-326631-7gd3hjc3	41	22	bounded	bound	VERB
cord-326631-7gd3hjc3	41	23	.	.	PUNCT
cord-326631-7gd3hjc3	42	1	hence	hence	ADV
cord-326631-7gd3hjc3	42	2	lim	lim	PROPN
cord-326631-7gd3hjc3	42	3	t→∞	t→∞	PRON
cord-326631-7gd3hjc3	42	4	d	d	X
cord-326631-7gd3hjc3	42	5	dt	dt	PROPN
cord-326631-7gd3hjc3	42	6	(	(	PUNCT
cord-326631-7gd3hjc3	42	7	s	s	PROPN
cord-326631-7gd3hjc3	42	8	+	+	X
cord-326631-7gd3hjc3	42	9	i	i	NOUN
cord-326631-7gd3hjc3	42	10	)	)	PUNCT
cord-326631-7gd3hjc3	42	11	=	=	SYM
cord-326631-7gd3hjc3	42	12	0	0	NUM
cord-326631-7gd3hjc3	42	13	,	,	PUNCT
cord-326631-7gd3hjc3	42	14	so	so	CCONJ
cord-326631-7gd3hjc3	42	15	eq	eq	NOUN
cord-326631-7gd3hjc3	42	16	.	.	PUNCT
cord-326631-7gd3hjc3	43	1	(	(	PUNCT
cord-326631-7gd3hjc3	43	2	2	2	X
cord-326631-7gd3hjc3	43	3	)	)	PUNCT
cord-326631-7gd3hjc3	43	4	yields	yield	NOUN
cord-326631-7gd3hjc3	43	5	i(∞	i(∞	PROPN
cord-326631-7gd3hjc3	43	6	)	)	PUNCT
cord-326631-7gd3hjc3	43	7	=	=	NOUN
cord-326631-7gd3hjc3	43	8	0	0	X
cord-326631-7gd3hjc3	43	9	.	.	PUNCT
cord-326631-7gd3hjc3	44	1	this	this	DET
cord-326631-7gd3hjc3	44	2	model	model	NOUN
cord-326631-7gd3hjc3	44	3	(	(	PUNCT
cord-326631-7gd3hjc3	44	4	1	1	NUM
cord-326631-7gd3hjc3	44	5	)	)	PUNCT
cord-326631-7gd3hjc3	44	6	is	be	AUX
cord-326631-7gd3hjc3	44	7	sufficiently	sufficiently	ADV
cord-326631-7gd3hjc3	44	8	simple	simple	ADJ
cord-326631-7gd3hjc3	44	9	that	that	SCONJ
cord-326631-7gd3hjc3	44	10	an	an	DET
cord-326631-7gd3hjc3	44	11	exact	exact	ADJ
cord-326631-7gd3hjc3	44	12	solution	solution	NOUN
cord-326631-7gd3hjc3	44	13	can	can	AUX
cord-326631-7gd3hjc3	44	14	be	be	AUX
cord-326631-7gd3hjc3	44	15	obtained	obtain	VERB
cord-326631-7gd3hjc3	44	16	for	for	ADP
cord-326631-7gd3hjc3	44	17	the	the	DET
cord-326631-7gd3hjc3	44	18	phase	phase	NOUN
cord-326631-7gd3hjc3	44	19	portrait	portrait	NOUN
cord-326631-7gd3hjc3	44	20	.	.	PUNCT
cord-326631-7gd3hjc3	45	1	forming	form	VERB
cord-326631-7gd3hjc3	45	2	di	di	PROPN
cord-326631-7gd3hjc3	45	3	/	/	SYM
cord-326631-7gd3hjc3	45	4	ds	ds	PROPN
cord-326631-7gd3hjc3	45	5	and	and	CCONJ
cord-326631-7gd3hjc3	45	6	integrating	integrate	VERB
cord-326631-7gd3hjc3	45	7	yields	yield	NOUN
cord-326631-7gd3hjc3	45	8	an	an	DET
cord-326631-7gd3hjc3	45	9	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	45	10	ends	end	NOUN
cord-326631-7gd3hjc3	45	11	when	when	SCONJ
cord-326631-7gd3hjc3	45	12	no	no	DET
cord-326631-7gd3hjc3	45	13	infectives	infective	NOUN
cord-326631-7gd3hjc3	45	14	remain	remain	VERB
cord-326631-7gd3hjc3	45	15	.	.	PUNCT
cord-326631-7gd3hjc3	46	1	consequently	consequently	ADV
cord-326631-7gd3hjc3	46	2	,	,	PUNCT
cord-326631-7gd3hjc3	46	3	we	we	PRON
cord-326631-7gd3hjc3	46	4	can	can	AUX
cord-326631-7gd3hjc3	46	5	find	find	VERB
cord-326631-7gd3hjc3	46	6	the	the	DET
cord-326631-7gd3hjc3	46	7	final	final	ADJ
cord-326631-7gd3hjc3	46	8	size	size	NOUN
cord-326631-7gd3hjc3	46	9	z	z	X
cord-326631-7gd3hjc3	46	10	by	by	ADP
cord-326631-7gd3hjc3	46	11	setting	set	VERB
cord-326631-7gd3hjc3	46	12	i	i	PRON
cord-326631-7gd3hjc3	46	13	=	=	NOUN
cord-326631-7gd3hjc3	46	14	0	0	NUM
cord-326631-7gd3hjc3	46	15	in	in	ADP
cord-326631-7gd3hjc3	46	16	eq	eq	PROPN
cord-326631-7gd3hjc3	46	17	.	.	PUNCT
cord-326631-7gd3hjc3	47	1	(	(	PUNCT
cord-326631-7gd3hjc3	47	2	3	3	NUM
cord-326631-7gd3hjc3	47	3	)	)	PUNCT
cord-326631-7gd3hjc3	47	4	and	and	CCONJ
cord-326631-7gd3hjc3	47	5	solving	solve	VERB
cord-326631-7gd3hjc3	47	6	for	for	ADP
cord-326631-7gd3hjc3	47	7	z	z	NOUN
cord-326631-7gd3hjc3	47	8	=	=	NOUN
cord-326631-7gd3hjc3	47	9	s(0	s(0	PROPN
cord-326631-7gd3hjc3	47	10	)	)	PUNCT
cord-326631-7gd3hjc3	47	11	−	−	PROPN
cord-326631-7gd3hjc3	47	12	s.	s.	PROPN
cord-326631-7gd3hjc3	47	13	this	this	PRON
cord-326631-7gd3hjc3	47	14	yields	yield	VERB
cord-326631-7gd3hjc3	47	15	the	the	DET
cord-326631-7gd3hjc3	47	16	implicit	implicit	ADJ
cord-326631-7gd3hjc3	47	17	relation	relation	NOUN
cord-326631-7gd3hjc3	47	18	(	(	PUNCT
cord-326631-7gd3hjc3	47	19	an	an	DET
cord-326631-7gd3hjc3	47	20	explicit	explicit	ADJ
cord-326631-7gd3hjc3	47	21	form	form	NOUN
cord-326631-7gd3hjc3	47	22	is	be	AUX
cord-326631-7gd3hjc3	47	23	given	give	VERB
cord-326631-7gd3hjc3	47	24	in	in	ADP
cord-326631-7gd3hjc3	47	25	appendix	appendix	PROPN
cord-326631-7gd3hjc3	47	26	a	a	PRON
cord-326631-7gd3hjc3	47	27	)	)	PUNCT
cord-326631-7gd3hjc3	47	28	.	.	PUNCT
cord-326631-7gd3hjc3	48	1	the	the	DET
cord-326631-7gd3hjc3	48	2	general	general	ADJ
cord-326631-7gd3hjc3	48	3	formula	formula	NOUN
cord-326631-7gd3hjc3	48	4	(	(	PUNCT
cord-326631-7gd3hjc3	48	5	4	4	NUM
cord-326631-7gd3hjc3	48	6	)	)	PUNCT
cord-326631-7gd3hjc3	48	7	applies	apply	VERB
cord-326631-7gd3hjc3	48	8	regardless	regardless	ADV
cord-326631-7gd3hjc3	48	9	of	of	ADP
cord-326631-7gd3hjc3	48	10	the	the	DET
cord-326631-7gd3hjc3	48	11	proportions	proportion	NOUN
cord-326631-7gd3hjc3	48	12	of	of	ADP
cord-326631-7gd3hjc3	48	13	the	the	DET
cord-326631-7gd3hjc3	48	14	population	population	NOUN
cord-326631-7gd3hjc3	48	15	that	that	PRON
cord-326631-7gd3hjc3	48	16	are	be	AUX
cord-326631-7gd3hjc3	48	17	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	48	18	and	and	CCONJ
cord-326631-7gd3hjc3	48	19	infective	infective	ADJ
cord-326631-7gd3hjc3	48	20	initially	initially	ADV
cord-326631-7gd3hjc3	48	21	.	.	PUNCT
cord-326631-7gd3hjc3	49	1	a	a	DET
cord-326631-7gd3hjc3	49	2	less	less	ADV
cord-326631-7gd3hjc3	49	3	than	than	ADP
cord-326631-7gd3hjc3	49	4	fully	fully	ADV
cord-326631-7gd3hjc3	49	5	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	49	6	population	population	NOUN
cord-326631-7gd3hjc3	49	7	must	must	AUX
cord-326631-7gd3hjc3	49	8	be	be	AUX
cord-326631-7gd3hjc3	49	9	taken	take	VERB
cord-326631-7gd3hjc3	49	10	into	into	ADP
cord-326631-7gd3hjc3	49	11	account	account	NOUN
cord-326631-7gd3hjc3	49	12	if	if	SCONJ
cord-326631-7gd3hjc3	49	13	some	some	DET
cord-326631-7gd3hjc3	49	14	individuals	individual	NOUN
cord-326631-7gd3hjc3	49	15	have	have	AUX
cord-326631-7gd3hjc3	49	16	been	be	AUX
cord-326631-7gd3hjc3	49	17	vaccinated	vaccinate	VERB
cord-326631-7gd3hjc3	49	18	or	or	CCONJ
cord-326631-7gd3hjc3	49	19	retain	retain	VERB
cord-326631-7gd3hjc3	49	20	immunity	immunity	NOUN
cord-326631-7gd3hjc3	49	21	from	from	ADP
cord-326631-7gd3hjc3	49	22	previous	previous	ADJ
cord-326631-7gd3hjc3	49	23	exposures	exposure	NOUN
cord-326631-7gd3hjc3	49	24	.	.	PUNCT
cord-326631-7gd3hjc3	50	1	however	however	ADV
cord-326631-7gd3hjc3	50	2	,	,	PUNCT
cord-326631-7gd3hjc3	50	3	in	in	ADP
cord-326631-7gd3hjc3	50	4	the	the	DET
cord-326631-7gd3hjc3	50	5	important	important	ADJ
cord-326631-7gd3hjc3	50	6	special	special	ADJ
cord-326631-7gd3hjc3	50	7	case	case	NOUN
cord-326631-7gd3hjc3	50	8	where	where	SCONJ
cord-326631-7gd3hjc3	50	9	a	a	DET
cord-326631-7gd3hjc3	50	10	new	new	ADJ
cord-326631-7gd3hjc3	50	11	pathogen	pathogen	PROPN
cord-326631-7gd3hjc3	50	12	enters	enter	VERB
cord-326631-7gd3hjc3	50	13	a	a	DET
cord-326631-7gd3hjc3	50	14	fully	fully	ADV
cord-326631-7gd3hjc3	50	15	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	50	16	population	population	NOUN
cord-326631-7gd3hjc3	50	17	,	,	PUNCT
cord-326631-7gd3hjc3	50	18	we	we	PRON
cord-326631-7gd3hjc3	50	19	have	have	VERB
cord-326631-7gd3hjc3	50	20	both	both	PRON
cord-326631-7gd3hjc3	50	21	i(0	i(0	NOUN
cord-326631-7gd3hjc3	50	22	)	)	PUNCT
cord-326631-7gd3hjc3	50	23	1	1	NUM
cord-326631-7gd3hjc3	50	24	and	and	CCONJ
cord-326631-7gd3hjc3	50	25	s(0	s(0	NOUN
cord-326631-7gd3hjc3	50	26	)	)	PUNCT
cord-326631-7gd3hjc3	51	1	∼	∼	PROPN
cord-326631-7gd3hjc3	51	2	1	1	NUM
cord-326631-7gd3hjc3	51	3	.	.	PUNCT
cord-326631-7gd3hjc3	52	1	in	in	ADP
cord-326631-7gd3hjc3	52	2	the	the	DET
cord-326631-7gd3hjc3	52	3	limit	limit	NOUN
cord-326631-7gd3hjc3	52	4	i(0	i(0	NOUN
cord-326631-7gd3hjc3	52	5	)	)	PUNCT
cord-326631-7gd3hjc3	52	6	→	→	PUNCT
cord-326631-7gd3hjc3	52	7	0	0	NUM
cord-326631-7gd3hjc3	52	8	,	,	PUNCT
cord-326631-7gd3hjc3	52	9	s(0	s(0	PROPN
cord-326631-7gd3hjc3	52	10	)	)	PUNCT
cord-326631-7gd3hjc3	52	11	→	→	NUM
cord-326631-7gd3hjc3	52	12	1	1	NUM
cord-326631-7gd3hjc3	52	13	,	,	PUNCT
cord-326631-7gd3hjc3	52	14	which	which	PRON
cord-326631-7gd3hjc3	52	15	is	be	AUX
cord-326631-7gd3hjc3	52	16	the	the	DET
cord-326631-7gd3hjc3	52	17	usual	usual	ADJ
cord-326631-7gd3hjc3	52	18	final	final	ADJ
cord-326631-7gd3hjc3	52	19	size	size	NOUN
cord-326631-7gd3hjc3	52	20	formula	formula	NOUN
cord-326631-7gd3hjc3	52	21	.	.	PUNCT
cord-326631-7gd3hjc3	53	1	the	the	DET
cord-326631-7gd3hjc3	53	2	practical	practical	ADJ
cord-326631-7gd3hjc3	53	3	utility	utility	NOUN
cord-326631-7gd3hjc3	53	4	of	of	ADP
cord-326631-7gd3hjc3	53	5	the	the	DET
cord-326631-7gd3hjc3	53	6	final	final	ADJ
cord-326631-7gd3hjc3	53	7	size	size	NOUN
cord-326631-7gd3hjc3	53	8	formula	formula	NOUN
cord-326631-7gd3hjc3	53	9	would	would	AUX
cord-326631-7gd3hjc3	53	10	appear	appear	VERB
cord-326631-7gd3hjc3	53	11	to	to	PART
cord-326631-7gd3hjc3	53	12	be	be	AUX
cord-326631-7gd3hjc3	53	13	limited	limit	VERB
cord-326631-7gd3hjc3	53	14	by	by	ADP
cord-326631-7gd3hjc3	53	15	the	the	DET
cord-326631-7gd3hjc3	53	16	fact	fact	NOUN
cord-326631-7gd3hjc3	53	17	that	that	SCONJ
cord-326631-7gd3hjc3	53	18	it	it	PRON
cord-326631-7gd3hjc3	53	19	is	be	AUX
cord-326631-7gd3hjc3	53	20	derived	derive	VERB
cord-326631-7gd3hjc3	53	21	from	from	ADP
cord-326631-7gd3hjc3	53	22	the	the	DET
cord-326631-7gd3hjc3	53	23	overly	overly	ADV
cord-326631-7gd3hjc3	53	24	simplistic	simplistic	ADJ
cord-326631-7gd3hjc3	53	25	standard	standard	ADJ
cord-326631-7gd3hjc3	53	26	sir	sir	PROPN
cord-326631-7gd3hjc3	53	27	model	model	NOUN
cord-326631-7gd3hjc3	53	28	.	.	PUNCT
cord-326631-7gd3hjc3	54	1	in	in	ADP
cord-326631-7gd3hjc3	54	2	the	the	DET
cord-326631-7gd3hjc3	54	3	remainder	remainder	NOUN
cord-326631-7gd3hjc3	54	4	of	of	ADP
cord-326631-7gd3hjc3	54	5	this	this	DET
cord-326631-7gd3hjc3	54	6	paper	paper	NOUN
cord-326631-7gd3hjc3	54	7	we	we	PRON
cord-326631-7gd3hjc3	54	8	show	show	VERB
cord-326631-7gd3hjc3	54	9	that	that	SCONJ
cord-326631-7gd3hjc3	54	10	,	,	PUNCT
cord-326631-7gd3hjc3	54	11	in	in	ADP
cord-326631-7gd3hjc3	54	12	fact	fact	NOUN
cord-326631-7gd3hjc3	54	13	,	,	PUNCT
cord-326631-7gd3hjc3	54	14	the	the	DET
cord-326631-7gd3hjc3	54	15	formula	formula	NOUN
cord-326631-7gd3hjc3	54	16	is	be	AUX
cord-326631-7gd3hjc3	54	17	valid	valid	ADJ
cord-326631-7gd3hjc3	54	18	under	under	ADP
cord-326631-7gd3hjc3	54	19	very	very	ADV
cord-326631-7gd3hjc3	54	20	general	general	ADJ
cord-326631-7gd3hjc3	54	21	circumstances	circumstance	NOUN
cord-326631-7gd3hjc3	54	22	.	.	PUNCT
cord-326631-7gd3hjc3	55	1	we	we	PRON
cord-326631-7gd3hjc3	55	2	generalize	generalize	VERB
cord-326631-7gd3hjc3	55	3	the	the	DET
cord-326631-7gd3hjc3	55	4	model	model	NOUN
cord-326631-7gd3hjc3	55	5	in	in	ADP
cord-326631-7gd3hjc3	55	6	several	several	ADJ
cord-326631-7gd3hjc3	55	7	steps	step	NOUN
cord-326631-7gd3hjc3	55	8	,	,	PUNCT
cord-326631-7gd3hjc3	55	9	in	in	ADP
cord-326631-7gd3hjc3	55	10	order	order	NOUN
cord-326631-7gd3hjc3	55	11	to	to	PART
cord-326631-7gd3hjc3	55	12	explain	explain	VERB
cord-326631-7gd3hjc3	55	13	the	the	DET
cord-326631-7gd3hjc3	55	14	ideas	idea	NOUN
cord-326631-7gd3hjc3	55	15	clearly	clearly	ADV
cord-326631-7gd3hjc3	55	16	and	and	CCONJ
cord-326631-7gd3hjc3	55	17	to	to	PART
cord-326631-7gd3hjc3	55	18	avoid	avoid	VERB
cord-326631-7gd3hjc3	55	19	exposing	expose	VERB
cord-326631-7gd3hjc3	55	20	the	the	DET
cord-326631-7gd3hjc3	55	21	reader	reader	NOUN
cord-326631-7gd3hjc3	55	22	to	to	ADP
cord-326631-7gd3hjc3	55	23	a	a	DET
cord-326631-7gd3hjc3	55	24	notational	notational	ADJ
cord-326631-7gd3hjc3	55	25	burden	burden	NOUN
cord-326631-7gd3hjc3	55	26	at	at	ADP
cord-326631-7gd3hjc3	55	27	the	the	DET
cord-326631-7gd3hjc3	55	28	outset	outset	NOUN
cord-326631-7gd3hjc3	55	29	.	.	PUNCT
cord-326631-7gd3hjc3	56	1	the	the	DET
cord-326631-7gd3hjc3	56	2	standard	standard	ADJ
cord-326631-7gd3hjc3	56	3	sir	sir	PROPN
cord-326631-7gd3hjc3	56	4	model	model	NOUN
cord-326631-7gd3hjc3	56	5	ignores	ignore	VERB
cord-326631-7gd3hjc3	56	6	any	any	DET
cord-326631-7gd3hjc3	56	7	delay	delay	NOUN
cord-326631-7gd3hjc3	56	8	between	between	ADP
cord-326631-7gd3hjc3	56	9	the	the	DET
cord-326631-7gd3hjc3	56	10	time	time	NOUN
cord-326631-7gd3hjc3	56	11	an	an	DET
cord-326631-7gd3hjc3	56	12	individual	individual	NOUN
cord-326631-7gd3hjc3	56	13	is	be	AUX
cord-326631-7gd3hjc3	56	14	infected	infect	VERB
cord-326631-7gd3hjc3	56	15	and	and	CCONJ
cord-326631-7gd3hjc3	56	16	the	the	DET
cord-326631-7gd3hjc3	56	17	onset	onset	NOUN
cord-326631-7gd3hjc3	56	18	of	of	ADP
cord-326631-7gd3hjc3	56	19	infectiousness	infectiousness	NOUN
cord-326631-7gd3hjc3	56	20	.	.	PUNCT
cord-326631-7gd3hjc3	57	1	this	this	DET
cord-326631-7gd3hjc3	57	2	latent	latent	ADJ
cord-326631-7gd3hjc3	57	3	period	period	NOUN
cord-326631-7gd3hjc3	57	4	is	be	AUX
cord-326631-7gd3hjc3	57	5	often	often	ADV
cord-326631-7gd3hjc3	57	6	substantial	substantial	ADJ
cord-326631-7gd3hjc3	57	7	compared	compare	VERB
cord-326631-7gd3hjc3	57	8	with	with	ADP
cord-326631-7gd3hjc3	57	9	the	the	DET
cord-326631-7gd3hjc3	57	10	infectious	infectious	ADJ
cord-326631-7gd3hjc3	57	11	period	period	NOUN
cord-326631-7gd3hjc3	57	12	(	(	PUNCT
cord-326631-7gd3hjc3	57	13	anderson	anderson	PROPN
cord-326631-7gd3hjc3	57	14	and	and	CCONJ
cord-326631-7gd3hjc3	57	15	may	may	PROPN
cord-326631-7gd3hjc3	57	16	,	,	PUNCT
cord-326631-7gd3hjc3	57	17	1991	1991	NUM
cord-326631-7gd3hjc3	57	18	)	)	PUNCT
cord-326631-7gd3hjc3	57	19	.	.	PUNCT
cord-326631-7gd3hjc3	58	1	in	in	ADP
cord-326631-7gd3hjc3	58	2	addition	addition	NOUN
cord-326631-7gd3hjc3	58	3	,	,	PUNCT
cord-326631-7gd3hjc3	58	4	some	some	DET
cord-326631-7gd3hjc3	58	5	pathogens	pathogen	NOUN
cord-326631-7gd3hjc3	58	6	(	(	PUNCT
cord-326631-7gd3hjc3	58	7	notably	notably	ADV
cord-326631-7gd3hjc3	58	8	hiv	hiv	PROPN
cord-326631-7gd3hjc3	58	9	)	)	PUNCT
cord-326631-7gd3hjc3	58	10	give	give	VERB
cord-326631-7gd3hjc3	58	11	rise	rise	NOUN
cord-326631-7gd3hjc3	58	12	to	to	ADP
cord-326631-7gd3hjc3	58	13	a	a	DET
cord-326631-7gd3hjc3	58	14	sequence	sequence	NOUN
cord-326631-7gd3hjc3	58	15	of	of	ADP
cord-326631-7gd3hjc3	58	16	distinct	distinct	ADJ
cord-326631-7gd3hjc3	58	17	stages	stage	NOUN
cord-326631-7gd3hjc3	58	18	of	of	ADP
cord-326631-7gd3hjc3	58	19	infection	infection	NOUN
cord-326631-7gd3hjc3	58	20	,	,	PUNCT
cord-326631-7gd3hjc3	58	21	each	each	PRON
cord-326631-7gd3hjc3	58	22	yielding	yield	VERB
cord-326631-7gd3hjc3	58	23	a	a	DET
cord-326631-7gd3hjc3	58	24	different	different	ADJ
cord-326631-7gd3hjc3	58	25	transmission	transmission	NOUN
cord-326631-7gd3hjc3	58	26	rate	rate	NOUN
cord-326631-7gd3hjc3	58	27	(	(	PUNCT
cord-326631-7gd3hjc3	58	28	redfield	redfield	PROPN
cord-326631-7gd3hjc3	58	29	et	et	PROPN
cord-326631-7gd3hjc3	58	30	al	al	PROPN
cord-326631-7gd3hjc3	58	31	.	.	PROPN
cord-326631-7gd3hjc3	58	32	,	,	PUNCT
cord-326631-7gd3hjc3	58	33	1986	1986	NUM
cord-326631-7gd3hjc3	58	34	;	;	PUNCT
cord-326631-7gd3hjc3	58	35	seligmann	seligmann	PROPN
cord-326631-7gd3hjc3	58	36	et	et	PROPN
cord-326631-7gd3hjc3	58	37	al	al	PROPN
cord-326631-7gd3hjc3	58	38	.	.	PROPN
cord-326631-7gd3hjc3	58	39	,	,	PUNCT
cord-326631-7gd3hjc3	58	40	1987	1987	NUM
cord-326631-7gd3hjc3	58	41	)	)	PUNCT
cord-326631-7gd3hjc3	58	42	.	.	PUNCT
cord-326631-7gd3hjc3	59	1	it	it	PRON
cord-326631-7gd3hjc3	59	2	is	be	AUX
cord-326631-7gd3hjc3	59	3	common	common	ADJ
cord-326631-7gd3hjc3	59	4	to	to	PART
cord-326631-7gd3hjc3	59	5	incorporate	incorporate	VERB
cord-326631-7gd3hjc3	59	6	latency	latency	NOUN
cord-326631-7gd3hjc3	59	7	by	by	ADP
cord-326631-7gd3hjc3	59	8	including	include	VERB
cord-326631-7gd3hjc3	59	9	an	an	DET
cord-326631-7gd3hjc3	59	10	"	"	PUNCT
cord-326631-7gd3hjc3	59	11	exposed	expose	VERB
cord-326631-7gd3hjc3	59	12	"	"	PUNCT
cord-326631-7gd3hjc3	59	13	class	class	NOUN
cord-326631-7gd3hjc3	59	14	(	(	PUNCT
cord-326631-7gd3hjc3	59	15	e	e	NOUN
cord-326631-7gd3hjc3	59	16	)	)	PUNCT
cord-326631-7gd3hjc3	59	17	,	,	PUNCT
cord-326631-7gd3hjc3	59	18	yielding	yield	VERB
cord-326631-7gd3hjc3	59	19	an	an	DET
cord-326631-7gd3hjc3	59	20	seir	seir	ADJ
cord-326631-7gd3hjc3	59	21	model	model	NOUN
cord-326631-7gd3hjc3	59	22	(	(	PUNCT
cord-326631-7gd3hjc3	59	23	schwartz	schwartz	NOUN
cord-326631-7gd3hjc3	59	24	and	and	CCONJ
cord-326631-7gd3hjc3	59	25	smith	smith	PROPN
cord-326631-7gd3hjc3	59	26	,	,	PUNCT
cord-326631-7gd3hjc3	59	27	1983	1983	NUM
cord-326631-7gd3hjc3	59	28	;	;	PUNCT
cord-326631-7gd3hjc3	59	29	earn	earn	VERB
cord-326631-7gd3hjc3	59	30	et	et	PROPN
cord-326631-7gd3hjc3	59	31	al	al	PROPN
cord-326631-7gd3hjc3	59	32	.	.	PROPN
cord-326631-7gd3hjc3	59	33	,	,	PUNCT
cord-326631-7gd3hjc3	59	34	2000a	2000a	NUM
cord-326631-7gd3hjc3	59	35	)	)	PUNCT
cord-326631-7gd3hjc3	59	36	.	.	PUNCT
cord-326631-7gd3hjc3	60	1	however	however	ADV
cord-326631-7gd3hjc3	60	2	,	,	PUNCT
cord-326631-7gd3hjc3	60	3	noting	note	VERB
cord-326631-7gd3hjc3	60	4	that	that	SCONJ
cord-326631-7gd3hjc3	60	5	the	the	DET
cord-326631-7gd3hjc3	60	6	exposed	expose	VERB
cord-326631-7gd3hjc3	60	7	stage	stage	NOUN
cord-326631-7gd3hjc3	60	8	can	can	AUX
cord-326631-7gd3hjc3	60	9	be	be	AUX
cord-326631-7gd3hjc3	60	10	regarded	regard	VERB
cord-326631-7gd3hjc3	60	11	as	as	ADP
cord-326631-7gd3hjc3	60	12	an	an	DET
cord-326631-7gd3hjc3	60	13	infectious	infectious	ADJ
cord-326631-7gd3hjc3	60	14	stage	stage	NOUN
cord-326631-7gd3hjc3	60	15	during	during	ADP
cord-326631-7gd3hjc3	60	16	which	which	PRON
cord-326631-7gd3hjc3	60	17	the	the	DET
cord-326631-7gd3hjc3	60	18	transmission	transmission	NOUN
cord-326631-7gd3hjc3	60	19	rate	rate	NOUN
cord-326631-7gd3hjc3	60	20	happens	happen	VERB
cord-326631-7gd3hjc3	60	21	to	to	PART
cord-326631-7gd3hjc3	60	22	be	be	AUX
cord-326631-7gd3hjc3	60	23	zero	zero	NUM
cord-326631-7gd3hjc3	60	24	,	,	PUNCT
cord-326631-7gd3hjc3	60	25	we	we	PRON
cord-326631-7gd3hjc3	60	26	lose	lose	VERB
cord-326631-7gd3hjc3	60	27	no	no	DET
cord-326631-7gd3hjc3	60	28	generality	generality	NOUN
cord-326631-7gd3hjc3	60	29	by	by	ADP
cord-326631-7gd3hjc3	60	30	restricting	restrict	VERB
cord-326631-7gd3hjc3	60	31	attention	attention	NOUN
cord-326631-7gd3hjc3	60	32	to	to	ADP
cord-326631-7gd3hjc3	60	33	multiple	multiple	ADJ
cord-326631-7gd3hjc3	60	34	infectious	infectious	ADJ
cord-326631-7gd3hjc3	60	35	stage	stage	NOUN
cord-326631-7gd3hjc3	60	36	models	model	NOUN
cord-326631-7gd3hjc3	60	37	,	,	PUNCT
cord-326631-7gd3hjc3	60	38	which	which	PRON
cord-326631-7gd3hjc3	60	39	we	we	PRON
cord-326631-7gd3hjc3	60	40	refer	refer	VERB
cord-326631-7gd3hjc3	60	41	to	to	ADP
cord-326631-7gd3hjc3	60	42	as	as	ADP
cord-326631-7gd3hjc3	60	43	si	si	PROPN
cord-326631-7gd3hjc3	60	44	n	n	NOUN
cord-326631-7gd3hjc3	60	45	r	r	NOUN
cord-326631-7gd3hjc3	60	46	models	model	NOUN
cord-326631-7gd3hjc3	60	47	if	if	SCONJ
cord-326631-7gd3hjc3	60	48	there	there	PRON
cord-326631-7gd3hjc3	60	49	are	be	VERB
cord-326631-7gd3hjc3	60	50	n	n	ADV
cord-326631-7gd3hjc3	60	51	infectious	infectious	ADJ
cord-326631-7gd3hjc3	60	52	stages	stage	NOUN
cord-326631-7gd3hjc3	60	53	.	.	PUNCT
cord-326631-7gd3hjc3	61	1	generalizing	generalize	VERB
cord-326631-7gd3hjc3	61	2	the	the	DET
cord-326631-7gd3hjc3	61	3	sir	sir	PROPN
cord-326631-7gd3hjc3	61	4	model	model	NOUN
cord-326631-7gd3hjc3	61	5	(	(	PUNCT
cord-326631-7gd3hjc3	61	6	1	1	NUM
cord-326631-7gd3hjc3	61	7	)	)	PUNCT
cord-326631-7gd3hjc3	61	8	to	to	PART
cord-326631-7gd3hjc3	61	9	include	include	VERB
cord-326631-7gd3hjc3	61	10	multiple	multiple	ADJ
cord-326631-7gd3hjc3	61	11	infectious	infectious	ADJ
cord-326631-7gd3hjc3	61	12	stages	stage	NOUN
cord-326631-7gd3hjc3	61	13	,	,	PUNCT
cord-326631-7gd3hjc3	61	14	the	the	DET
cord-326631-7gd3hjc3	61	15	equations	equation	NOUN
cord-326631-7gd3hjc3	61	16	for	for	ADP
cord-326631-7gd3hjc3	61	17	an	an	DET
cord-326631-7gd3hjc3	61	18	si	si	PROPN
cord-326631-7gd3hjc3	61	19	n	n	NOUN
cord-326631-7gd3hjc3	61	20	r	r	NOUN
cord-326631-7gd3hjc3	61	21	arė	arė	PROPN
cord-326631-7gd3hjc3	61	22	where	where	SCONJ
cord-326631-7gd3hjc3	61	23	i	i	PRON
cord-326631-7gd3hjc3	61	24	i	i	PRON
cord-326631-7gd3hjc3	61	25	is	be	AUX
cord-326631-7gd3hjc3	61	26	the	the	DET
cord-326631-7gd3hjc3	61	27	density	density	NOUN
cord-326631-7gd3hjc3	61	28	of	of	ADP
cord-326631-7gd3hjc3	61	29	individuals	individual	NOUN
cord-326631-7gd3hjc3	61	30	in	in	ADP
cord-326631-7gd3hjc3	61	31	the	the	DET
cord-326631-7gd3hjc3	61	32	ith	ith	PROPN
cord-326631-7gd3hjc3	61	33	infectious	infectious	ADJ
cord-326631-7gd3hjc3	61	34	stage	stage	NOUN
cord-326631-7gd3hjc3	61	35	,	,	PUNCT
cord-326631-7gd3hjc3	61	36	β	β	NOUN
cord-326631-7gd3hjc3	61	37	i	i	PRON
cord-326631-7gd3hjc3	61	38	is	be	AUX
cord-326631-7gd3hjc3	61	39	the	the	DET
cord-326631-7gd3hjc3	61	40	transmission	transmission	NOUN
cord-326631-7gd3hjc3	61	41	rate	rate	NOUN
cord-326631-7gd3hjc3	61	42	for	for	ADP
cord-326631-7gd3hjc3	61	43	contact	contact	NOUN
cord-326631-7gd3hjc3	61	44	with	with	ADP
cord-326631-7gd3hjc3	61	45	individuals	individual	NOUN
cord-326631-7gd3hjc3	61	46	in	in	ADP
cord-326631-7gd3hjc3	61	47	this	this	DET
cord-326631-7gd3hjc3	61	48	stage	stage	NOUN
cord-326631-7gd3hjc3	61	49	,	,	PUNCT
cord-326631-7gd3hjc3	61	50	and	and	CCONJ
cord-326631-7gd3hjc3	61	51	1	1	NUM
cord-326631-7gd3hjc3	61	52	γi	γi	NOUN
cord-326631-7gd3hjc3	61	53	is	be	AUX
cord-326631-7gd3hjc3	61	54	the	the	DET
cord-326631-7gd3hjc3	61	55	mean	mean	ADJ
cord-326631-7gd3hjc3	61	56	duration	duration	NOUN
cord-326631-7gd3hjc3	61	57	of	of	ADP
cord-326631-7gd3hjc3	61	58	this	this	DET
cord-326631-7gd3hjc3	61	59	stage	stage	NOUN
cord-326631-7gd3hjc3	61	60	.	.	PUNCT
cord-326631-7gd3hjc3	62	1	the	the	DET
cord-326631-7gd3hjc3	62	2	sum	sum	NOUN
cord-326631-7gd3hjc3	62	3	of	of	ADP
cord-326631-7gd3hjc3	62	4	eqs	eqs	PROPN
cord-326631-7gd3hjc3	62	5	.	.	PUNCT
cord-326631-7gd3hjc3	63	1	(	(	PUNCT
cord-326631-7gd3hjc3	63	2	6	6	NUM
cord-326631-7gd3hjc3	63	3	)	)	PUNCT
cord-326631-7gd3hjc3	63	4	is	be	AUX
cord-326631-7gd3hjc3	63	5	zero	zero	NUM
cord-326631-7gd3hjc3	63	6	,	,	PUNCT
cord-326631-7gd3hjc3	63	7	implying	imply	VERB
cord-326631-7gd3hjc3	63	8	that	that	SCONJ
cord-326631-7gd3hjc3	63	9	s	s	NOUN
cord-326631-7gd3hjc3	63	10	+	+	NOUN
cord-326631-7gd3hjc3	63	11	n	n	NOUN
cord-326631-7gd3hjc3	63	12	i=1	i=1	NOUN
cord-326631-7gd3hjc3	64	1	i	i	PRON
cord-326631-7gd3hjc3	65	1	i	i	PRON
cord-326631-7gd3hjc3	65	2	+	+	CCONJ
cord-326631-7gd3hjc3	65	3	r	r	NOUN
cord-326631-7gd3hjc3	65	4	is	be	AUX
cord-326631-7gd3hjc3	65	5	invariant	invariant	ADJ
cord-326631-7gd3hjc3	65	6	(	(	PUNCT
cord-326631-7gd3hjc3	65	7	and	and	CCONJ
cord-326631-7gd3hjc3	65	8	hence	hence	ADV
cord-326631-7gd3hjc3	65	9	that	that	PRON
cord-326631-7gd3hjc3	66	1	eq	eq	NOUN
cord-326631-7gd3hjc3	66	2	.	.	PUNCT
cord-326631-7gd3hjc3	66	3	(	(	PUNCT
cord-326631-7gd3hjc3	66	4	6d	6d	NUM
cord-326631-7gd3hjc3	66	5	)	)	PUNCT
cord-326631-7gd3hjc3	66	6	is	be	AUX
cord-326631-7gd3hjc3	66	7	superfluous	superfluous	ADJ
cord-326631-7gd3hjc3	66	8	,	,	PUNCT
cord-326631-7gd3hjc3	66	9	as	as	ADP
cord-326631-7gd3hjc3	66	10	in	in	ADP
cord-326631-7gd3hjc3	66	11	the	the	DET
cord-326631-7gd3hjc3	66	12	basic	basic	ADJ
cord-326631-7gd3hjc3	66	13	sir	sir	PROPN
cord-326631-7gd3hjc3	66	14	model	model	NOUN
cord-326631-7gd3hjc3	66	15	)	)	PUNCT
cord-326631-7gd3hjc3	66	16	.	.	PUNCT
cord-326631-7gd3hjc3	67	1	to	to	PART
cord-326631-7gd3hjc3	67	2	see	see	VERB
cord-326631-7gd3hjc3	67	3	that	that	SCONJ
cord-326631-7gd3hjc3	67	4	the	the	DET
cord-326631-7gd3hjc3	67	5	final	final	ADJ
cord-326631-7gd3hjc3	67	6	size	size	NOUN
cord-326631-7gd3hjc3	67	7	is	be	AUX
cord-326631-7gd3hjc3	67	8	well	well	ADV
cord-326631-7gd3hjc3	67	9	-	-	PUNCT
cord-326631-7gd3hjc3	67	10	defined	define	VERB
cord-326631-7gd3hjc3	67	11	in	in	ADP
cord-326631-7gd3hjc3	67	12	this	this	DET
cord-326631-7gd3hjc3	67	13	model	model	NOUN
cord-326631-7gd3hjc3	67	14	,	,	PUNCT
cord-326631-7gd3hjc3	67	15	we	we	PRON
cord-326631-7gd3hjc3	67	16	generalize	generalize	VERB
cord-326631-7gd3hjc3	67	17	the	the	DET
cord-326631-7gd3hjc3	67	18	argument	argument	NOUN
cord-326631-7gd3hjc3	67	19	given	give	VERB
cord-326631-7gd3hjc3	67	20	for	for	ADP
cord-326631-7gd3hjc3	67	21	the	the	DET
cord-326631-7gd3hjc3	67	22	simple	simple	ADJ
cord-326631-7gd3hjc3	67	23	sir	sir	NOUN
cord-326631-7gd3hjc3	67	24	model	model	NOUN
cord-326631-7gd3hjc3	67	25	in	in	ADP
cord-326631-7gd3hjc3	67	26	section	section	NOUN
cord-326631-7gd3hjc3	67	27	2	2	NUM
cord-326631-7gd3hjc3	67	28	.	.	PUNCT
cord-326631-7gd3hjc3	68	1	let	let	VERB
cord-326631-7gd3hjc3	68	2	j	j	PROPN
cord-326631-7gd3hjc3	68	3	k	k	PROPN
cord-326631-7gd3hjc3	68	4	=	=	SYM
cord-326631-7gd3hjc3	68	5	s	s	PROPN
cord-326631-7gd3hjc3	69	1	+	+	X
cord-326631-7gd3hjc3	70	1	k	k	NOUN
cord-326631-7gd3hjc3	70	2	i=1	i=1	PUNCT
cord-326631-7gd3hjc3	71	1	i	i	PRON
cord-326631-7gd3hjc3	71	2	i	i	PRON
cord-326631-7gd3hjc3	71	3	.	.	PUNCT
cord-326631-7gd3hjc3	72	1	then	then	ADV
cord-326631-7gd3hjc3	72	2	d	d	PROPN
cord-326631-7gd3hjc3	72	3	dt	dt	PROPN
cord-326631-7gd3hjc3	72	4	j	j	PROPN
cord-326631-7gd3hjc3	72	5	k	k	PROPN
cord-326631-7gd3hjc3	72	6	=	=	SYM
cord-326631-7gd3hjc3	72	7	−γ	−γ	PROPN
cord-326631-7gd3hjc3	72	8	k	k	PROPN
cord-326631-7gd3hjc3	73	1	i	i	INTJ
cord-326631-7gd3hjc3	74	1	k	k	X
cord-326631-7gd3hjc3	74	2	,	,	PUNCT
cord-326631-7gd3hjc3	75	1	so	so	ADV
cord-326631-7gd3hjc3	75	2	i	i	PRON
cord-326631-7gd3hjc3	75	3	k	k	X
cord-326631-7gd3hjc3	75	4	>	>	X
cord-326631-7gd3hjc3	75	5	0	0	PUNCT
cord-326631-7gd3hjc3	75	6	implies	imply	VERB
cord-326631-7gd3hjc3	75	7	j	j	PROPN
cord-326631-7gd3hjc3	75	8	k	k	PROPN
cord-326631-7gd3hjc3	75	9	is	be	AUX
cord-326631-7gd3hjc3	75	10	decreasing	decrease	VERB
cord-326631-7gd3hjc3	75	11	and	and	CCONJ
cord-326631-7gd3hjc3	75	12	lim	lim	PROPN
cord-326631-7gd3hjc3	75	13	t→∞	t→∞	PRON
cord-326631-7gd3hjc3	75	14	d	d	PROPN
cord-326631-7gd3hjc3	75	15	dt	dt	PROPN
cord-326631-7gd3hjc3	75	16	j	j	PROPN
cord-326631-7gd3hjc3	75	17	k	k	PROPN
cord-326631-7gd3hjc3	75	18	=	=	SYM
cord-326631-7gd3hjc3	75	19	0	0	NUM
cord-326631-7gd3hjc3	75	20	.	.	PUNCT
cord-326631-7gd3hjc3	76	1	hence	hence	ADV
cord-326631-7gd3hjc3	76	2	i	i	PRON
cord-326631-7gd3hjc3	76	3	k	k	PROPN
cord-326631-7gd3hjc3	76	4	(	(	PUNCT
cord-326631-7gd3hjc3	76	5	∞	∞	NUM
cord-326631-7gd3hjc3	76	6	)	)	PUNCT
cord-326631-7gd3hjc3	76	7	=	=	NOUN
cord-326631-7gd3hjc3	76	8	0	0	NUM
cord-326631-7gd3hjc3	76	9	for	for	ADP
cord-326631-7gd3hjc3	76	10	all	all	DET
cord-326631-7gd3hjc3	76	11	k.	k.	NOUN
cord-326631-7gd3hjc3	76	12	before	before	SCONJ
cord-326631-7gd3hjc3	76	13	a	a	DET
cord-326631-7gd3hjc3	76	14	new	new	ADJ
cord-326631-7gd3hjc3	76	15	disease	disease	NOUN
cord-326631-7gd3hjc3	76	16	is	be	AUX
cord-326631-7gd3hjc3	76	17	introduced	introduce	VERB
cord-326631-7gd3hjc3	76	18	into	into	ADP
cord-326631-7gd3hjc3	76	19	a	a	DET
cord-326631-7gd3hjc3	76	20	population	population	NOUN
cord-326631-7gd3hjc3	76	21	,	,	PUNCT
cord-326631-7gd3hjc3	76	22	everyone	everyone	PRON
cord-326631-7gd3hjc3	76	23	is	be	AUX
cord-326631-7gd3hjc3	76	24	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	76	25	,	,	PUNCT
cord-326631-7gd3hjc3	76	26	i.e.	i.e.	X
cord-326631-7gd3hjc3	76	27	,	,	PUNCT
cord-326631-7gd3hjc3	76	28	s	s	PROPN
cord-326631-7gd3hjc3	76	29	=	=	NOUN
cord-326631-7gd3hjc3	76	30	1	1	NUM
cord-326631-7gd3hjc3	76	31	,	,	PUNCT
cord-326631-7gd3hjc3	76	32	i	i	PRON
cord-326631-7gd3hjc3	76	33	1	1	NUM
cord-326631-7gd3hjc3	76	34	=	=	X
cord-326631-7gd3hjc3	76	35	·	·	PUNCT
cord-326631-7gd3hjc3	76	36	·	·	PUNCT
cord-326631-7gd3hjc3	76	37	·	·	PUNCT
cord-326631-7gd3hjc3	76	38	=	=	NOUN
cord-326631-7gd3hjc3	76	39	i	i	PROPN
cord-326631-7gd3hjc3	76	40	n	n	NOUN
cord-326631-7gd3hjc3	76	41	=	=	NOUN
cord-326631-7gd3hjc3	76	42	0	0	NUM
cord-326631-7gd3hjc3	76	43	and	and	CCONJ
cord-326631-7gd3hjc3	76	44	r	r	NOUN
cord-326631-7gd3hjc3	76	45	=	=	NOUN
cord-326631-7gd3hjc3	76	46	0	0	NUM
cord-326631-7gd3hjc3	76	47	,	,	PUNCT
cord-326631-7gd3hjc3	76	48	which	which	PRON
cord-326631-7gd3hjc3	76	49	is	be	AUX
cord-326631-7gd3hjc3	76	50	known	know	VERB
cord-326631-7gd3hjc3	76	51	as	as	ADP
cord-326631-7gd3hjc3	76	52	the	the	DET
cord-326631-7gd3hjc3	76	53	disease	disease	NOUN
cord-326631-7gd3hjc3	76	54	free	free	ADJ
cord-326631-7gd3hjc3	76	55	equilibrium	equilibrium	NOUN
cord-326631-7gd3hjc3	76	56	(	(	PUNCT
cord-326631-7gd3hjc3	76	57	dfe	dfe	PROPN
cord-326631-7gd3hjc3	76	58	)	)	PUNCT
cord-326631-7gd3hjc3	76	59	.	.	PUNCT
cord-326631-7gd3hjc3	77	1	the	the	DET
cord-326631-7gd3hjc3	77	2	stability	stability	NOUN
cord-326631-7gd3hjc3	77	3	of	of	ADP
cord-326631-7gd3hjc3	77	4	the	the	DET
cord-326631-7gd3hjc3	77	5	dfe	dfe	PROPN
cord-326631-7gd3hjc3	77	6	determines	determine	VERB
cord-326631-7gd3hjc3	77	7	whether	whether	SCONJ
cord-326631-7gd3hjc3	77	8	the	the	DET
cord-326631-7gd3hjc3	77	9	new	new	ADJ
cord-326631-7gd3hjc3	77	10	disease	disease	NOUN
cord-326631-7gd3hjc3	77	11	can	can	AUX
cord-326631-7gd3hjc3	77	12	cause	cause	VERB
cord-326631-7gd3hjc3	77	13	an	an	DET
cord-326631-7gd3hjc3	77	14	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	77	15	.	.	PUNCT
cord-326631-7gd3hjc3	78	1	hyman	hyman	PROPN
cord-326631-7gd3hjc3	78	2	et	et	PROPN
cord-326631-7gd3hjc3	78	3	al	al	PROPN
cord-326631-7gd3hjc3	78	4	.	.	PUNCT
cord-326631-7gd3hjc3	78	5	(	(	PUNCT
cord-326631-7gd3hjc3	78	6	1999	1999	NUM
cord-326631-7gd3hjc3	78	7	)	)	PUNCT
cord-326631-7gd3hjc3	78	8	proved	prove	VERB
cord-326631-7gd3hjc3	78	9	that	that	SCONJ
cord-326631-7gd3hjc3	78	10	the	the	DET
cord-326631-7gd3hjc3	78	11	quantity	quantity	NOUN
cord-326631-7gd3hjc3	78	12	determines	determine	VERB
cord-326631-7gd3hjc3	78	13	the	the	DET
cord-326631-7gd3hjc3	78	14	stability	stability	NOUN
cord-326631-7gd3hjc3	78	15	of	of	ADP
cord-326631-7gd3hjc3	78	16	the	the	DET
cord-326631-7gd3hjc3	78	17	dfe	dfe	PROPN
cord-326631-7gd3hjc3	78	18	,	,	PUNCT
cord-326631-7gd3hjc3	78	19	i.e.	i.e.	X
cord-326631-7gd3hjc3	78	20	,	,	PUNCT
cord-326631-7gd3hjc3	78	21	the	the	DET
cord-326631-7gd3hjc3	78	22	dfe	dfe	PROPN
cord-326631-7gd3hjc3	78	23	is	be	AUX
cord-326631-7gd3hjc3	78	24	locally	locally	ADV
cord-326631-7gd3hjc3	78	25	stable	stable	ADJ
cord-326631-7gd3hjc3	78	26	if	if	SCONJ
cord-326631-7gd3hjc3	78	27	r	r	NOUN
cord-326631-7gd3hjc3	78	28	0	0	NUM
cord-326631-7gd3hjc3	78	29	<	<	X
cord-326631-7gd3hjc3	78	30	1	1	NUM
cord-326631-7gd3hjc3	78	31	and	and	CCONJ
cord-326631-7gd3hjc3	78	32	unstable	unstable	ADJ
cord-326631-7gd3hjc3	78	33	if	if	SCONJ
cord-326631-7gd3hjc3	78	34	r	r	NOUN
cord-326631-7gd3hjc3	78	35	0	0	PUNCT
cord-326631-7gd3hjc3	78	36	>	>	SYM
cord-326631-7gd3hjc3	78	37	1	1	NUM
cord-326631-7gd3hjc3	78	38	.	.	PUNCT
cord-326631-7gd3hjc3	78	39	note	note	VERB
cord-326631-7gd3hjc3	78	40	r	r	NOUN
cord-326631-7gd3hjc3	78	41	0	0	PUNCT
cord-326631-7gd3hjc3	78	42	as	as	SCONJ
cord-326631-7gd3hjc3	78	43	defined	define	VERB
cord-326631-7gd3hjc3	78	44	by	by	ADP
cord-326631-7gd3hjc3	78	45	(	(	PUNCT
cord-326631-7gd3hjc3	78	46	7	7	NUM
cord-326631-7gd3hjc3	78	47	)	)	PUNCT
cord-326631-7gd3hjc3	78	48	is	be	AUX
cord-326631-7gd3hjc3	78	49	the	the	DET
cord-326631-7gd3hjc3	78	50	sum	sum	NOUN
cord-326631-7gd3hjc3	78	51	of	of	ADP
cord-326631-7gd3hjc3	78	52	the	the	DET
cord-326631-7gd3hjc3	78	53	products	product	NOUN
cord-326631-7gd3hjc3	78	54	of	of	ADP
cord-326631-7gd3hjc3	78	55	the	the	DET
cord-326631-7gd3hjc3	78	56	transmission	transmission	NOUN
cord-326631-7gd3hjc3	78	57	rate	rate	NOUN
cord-326631-7gd3hjc3	78	58	and	and	CCONJ
cord-326631-7gd3hjc3	78	59	mean	mean	ADJ
cord-326631-7gd3hjc3	78	60	duration	duration	NOUN
cord-326631-7gd3hjc3	78	61	in	in	ADP
cord-326631-7gd3hjc3	78	62	each	each	DET
cord-326631-7gd3hjc3	78	63	infectious	infectious	ADJ
cord-326631-7gd3hjc3	78	64	stage	stage	NOUN
cord-326631-7gd3hjc3	78	65	,	,	PUNCT
cord-326631-7gd3hjc3	78	66	i.e.	i.e.	X
cord-326631-7gd3hjc3	78	67	,	,	PUNCT
cord-326631-7gd3hjc3	78	68	it	it	PRON
cord-326631-7gd3hjc3	78	69	is	be	AUX
cord-326631-7gd3hjc3	78	70	the	the	DET
cord-326631-7gd3hjc3	78	71	basic	basic	ADJ
cord-326631-7gd3hjc3	78	72	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	78	73	number	number	NOUN
cord-326631-7gd3hjc3	78	74	for	for	ADP
cord-326631-7gd3hjc3	78	75	this	this	DET
cord-326631-7gd3hjc3	78	76	model	model	NOUN
cord-326631-7gd3hjc3	78	77	.	.	PUNCT
cord-326631-7gd3hjc3	79	1	we	we	PRON
cord-326631-7gd3hjc3	79	2	now	now	ADV
cord-326631-7gd3hjc3	79	3	proceed	proceed	VERB
cord-326631-7gd3hjc3	79	4	to	to	PART
cord-326631-7gd3hjc3	79	5	show	show	VERB
cord-326631-7gd3hjc3	79	6	that	that	SCONJ
cord-326631-7gd3hjc3	79	7	eqs	eqs	PROPN
cord-326631-7gd3hjc3	79	8	.	.	PUNCT
cord-326631-7gd3hjc3	80	1	(	(	PUNCT
cord-326631-7gd3hjc3	80	2	6	6	X
cord-326631-7gd3hjc3	80	3	)	)	PUNCT
cord-326631-7gd3hjc3	80	4	yield	yield	VERB
cord-326631-7gd3hjc3	80	5	the	the	DET
cord-326631-7gd3hjc3	80	6	same	same	ADJ
cord-326631-7gd3hjc3	80	7	final	final	ADJ
cord-326631-7gd3hjc3	80	8	size	size	NOUN
cord-326631-7gd3hjc3	80	9	formula	formula	NOUN
cord-326631-7gd3hjc3	80	10	as	as	ADP
cord-326631-7gd3hjc3	80	11	(	(	PUNCT
cord-326631-7gd3hjc3	80	12	5	5	NUM
cord-326631-7gd3hjc3	80	13	)	)	PUNCT
cord-326631-7gd3hjc3	80	14	.	.	PUNCT
cord-326631-7gd3hjc3	81	1	anderson	anderson	PROPN
cord-326631-7gd3hjc3	81	2	and	and	CCONJ
cord-326631-7gd3hjc3	81	3	watsons	watson	NOUN
cord-326631-7gd3hjc3	81	4	(	(	PUNCT
cord-326631-7gd3hjc3	81	5	1980	1980	NUM
cord-326631-7gd3hjc3	81	6	)	)	PUNCT
cord-326631-7gd3hjc3	81	7	established	establish	VERB
cord-326631-7gd3hjc3	81	8	this	this	PRON
cord-326631-7gd3hjc3	81	9	for	for	ADP
cord-326631-7gd3hjc3	81	10	the	the	DET
cord-326631-7gd3hjc3	81	11	special	special	ADJ
cord-326631-7gd3hjc3	81	12	case	case	NOUN
cord-326631-7gd3hjc3	81	13	in	in	ADP
cord-326631-7gd3hjc3	81	14	which	which	PRON
cord-326631-7gd3hjc3	81	15	each	each	DET
cord-326631-7gd3hjc3	81	16	stage	stage	NOUN
cord-326631-7gd3hjc3	81	17	has	have	VERB
cord-326631-7gd3hjc3	81	18	the	the	DET
cord-326631-7gd3hjc3	81	19	same	same	ADJ
cord-326631-7gd3hjc3	81	20	transmission	transmission	NOUN
cord-326631-7gd3hjc3	81	21	rate	rate	NOUN
cord-326631-7gd3hjc3	81	22	and	and	CCONJ
cord-326631-7gd3hjc3	81	23	duration	duration	NOUN
cord-326631-7gd3hjc3	81	24	(	(	PUNCT
cord-326631-7gd3hjc3	81	25	β	β	PROPN
cord-326631-7gd3hjc3	81	26	i	i	NOUN
cord-326631-7gd3hjc3	81	27	=	=	NOUN
cord-326631-7gd3hjc3	81	28	β	β	NOUN
cord-326631-7gd3hjc3	81	29	and	and	CCONJ
cord-326631-7gd3hjc3	81	30	γ	γ	NOUN
cord-326631-7gd3hjc3	81	31	i	i	NOUN
cord-326631-7gd3hjc3	81	32	=	=	VERB
cord-326631-7gd3hjc3	81	33	γ	γ	NOUN
cord-326631-7gd3hjc3	81	34	for	for	ADP
cord-326631-7gd3hjc3	81	35	all	all	PRON
cord-326631-7gd3hjc3	81	36	i	i	NOUN
cord-326631-7gd3hjc3	81	37	)	)	PUNCT
cord-326631-7gd3hjc3	81	38	.	.	PUNCT
cord-326631-7gd3hjc3	82	1	their	their	PRON
cord-326631-7gd3hjc3	82	2	method	method	NOUN
cord-326631-7gd3hjc3	82	3	can	can	AUX
cord-326631-7gd3hjc3	82	4	easily	easily	ADV
cord-326631-7gd3hjc3	82	5	be	be	AUX
cord-326631-7gd3hjc3	82	6	generalized	generalize	VERB
cord-326631-7gd3hjc3	82	7	to	to	ADP
cord-326631-7gd3hjc3	82	8	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	82	9	β	β	PROPN
cord-326631-7gd3hjc3	83	1	i	i	PRON
cord-326631-7gd3hjc3	83	2	and	and	CCONJ
cord-326631-7gd3hjc3	83	3	γ	γ	NOUN
cord-326631-7gd3hjc3	83	4	i	i	PRON
cord-326631-7gd3hjc3	83	5	as	as	SCONJ
cord-326631-7gd3hjc3	83	6	follows	follow	VERB
cord-326631-7gd3hjc3	83	7	:	:	PUNCT
cord-326631-7gd3hjc3	83	8	let	let	VERB
cord-326631-7gd3hjc3	84	1	g	g	PROPN
cord-326631-7gd3hjc3	84	2	k	k	PROPN
cord-326631-7gd3hjc3	84	3	=	=	PROPN
cord-326631-7gd3hjc3	84	4	n	n	NOUN
cord-326631-7gd3hjc3	84	5	i	i	PROPN
cord-326631-7gd3hjc3	84	6	=	=	NOUN
cord-326631-7gd3hjc3	84	7	k+1	k+1	X
cord-326631-7gd3hjc3	84	8	i	i	PRON
cord-326631-7gd3hjc3	84	9	i	i	PRON
cord-326631-7gd3hjc3	84	10	+	+	NOUN
cord-326631-7gd3hjc3	84	11	r	r	X
cord-326631-7gd3hjc3	84	12	,	,	PUNCT
cord-326631-7gd3hjc3	84	13	k	k	PROPN
cord-326631-7gd3hjc3	84	14	=	=	SYM
cord-326631-7gd3hjc3	84	15	1	1	NUM
cord-326631-7gd3hjc3	84	16	,	,	PUNCT
cord-326631-7gd3hjc3	84	17	.	.	PUNCT
cord-326631-7gd3hjc3	84	18	.	.	PUNCT
cord-326631-7gd3hjc3	84	19	.	.	PUNCT
cord-326631-7gd3hjc3	85	1	,	,	PUNCT
cord-326631-7gd3hjc3	85	2	n	n	ADV
cord-326631-7gd3hjc3	85	3	−	−	PROPN
cord-326631-7gd3hjc3	85	4	1	1	NUM
cord-326631-7gd3hjc3	85	5	and	and	CCONJ
cord-326631-7gd3hjc3	85	6	g	g	PROPN
cord-326631-7gd3hjc3	85	7	n	n	PROPN
cord-326631-7gd3hjc3	85	8	=	=	PROPN
cord-326631-7gd3hjc3	85	9	r.	r.	PROPN
cord-326631-7gd3hjc3	85	10	then	then	ADV
cord-326631-7gd3hjc3	85	11	eqs	eqs	PROPN
cord-326631-7gd3hjc3	85	12	.	.	PUNCT
cord-326631-7gd3hjc3	86	1	(	(	PUNCT
cord-326631-7gd3hjc3	86	2	6c	6c	NUM
cord-326631-7gd3hjc3	86	3	)	)	PUNCT
cord-326631-7gd3hjc3	86	4	and	and	CCONJ
cord-326631-7gd3hjc3	86	5	(	(	PUNCT
cord-326631-7gd3hjc3	86	6	6d	6d	NUM
cord-326631-7gd3hjc3	86	7	)	)	PUNCT
cord-326631-7gd3hjc3	86	8	imply	imply	VERB
cord-326631-7gd3hjc3	86	9	d	d	PROPN
cord-326631-7gd3hjc3	86	10	dt	dt	PROPN
cord-326631-7gd3hjc3	87	1	g	g	PROPN
cord-326631-7gd3hjc3	87	2	k	k	PROPN
cord-326631-7gd3hjc3	87	3	=	=	SYM
cord-326631-7gd3hjc3	87	4	γ	γ	X
cord-326631-7gd3hjc3	88	1	k	k	NOUN
cord-326631-7gd3hjc3	88	2	i	i	INTJ
cord-326631-7gd3hjc3	88	3	k	k	NOUN
cord-326631-7gd3hjc3	88	4	for	for	ADP
cord-326631-7gd3hjc3	88	5	each	each	DET
cord-326631-7gd3hjc3	88	6	k	k	PROPN
cord-326631-7gd3hjc3	88	7	=	=	SYM
cord-326631-7gd3hjc3	88	8	1	1	NUM
cord-326631-7gd3hjc3	88	9	,	,	PUNCT
cord-326631-7gd3hjc3	88	10	.	.	PUNCT
cord-326631-7gd3hjc3	88	11	.	.	PUNCT
cord-326631-7gd3hjc3	88	12	.	.	PUNCT
cord-326631-7gd3hjc3	89	1	,	,	PUNCT
cord-326631-7gd3hjc3	89	2	n.	n.	PROPN
cord-326631-7gd3hjc3	89	3	consequently	consequently	ADV
cord-326631-7gd3hjc3	89	4	,	,	PUNCT
cord-326631-7gd3hjc3	89	5	eq	eq	PROPN
cord-326631-7gd3hjc3	89	6	.	.	PUNCT
cord-326631-7gd3hjc3	89	7	(	(	PUNCT
cord-326631-7gd3hjc3	89	8	6a	6a	NOUN
cord-326631-7gd3hjc3	89	9	)	)	PUNCT
cord-326631-7gd3hjc3	89	10	implies	imply	VERB
cord-326631-7gd3hjc3	89	11	that	that	SCONJ
cord-326631-7gd3hjc3	89	12	the	the	DET
cord-326631-7gd3hjc3	89	13	function	function	NOUN
cord-326631-7gd3hjc3	89	14	is	be	AUX
cord-326631-7gd3hjc3	89	15	a	a	DET
cord-326631-7gd3hjc3	89	16	constant	constant	NOUN
cord-326631-7gd3hjc3	89	17	of	of	ADP
cord-326631-7gd3hjc3	89	18	the	the	DET
cord-326631-7gd3hjc3	89	19	motion	motion	NOUN
cord-326631-7gd3hjc3	89	20	.	.	PUNCT
cord-326631-7gd3hjc3	90	1	for	for	ADP
cord-326631-7gd3hjc3	90	2	a	a	DET
cord-326631-7gd3hjc3	90	3	newly	newly	ADV
cord-326631-7gd3hjc3	90	4	invading	invading	NOUN
cord-326631-7gd3hjc3	90	5	disease	disease	NOUN
cord-326631-7gd3hjc3	90	6	,	,	PUNCT
cord-326631-7gd3hjc3	90	7	s(0	s(0	PROPN
cord-326631-7gd3hjc3	90	8	)	)	PUNCT
cord-326631-7gd3hjc3	90	9	→	→	NUM
cord-326631-7gd3hjc3	90	10	1	1	X
cord-326631-7gd3hjc3	90	11	,	,	PUNCT
cord-326631-7gd3hjc3	90	12	i	i	PRON
cord-326631-7gd3hjc3	90	13	k	k	NOUN
cord-326631-7gd3hjc3	90	14	(	(	PUNCT
cord-326631-7gd3hjc3	90	15	0	0	NUM
cord-326631-7gd3hjc3	90	16	)	)	PUNCT
cord-326631-7gd3hjc3	90	17	→	→	NUM
cord-326631-7gd3hjc3	90	18	0	0	PUNCT
cord-326631-7gd3hjc3	90	19	and	and	CCONJ
cord-326631-7gd3hjc3	90	20	recalling	recall	VERB
cord-326631-7gd3hjc3	90	21	that	that	PRON
cord-326631-7gd3hjc3	90	22	z	z	PROPN
cord-326631-7gd3hjc3	90	23	=	=	SYM
cord-326631-7gd3hjc3	90	24	r(∞	r(∞	NOUN
cord-326631-7gd3hjc3	90	25	)	)	PUNCT
cord-326631-7gd3hjc3	90	26	=	=	SYM
cord-326631-7gd3hjc3	90	27	1	1	NUM
cord-326631-7gd3hjc3	90	28	−	−	PROPN
cord-326631-7gd3hjc3	90	29	s(∞	s(∞	PROPN
cord-326631-7gd3hjc3	90	30	)	)	PUNCT
cord-326631-7gd3hjc3	90	31	,	,	PUNCT
cord-326631-7gd3hjc3	90	32	and	and	CCONJ
cord-326631-7gd3hjc3	90	33	eq	eq	PROPN
cord-326631-7gd3hjc3	90	34	.	.	PUNCT
cord-326631-7gd3hjc3	90	35	(	(	PUNCT
cord-326631-7gd3hjc3	90	36	7	7	NUM
cord-326631-7gd3hjc3	90	37	)	)	PUNCT
cord-326631-7gd3hjc3	90	38	,	,	PUNCT
cord-326631-7gd3hjc3	90	39	the	the	DET
cord-326631-7gd3hjc3	90	40	final	final	ADJ
cord-326631-7gd3hjc3	90	41	size	size	NOUN
cord-326631-7gd3hjc3	90	42	formula	formula	NOUN
cord-326631-7gd3hjc3	90	43	eq	eq	NOUN
cord-326631-7gd3hjc3	90	44	.	.	PUNCT
cord-326631-7gd3hjc3	90	45	(	(	PUNCT
cord-326631-7gd3hjc3	90	46	5	5	X
cord-326631-7gd3hjc3	90	47	)	)	PUNCT
cord-326631-7gd3hjc3	90	48	immediately	immediately	ADV
cord-326631-7gd3hjc3	90	49	follows	follow	VERB
cord-326631-7gd3hjc3	90	50	.	.	PUNCT
cord-326631-7gd3hjc3	91	1	consideration	consideration	NOUN
cord-326631-7gd3hjc3	91	2	of	of	ADP
cord-326631-7gd3hjc3	91	3	a	a	DET
cord-326631-7gd3hjc3	91	4	special	special	ADJ
cord-326631-7gd3hjc3	91	5	case	case	NOUN
cord-326631-7gd3hjc3	91	6	of	of	ADP
cord-326631-7gd3hjc3	91	7	the	the	DET
cord-326631-7gd3hjc3	91	8	model	model	NOUN
cord-326631-7gd3hjc3	91	9	in	in	ADP
cord-326631-7gd3hjc3	91	10	the	the	DET
cord-326631-7gd3hjc3	91	11	previous	previous	ADJ
cord-326631-7gd3hjc3	91	12	section	section	NOUN
cord-326631-7gd3hjc3	91	13	allows	allow	VERB
cord-326631-7gd3hjc3	91	14	us	we	PRON
cord-326631-7gd3hjc3	91	15	to	to	PART
cord-326631-7gd3hjc3	91	16	infer	infer	VERB
cord-326631-7gd3hjc3	91	17	that	that	SCONJ
cord-326631-7gd3hjc3	91	18	the	the	DET
cord-326631-7gd3hjc3	91	19	distribution	distribution	NOUN
cord-326631-7gd3hjc3	91	20	of	of	ADP
cord-326631-7gd3hjc3	91	21	stage	stage	NOUN
cord-326631-7gd3hjc3	91	22	durations	duration	NOUN
cord-326631-7gd3hjc3	91	23	in	in	ADP
cord-326631-7gd3hjc3	91	24	any	any	DET
cord-326631-7gd3hjc3	91	25	infectious	infectious	ADJ
cord-326631-7gd3hjc3	91	26	stage	stage	NOUN
cord-326631-7gd3hjc3	91	27	need	need	AUX
cord-326631-7gd3hjc3	91	28	not	not	PART
cord-326631-7gd3hjc3	91	29	be	be	AUX
cord-326631-7gd3hjc3	91	30	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	91	31	distributed	distribute	VERB
cord-326631-7gd3hjc3	91	32	.	.	PUNCT
cord-326631-7gd3hjc3	92	1	the	the	DET
cord-326631-7gd3hjc3	92	2	final	final	ADJ
cord-326631-7gd3hjc3	92	3	size	size	NOUN
cord-326631-7gd3hjc3	92	4	formula	formula	NOUN
cord-326631-7gd3hjc3	92	5	(	(	PUNCT
cord-326631-7gd3hjc3	92	6	5	5	NUM
cord-326631-7gd3hjc3	92	7	)	)	PUNCT
cord-326631-7gd3hjc3	92	8	holds	hold	VERB
cord-326631-7gd3hjc3	92	9	true	true	ADJ
cord-326631-7gd3hjc3	92	10	if	if	SCONJ
cord-326631-7gd3hjc3	92	11	the	the	DET
cord-326631-7gd3hjc3	92	12	stage	stage	NOUN
cord-326631-7gd3hjc3	92	13	durations	duration	NOUN
cord-326631-7gd3hjc3	92	14	follow	follow	VERB
cord-326631-7gd3hjc3	92	15	a	a	DET
cord-326631-7gd3hjc3	92	16	gamma	gamma	NOUN
cord-326631-7gd3hjc3	92	17	distribution	distribution	NOUN
cord-326631-7gd3hjc3	92	18	,	,	PUNCT
cord-326631-7gd3hjc3	92	19	which	which	PRON
cord-326631-7gd3hjc3	92	20	has	have	VERB
cord-326631-7gd3hjc3	92	21	probability	probability	NOUN
cord-326631-7gd3hjc3	92	22	density	density	NOUN
cord-326631-7gd3hjc3	92	23	here	here	ADV
cord-326631-7gd3hjc3	92	24	,	,	PUNCT
cord-326631-7gd3hjc3	92	25	the	the	DET
cord-326631-7gd3hjc3	92	26	shape	shape	NOUN
cord-326631-7gd3hjc3	92	27	parameter	parameter	NOUN
cord-326631-7gd3hjc3	92	28	k	k	PROPN
cord-326631-7gd3hjc3	92	29	is	be	AUX
cord-326631-7gd3hjc3	92	30	a	a	DET
cord-326631-7gd3hjc3	92	31	positive	positive	ADJ
cord-326631-7gd3hjc3	92	32	integer	integer	NOUN
cord-326631-7gd3hjc3	92	33	and	and	CCONJ
cord-326631-7gd3hjc3	92	34	the	the	DET
cord-326631-7gd3hjc3	92	35	scale	scale	NOUN
cord-326631-7gd3hjc3	92	36	parameter	parameter	NOUN
cord-326631-7gd3hjc3	92	37	φ	φ	X
cord-326631-7gd3hjc3	92	38	>	>	PUNCT
cord-326631-7gd3hjc3	92	39	0	0	NUM
cord-326631-7gd3hjc3	92	40	.	.	PUNCT
cord-326631-7gd3hjc3	93	1	the	the	DET
cord-326631-7gd3hjc3	93	2	mean	mean	NOUN
cord-326631-7gd3hjc3	93	3	is	be	AUX
cord-326631-7gd3hjc3	93	4	k	k	PROPN
cord-326631-7gd3hjc3	93	5	/	/	SYM
cord-326631-7gd3hjc3	93	6	φ	φ	NOUN
cord-326631-7gd3hjc3	93	7	and	and	CCONJ
cord-326631-7gd3hjc3	93	8	the	the	DET
cord-326631-7gd3hjc3	93	9	variance	variance	NOUN
cord-326631-7gd3hjc3	93	10	is	be	AUX
cord-326631-7gd3hjc3	93	11	k	k	PROPN
cord-326631-7gd3hjc3	93	12	/	/	SYM
cord-326631-7gd3hjc3	93	13	φ	φ	NOUN
cord-326631-7gd3hjc3	93	14	2	2	NUM
cord-326631-7gd3hjc3	93	15	.	.	PUNCT
cord-326631-7gd3hjc3	94	1	this	this	DET
cord-326631-7gd3hjc3	94	2	family	family	NOUN
cord-326631-7gd3hjc3	94	3	of	of	ADP
cord-326631-7gd3hjc3	94	4	distributions	distribution	NOUN
cord-326631-7gd3hjc3	94	5	includes	include	VERB
cord-326631-7gd3hjc3	94	6	the	the	DET
cord-326631-7gd3hjc3	94	7	exponential	exponential	ADJ
cord-326631-7gd3hjc3	94	8	distribution	distribution	NOUN
cord-326631-7gd3hjc3	94	9	(	(	PUNCT
cord-326631-7gd3hjc3	94	10	k	k	PROPN
cord-326631-7gd3hjc3	94	11	=	=	SYM
cord-326631-7gd3hjc3	94	12	1	1	NUM
cord-326631-7gd3hjc3	94	13	)	)	PUNCT
cord-326631-7gd3hjc3	94	14	,	,	PUNCT
cord-326631-7gd3hjc3	94	15	nearly	nearly	ADV
cord-326631-7gd3hjc3	94	16	normal	normal	ADJ
cord-326631-7gd3hjc3	94	17	distributions	distribution	NOUN
cord-326631-7gd3hjc3	94	18	(	(	PUNCT
cord-326631-7gd3hjc3	94	19	k	k	PROPN
cord-326631-7gd3hjc3	94	20	large	large	ADJ
cord-326631-7gd3hjc3	94	21	)	)	PUNCT
cord-326631-7gd3hjc3	94	22	and	and	CCONJ
cord-326631-7gd3hjc3	94	23	the	the	DET
cord-326631-7gd3hjc3	94	24	delta	delta	NOUN
cord-326631-7gd3hjc3	94	25	distribution	distribution	NOUN
cord-326631-7gd3hjc3	94	26	,	,	PUNCT
cord-326631-7gd3hjc3	94	27	which	which	PRON
cord-326631-7gd3hjc3	94	28	yields	yield	VERB
cord-326631-7gd3hjc3	94	29	a	a	DET
cord-326631-7gd3hjc3	94	30	fixed	fixed	ADJ
cord-326631-7gd3hjc3	94	31	duration	duration	NOUN
cord-326631-7gd3hjc3	94	32	(	(	PUNCT
cord-326631-7gd3hjc3	94	33	k	k	NOUN
cord-326631-7gd3hjc3	94	34	→	→	SYM
cord-326631-7gd3hjc3	94	35	∞	∞	NUM
cord-326631-7gd3hjc3	94	36	)	)	PUNCT
cord-326631-7gd3hjc3	94	37	.	.	PUNCT
cord-326631-7gd3hjc3	95	1	the	the	DET
cord-326631-7gd3hjc3	95	2	term	term	NOUN
cord-326631-7gd3hjc3	95	3	−γ	−γ	VERB
cord-326631-7gd3hjc3	95	4	i	i	PRON
cord-326631-7gd3hjc3	95	5	in	in	ADP
cord-326631-7gd3hjc3	95	6	eq	eq	PROPN
cord-326631-7gd3hjc3	95	7	.	.	PUNCT
cord-326631-7gd3hjc3	96	1	(	(	PUNCT
cord-326631-7gd3hjc3	96	2	1b	1b	NUM
cord-326631-7gd3hjc3	96	3	)	)	PUNCT
cord-326631-7gd3hjc3	96	4	for	for	ADP
cord-326631-7gd3hjc3	96	5	the	the	DET
cord-326631-7gd3hjc3	96	6	simple	simple	ADJ
cord-326631-7gd3hjc3	96	7	sir	sir	PROPN
cord-326631-7gd3hjc3	96	8	model	model	NOUN
cord-326631-7gd3hjc3	96	9	implies	imply	VERB
cord-326631-7gd3hjc3	96	10	that	that	SCONJ
cord-326631-7gd3hjc3	96	11	the	the	DET
cord-326631-7gd3hjc3	96	12	durations	duration	NOUN
cord-326631-7gd3hjc3	96	13	of	of	ADP
cord-326631-7gd3hjc3	96	14	infectious	infectious	ADJ
cord-326631-7gd3hjc3	96	15	periods	period	NOUN
cord-326631-7gd3hjc3	96	16	are	be	AUX
cord-326631-7gd3hjc3	96	17	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	96	18	distributed	distribute	VERB
cord-326631-7gd3hjc3	96	19	with	with	ADP
cord-326631-7gd3hjc3	96	20	mean	mean	ADJ
cord-326631-7gd3hjc3	96	21	1	1	NUM
cord-326631-7gd3hjc3	96	22	/	/	SYM
cord-326631-7gd3hjc3	96	23	γ	γ	PROPN
cord-326631-7gd3hjc3	96	24	(	(	PUNCT
cord-326631-7gd3hjc3	96	25	brauer	brauer	PROPN
cord-326631-7gd3hjc3	96	26	and	and	CCONJ
cord-326631-7gd3hjc3	96	27	castillo	castillo	PROPN
cord-326631-7gd3hjc3	96	28	-	-	PUNCT
cord-326631-7gd3hjc3	96	29	chavez	chavez	PROPN
cord-326631-7gd3hjc3	96	30	,	,	PUNCT
cord-326631-7gd3hjc3	96	31	2001	2001	NUM
cord-326631-7gd3hjc3	96	32	)	)	PUNCT
cord-326631-7gd3hjc3	96	33	.	.	PUNCT
cord-326631-7gd3hjc3	97	1	since	since	SCONJ
cord-326631-7gd3hjc3	97	2	the	the	DET
cord-326631-7gd3hjc3	97	3	sum	sum	NOUN
cord-326631-7gd3hjc3	97	4	of	of	ADP
cord-326631-7gd3hjc3	97	5	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	97	6	distributed	distribute	VERB
cord-326631-7gd3hjc3	97	7	random	random	ADJ
cord-326631-7gd3hjc3	97	8	variables	variable	NOUN
cord-326631-7gd3hjc3	97	9	is	be	AUX
cord-326631-7gd3hjc3	97	10	gamma	gamma	PROPN
cord-326631-7gd3hjc3	97	11	distributed	distribute	VERB
cord-326631-7gd3hjc3	97	12	,	,	PUNCT
cord-326631-7gd3hjc3	97	13	a	a	DET
cord-326631-7gd3hjc3	97	14	standard	standard	ADJ
cord-326631-7gd3hjc3	97	15	trick	trick	NOUN
cord-326631-7gd3hjc3	97	16	(	(	PUNCT
cord-326631-7gd3hjc3	97	17	anderson	anderson	PROPN
cord-326631-7gd3hjc3	97	18	and	and	CCONJ
cord-326631-7gd3hjc3	97	19	watsons	watson	NOUN
cord-326631-7gd3hjc3	97	20	,	,	PUNCT
cord-326631-7gd3hjc3	97	21	1980	1980	NUM
cord-326631-7gd3hjc3	97	22	;	;	PUNCT
cord-326631-7gd3hjc3	97	23	lloyd	lloyd	PROPN
cord-326631-7gd3hjc3	97	24	,	,	PUNCT
cord-326631-7gd3hjc3	97	25	2001a	2001a	NUM
cord-326631-7gd3hjc3	97	26	,	,	PUNCT
cord-326631-7gd3hjc3	97	27	b	b	X
cord-326631-7gd3hjc3	97	28	)	)	PUNCT
cord-326631-7gd3hjc3	97	29	enables	enable	VERB
cord-326631-7gd3hjc3	97	30	us	we	PRON
cord-326631-7gd3hjc3	97	31	to	to	PART
cord-326631-7gd3hjc3	97	32	replace	replace	VERB
cord-326631-7gd3hjc3	97	33	an	an	DET
cord-326631-7gd3hjc3	97	34	exponential	exponential	ADJ
cord-326631-7gd3hjc3	97	35	distribution	distribution	NOUN
cord-326631-7gd3hjc3	97	36	with	with	ADP
cord-326631-7gd3hjc3	97	37	mean	mean	ADJ
cord-326631-7gd3hjc3	97	38	1	1	NUM
cord-326631-7gd3hjc3	97	39	/	/	SYM
cord-326631-7gd3hjc3	97	40	γ	γ	NOUN
cord-326631-7gd3hjc3	97	41	by	by	ADP
cord-326631-7gd3hjc3	97	42	a	a	DET
cord-326631-7gd3hjc3	97	43	gamma	gamma	NOUN
cord-326631-7gd3hjc3	97	44	distribution	distribution	NOUN
cord-326631-7gd3hjc3	97	45	g	g	PROPN
cord-326631-7gd3hjc3	97	46	k	k	PROPN
cord-326631-7gd3hjc3	97	47	,	,	PUNCT
cord-326631-7gd3hjc3	97	48	kγ	kγ	PROPN
cord-326631-7gd3hjc3	97	49	(	(	PUNCT
cord-326631-7gd3hjc3	97	50	which	which	PRON
cord-326631-7gd3hjc3	97	51	also	also	ADV
cord-326631-7gd3hjc3	97	52	has	have	AUX
cord-326631-7gd3hjc3	97	53	mean	mean	VERB
cord-326631-7gd3hjc3	97	54	1	1	NUM
cord-326631-7gd3hjc3	97	55	/	/	SYM
cord-326631-7gd3hjc3	97	56	γ	γ	NOUN
cord-326631-7gd3hjc3	97	57	)	)	PUNCT
cord-326631-7gd3hjc3	97	58	.	.	PUNCT
cord-326631-7gd3hjc3	98	1	the	the	DET
cord-326631-7gd3hjc3	98	2	trick	trick	NOUN
cord-326631-7gd3hjc3	98	3	is	be	AUX
cord-326631-7gd3hjc3	98	4	to	to	PART
cord-326631-7gd3hjc3	98	5	replace	replace	VERB
cord-326631-7gd3hjc3	98	6	a	a	DET
cord-326631-7gd3hjc3	98	7	single	single	ADJ
cord-326631-7gd3hjc3	98	8	infectious	infectious	ADJ
cord-326631-7gd3hjc3	98	9	stage	stage	NOUN
cord-326631-7gd3hjc3	98	10	with	with	ADP
cord-326631-7gd3hjc3	98	11	k	k	PROPN
cord-326631-7gd3hjc3	98	12	identical	identical	ADJ
cord-326631-7gd3hjc3	98	13	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	98	14	distributed	distribute	VERB
cord-326631-7gd3hjc3	98	15	substages	substage	NOUN
cord-326631-7gd3hjc3	98	16	of	of	ADP
cord-326631-7gd3hjc3	98	17	mean	mean	ADJ
cord-326631-7gd3hjc3	98	18	duration	duration	NOUN
cord-326631-7gd3hjc3	98	19	1/(kγ	1/(kγ	NUM
cord-326631-7gd3hjc3	98	20	)	)	PUNCT
cord-326631-7gd3hjc3	98	21	.	.	PUNCT
cord-326631-7gd3hjc3	99	1	the	the	DET
cord-326631-7gd3hjc3	99	2	model	model	NOUN
cord-326631-7gd3hjc3	99	3	then	then	ADV
cord-326631-7gd3hjc3	99	4	has	have	VERB
cord-326631-7gd3hjc3	99	5	precisely	precisely	ADV
cord-326631-7gd3hjc3	99	6	the	the	DET
cord-326631-7gd3hjc3	99	7	form	form	NOUN
cord-326631-7gd3hjc3	99	8	the	the	DET
cord-326631-7gd3hjc3	99	9	si	si	PROPN
cord-326631-7gd3hjc3	99	10	n	n	NOUN
cord-326631-7gd3hjc3	99	11	r	r	NOUN
cord-326631-7gd3hjc3	99	12	model	model	NOUN
cord-326631-7gd3hjc3	99	13	(	(	PUNCT
cord-326631-7gd3hjc3	99	14	6	6	NUM
cord-326631-7gd3hjc3	99	15	)	)	PUNCT
cord-326631-7gd3hjc3	99	16	,	,	PUNCT
cord-326631-7gd3hjc3	99	17	but	but	CCONJ
cord-326631-7gd3hjc3	99	18	with	with	ADP
cord-326631-7gd3hjc3	99	19	the	the	DET
cord-326631-7gd3hjc3	99	20	sequence	sequence	NOUN
cord-326631-7gd3hjc3	99	21	of	of	ADP
cord-326631-7gd3hjc3	99	22	infectious	infectious	ADJ
cord-326631-7gd3hjc3	99	23	stages	stage	NOUN
cord-326631-7gd3hjc3	99	24	being	be	AUX
cord-326631-7gd3hjc3	99	25	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	99	26	artefacts	artefact	NOUN
cord-326631-7gd3hjc3	99	27	rather	rather	ADV
cord-326631-7gd3hjc3	99	28	than	than	ADP
cord-326631-7gd3hjc3	99	29	biologically	biologically	ADV
cord-326631-7gd3hjc3	99	30	meaningful	meaningful	ADJ
cord-326631-7gd3hjc3	99	31	.	.	PUNCT
cord-326631-7gd3hjc3	100	1	since	since	SCONJ
cord-326631-7gd3hjc3	100	2	this	this	DET
cord-326631-7gd3hjc3	100	3	substage	substage	NOUN
cord-326631-7gd3hjc3	100	4	trick	trick	NOUN
cord-326631-7gd3hjc3	100	5	can	can	AUX
cord-326631-7gd3hjc3	100	6	be	be	AUX
cord-326631-7gd3hjc3	100	7	applied	apply	VERB
cord-326631-7gd3hjc3	100	8	equally	equally	ADV
cord-326631-7gd3hjc3	100	9	well	well	ADV
cord-326631-7gd3hjc3	100	10	to	to	ADP
cord-326631-7gd3hjc3	100	11	any	any	DET
cord-326631-7gd3hjc3	100	12	infectious	infectious	ADJ
cord-326631-7gd3hjc3	100	13	stage	stage	NOUN
cord-326631-7gd3hjc3	100	14	,	,	PUNCT
cord-326631-7gd3hjc3	100	15	anderson	anderson	PROPN
cord-326631-7gd3hjc3	100	16	and	and	CCONJ
cord-326631-7gd3hjc3	100	17	watson	watson	PROPN
cord-326631-7gd3hjc3	100	18	's	's	PART
cord-326631-7gd3hjc3	100	19	(	(	PUNCT
cord-326631-7gd3hjc3	100	20	1980	1980	NUM
cord-326631-7gd3hjc3	100	21	)	)	PUNCT
cord-326631-7gd3hjc3	100	22	conclusion	conclusion	NOUN
cord-326631-7gd3hjc3	100	23	that	that	SCONJ
cord-326631-7gd3hjc3	100	24	the	the	DET
cord-326631-7gd3hjc3	100	25	final	final	ADJ
cord-326631-7gd3hjc3	100	26	size	size	NOUN
cord-326631-7gd3hjc3	100	27	in	in	ADP
cord-326631-7gd3hjc3	100	28	an	an	DET
cord-326631-7gd3hjc3	100	29	sir	sir	NOUN
cord-326631-7gd3hjc3	100	30	model	model	NOUN
cord-326631-7gd3hjc3	100	31	with	with	ADP
cord-326631-7gd3hjc3	100	32	gamma	gamma	PROPN
cord-326631-7gd3hjc3	100	33	distributed	distribute	VERB
cord-326631-7gd3hjc3	100	34	infectious	infectious	ADJ
cord-326631-7gd3hjc3	100	35	periods	period	NOUN
cord-326631-7gd3hjc3	100	36	is	be	AUX
cord-326631-7gd3hjc3	100	37	given	give	VERB
cord-326631-7gd3hjc3	100	38	by	by	ADP
cord-326631-7gd3hjc3	100	39	the	the	DET
cord-326631-7gd3hjc3	100	40	usual	usual	ADJ
cord-326631-7gd3hjc3	100	41	formula	formula	NOUN
cord-326631-7gd3hjc3	100	42	(	(	PUNCT
cord-326631-7gd3hjc3	100	43	5	5	NUM
cord-326631-7gd3hjc3	100	44	)	)	PUNCT
cord-326631-7gd3hjc3	100	45	now	now	ADV
cord-326631-7gd3hjc3	100	46	generalizes	generalize	VERB
cord-326631-7gd3hjc3	100	47	to	to	ADP
cord-326631-7gd3hjc3	100	48	an	an	DET
cord-326631-7gd3hjc3	100	49	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	100	50	number	number	NOUN
cord-326631-7gd3hjc3	100	51	of	of	ADP
cord-326631-7gd3hjc3	100	52	stages	stage	NOUN
cord-326631-7gd3hjc3	100	53	,	,	PUNCT
cord-326631-7gd3hjc3	100	54	each	each	PRON
cord-326631-7gd3hjc3	100	55	with	with	ADP
cord-326631-7gd3hjc3	100	56	gamma	gamma	PROPN
cord-326631-7gd3hjc3	100	57	distributed	distribute	VERB
cord-326631-7gd3hjc3	100	58	durations	duration	NOUN
cord-326631-7gd3hjc3	100	59	.	.	PUNCT
cord-326631-7gd3hjc3	101	1	although	although	SCONJ
cord-326631-7gd3hjc3	101	2	expressed	express	VERB
cord-326631-7gd3hjc3	101	3	differently	differently	ADV
cord-326631-7gd3hjc3	101	4	,	,	PUNCT
cord-326631-7gd3hjc3	101	5	in	in	ADP
cord-326631-7gd3hjc3	101	6	their	their	PRON
cord-326631-7gd3hjc3	101	7	original	original	ADJ
cord-326631-7gd3hjc3	101	8	paper	paper	NOUN
cord-326631-7gd3hjc3	101	9	kermack	kermack	NOUN
cord-326631-7gd3hjc3	101	10	and	and	CCONJ
cord-326631-7gd3hjc3	101	11	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	101	12	(	(	PUNCT
cord-326631-7gd3hjc3	101	13	1927	1927	NUM
cord-326631-7gd3hjc3	101	14	)	)	PUNCT
cord-326631-7gd3hjc3	101	15	studied	study	VERB
cord-326631-7gd3hjc3	101	16	a	a	DET
cord-326631-7gd3hjc3	101	17	particular	particular	ADJ
cord-326631-7gd3hjc3	101	18	limit	limit	NOUN
cord-326631-7gd3hjc3	101	19	of	of	ADP
cord-326631-7gd3hjc3	101	20	the	the	DET
cord-326631-7gd3hjc3	101	21	gamma	gamma	PROPN
cord-326631-7gd3hjc3	101	22	distributed	distribute	VERB
cord-326631-7gd3hjc3	101	23	multiple	multiple	ADJ
cord-326631-7gd3hjc3	101	24	stage	stage	NOUN
cord-326631-7gd3hjc3	101	25	model	model	NOUN
cord-326631-7gd3hjc3	101	26	described	describe	VERB
cord-326631-7gd3hjc3	101	27	in	in	ADP
cord-326631-7gd3hjc3	101	28	the	the	DET
cord-326631-7gd3hjc3	101	29	previous	previous	ADJ
cord-326631-7gd3hjc3	101	30	section	section	NOUN
cord-326631-7gd3hjc3	101	31	.	.	PUNCT
cord-326631-7gd3hjc3	102	1	suppose	suppose	VERB
cord-326631-7gd3hjc3	102	2	we	we	PRON
cord-326631-7gd3hjc3	102	3	have	have	VERB
cord-326631-7gd3hjc3	102	4	a	a	DET
cord-326631-7gd3hjc3	102	5	sequence	sequence	NOUN
cord-326631-7gd3hjc3	102	6	of	of	ADP
cord-326631-7gd3hjc3	102	7	n	n	ADV
cord-326631-7gd3hjc3	102	8	infectious	infectious	ADJ
cord-326631-7gd3hjc3	102	9	stages	stage	NOUN
cord-326631-7gd3hjc3	102	10	,	,	PUNCT
cord-326631-7gd3hjc3	102	11	each	each	PRON
cord-326631-7gd3hjc3	102	12	with	with	ADP
cord-326631-7gd3hjc3	102	13	the	the	DET
cord-326631-7gd3hjc3	102	14	same	same	ADJ
cord-326631-7gd3hjc3	102	15	,	,	PUNCT
cord-326631-7gd3hjc3	102	16	fixed	fix	VERB
cord-326631-7gd3hjc3	102	17	stage	stage	NOUN
cord-326631-7gd3hjc3	102	18	duration	duration	NOUN
cord-326631-7gd3hjc3	102	19	τ	τ	NOUN
cord-326631-7gd3hjc3	102	20	.	.	PUNCT
cord-326631-7gd3hjc3	103	1	thus	thus	ADV
cord-326631-7gd3hjc3	103	2	,	,	PUNCT
cord-326631-7gd3hjc3	103	3	this	this	PRON
cord-326631-7gd3hjc3	103	4	is	be	AUX
cord-326631-7gd3hjc3	103	5	the	the	DET
cord-326631-7gd3hjc3	103	6	limit	limit	NOUN
cord-326631-7gd3hjc3	103	7	k	k	PROPN
cord-326631-7gd3hjc3	103	8	→	→	SYM
cord-326631-7gd3hjc3	103	9	∞	∞	PROPN
cord-326631-7gd3hjc3	103	10	in	in	ADP
cord-326631-7gd3hjc3	103	11	the	the	DET
cord-326631-7gd3hjc3	103	12	gamma	gamma	NOUN
cord-326631-7gd3hjc3	103	13	distribution	distribution	NOUN
cord-326631-7gd3hjc3	103	14	(	(	PUNCT
cord-326631-7gd3hjc3	103	15	10	10	NUM
cord-326631-7gd3hjc3	103	16	)	)	PUNCT
cord-326631-7gd3hjc3	103	17	,	,	PUNCT
cord-326631-7gd3hjc3	103	18	with	with	ADP
cord-326631-7gd3hjc3	103	19	φ	φ	NOUN
cord-326631-7gd3hjc3	103	20	=	=	NOUN
cord-326631-7gd3hjc3	103	21	1	1	NUM
cord-326631-7gd3hjc3	103	22	/	/	SYM
cord-326631-7gd3hjc3	103	23	τ	τ	NOUN
cord-326631-7gd3hjc3	103	24	.	.	PUNCT
cord-326631-7gd3hjc3	104	1	during	during	ADP
cord-326631-7gd3hjc3	104	2	stage	stage	NOUN
cord-326631-7gd3hjc3	104	3	i	i	PROPN
cord-326631-7gd3hjc3	104	4	,	,	PUNCT
cord-326631-7gd3hjc3	104	5	the	the	DET
cord-326631-7gd3hjc3	104	6	transmission	transmission	NOUN
cord-326631-7gd3hjc3	104	7	rate	rate	NOUN
cord-326631-7gd3hjc3	104	8	is	be	AUX
cord-326631-7gd3hjc3	104	9	β	β	NOUN
cord-326631-7gd3hjc3	105	1	i	i	NOUN
cord-326631-7gd3hjc3	106	1	(	(	PUNCT
cord-326631-7gd3hjc3	106	2	i	i	NOUN
cord-326631-7gd3hjc3	106	3	=	=	NOUN
cord-326631-7gd3hjc3	106	4	1	1	NUM
cord-326631-7gd3hjc3	106	5	,	,	PUNCT
cord-326631-7gd3hjc3	106	6	.	.	PUNCT
cord-326631-7gd3hjc3	106	7	.	.	PUNCT
cord-326631-7gd3hjc3	106	8	.	.	PUNCT
cord-326631-7gd3hjc3	107	1	,	,	PUNCT
cord-326631-7gd3hjc3	107	2	n	n	X
cord-326631-7gd3hjc3	107	3	)	)	PUNCT
cord-326631-7gd3hjc3	107	4	.	.	PUNCT
cord-326631-7gd3hjc3	108	1	if	if	SCONJ
cord-326631-7gd3hjc3	108	2	we	we	PRON
cord-326631-7gd3hjc3	108	3	now	now	ADV
cord-326631-7gd3hjc3	108	4	let	let	VERB
cord-326631-7gd3hjc3	108	5	the	the	DET
cord-326631-7gd3hjc3	108	6	number	number	NOUN
cord-326631-7gd3hjc3	108	7	of	of	ADP
cord-326631-7gd3hjc3	108	8	infectious	infectious	ADJ
cord-326631-7gd3hjc3	108	9	stages	stage	NOUN
cord-326631-7gd3hjc3	108	10	increase	increase	VERB
cord-326631-7gd3hjc3	108	11	(	(	PUNCT
cord-326631-7gd3hjc3	108	12	n	n	NOUN
cord-326631-7gd3hjc3	108	13	→	→	SYM
cord-326631-7gd3hjc3	108	14	∞	∞	NUM
cord-326631-7gd3hjc3	108	15	)	)	PUNCT
cord-326631-7gd3hjc3	108	16	and	and	CCONJ
cord-326631-7gd3hjc3	108	17	the	the	DET
cord-326631-7gd3hjc3	108	18	length	length	NOUN
cord-326631-7gd3hjc3	108	19	of	of	ADP
cord-326631-7gd3hjc3	108	20	each	each	DET
cord-326631-7gd3hjc3	108	21	stage	stage	NOUN
cord-326631-7gd3hjc3	108	22	decrease	decrease	NOUN
cord-326631-7gd3hjc3	108	23	(	(	PUNCT
cord-326631-7gd3hjc3	108	24	τ	τ	NOUN
cord-326631-7gd3hjc3	108	25	→	→	PUNCT
cord-326631-7gd3hjc3	108	26	0	0	NUM
cord-326631-7gd3hjc3	108	27	)	)	PUNCT
cord-326631-7gd3hjc3	108	28	,	,	PUNCT
cord-326631-7gd3hjc3	108	29	keeping	keep	VERB
cord-326631-7gd3hjc3	108	30	the	the	DET
cord-326631-7gd3hjc3	108	31	total	total	ADJ
cord-326631-7gd3hjc3	108	32	infectious	infectious	ADJ
cord-326631-7gd3hjc3	108	33	period	period	NOUN
cord-326631-7gd3hjc3	108	34	(	(	PUNCT
cord-326631-7gd3hjc3	108	35	t	t	NOUN
cord-326631-7gd3hjc3	108	36	=	=	NOUN
cord-326631-7gd3hjc3	108	37	nτ	nτ	INTJ
cord-326631-7gd3hjc3	108	38	)	)	PUNCT
cord-326631-7gd3hjc3	108	39	constant	constant	ADJ
cord-326631-7gd3hjc3	108	40	,	,	PUNCT
cord-326631-7gd3hjc3	108	41	then	then	ADV
cord-326631-7gd3hjc3	108	42	we	we	PRON
cord-326631-7gd3hjc3	108	43	arrive	arrive	VERB
cord-326631-7gd3hjc3	108	44	at	at	ADP
cord-326631-7gd3hjc3	108	45	a	a	DET
cord-326631-7gd3hjc3	108	46	model	model	NOUN
cord-326631-7gd3hjc3	108	47	in	in	ADP
cord-326631-7gd3hjc3	108	48	which	which	PRON
cord-326631-7gd3hjc3	108	49	the	the	DET
cord-326631-7gd3hjc3	108	50	transmission	transmission	NOUN
cord-326631-7gd3hjc3	108	51	rate	rate	NOUN
cord-326631-7gd3hjc3	108	52	(	(	PUNCT
cord-326631-7gd3hjc3	108	53	β	β	X
cord-326631-7gd3hjc3	108	54	)	)	PUNCT
cord-326631-7gd3hjc3	108	55	varies	vary	VERB
cord-326631-7gd3hjc3	108	56	continuously	continuously	ADV
cord-326631-7gd3hjc3	108	57	through	through	ADP
cord-326631-7gd3hjc3	108	58	the	the	DET
cord-326631-7gd3hjc3	108	59	infectious	infectious	ADJ
cord-326631-7gd3hjc3	108	60	period	period	NOUN
cord-326631-7gd3hjc3	108	61	.	.	PUNCT
cord-326631-7gd3hjc3	109	1	in	in	ADP
cord-326631-7gd3hjc3	109	2	such	such	DET
cord-326631-7gd3hjc3	109	3	a	a	DET
cord-326631-7gd3hjc3	109	4	model	model	NOUN
cord-326631-7gd3hjc3	109	5	,	,	PUNCT
cord-326631-7gd3hjc3	109	6	an	an	DET
cord-326631-7gd3hjc3	109	7	individual	individual	NOUN
cord-326631-7gd3hjc3	109	8	's	's	PART
cord-326631-7gd3hjc3	109	9	infectivity	infectivity	NOUN
cord-326631-7gd3hjc3	109	10	depends	depend	VERB
cord-326631-7gd3hjc3	109	11	on	on	ADP
cord-326631-7gd3hjc3	109	12	his	his	PRON
cord-326631-7gd3hjc3	109	13	/	/	SYM
cord-326631-7gd3hjc3	109	14	her	her	PRON
cord-326631-7gd3hjc3	109	15	stage	stage	NOUN
cord-326631-7gd3hjc3	109	16	-	-	PUNCT
cord-326631-7gd3hjc3	109	17	age	age	NOUN
cord-326631-7gd3hjc3	109	18	,	,	PUNCT
cord-326631-7gd3hjc3	109	19	i.e.	i.e.	X
cord-326631-7gd3hjc3	109	20	,	,	PUNCT
cord-326631-7gd3hjc3	109	21	the	the	DET
cord-326631-7gd3hjc3	109	22	amount	amount	NOUN
cord-326631-7gd3hjc3	109	23	of	of	ADP
cord-326631-7gd3hjc3	109	24	time	time	NOUN
cord-326631-7gd3hjc3	109	25	since	since	SCONJ
cord-326631-7gd3hjc3	109	26	initial	initial	ADJ
cord-326631-7gd3hjc3	109	27	infection	infection	NOUN
cord-326631-7gd3hjc3	109	28	.	.	PUNCT
cord-326631-7gd3hjc3	110	1	using	use	VERB
cord-326631-7gd3hjc3	110	2	a	a	DET
cord-326631-7gd3hjc3	110	3	stage	stage	NOUN
cord-326631-7gd3hjc3	110	4	-	-	PUNCT
cord-326631-7gd3hjc3	110	5	age	age	NOUN
cord-326631-7gd3hjc3	110	6	sir	sir	PROPN
cord-326631-7gd3hjc3	110	7	formulation	formulation	NOUN
cord-326631-7gd3hjc3	110	8	,	,	PUNCT
cord-326631-7gd3hjc3	110	9	kermack	kermack	PROPN
cord-326631-7gd3hjc3	110	10	and	and	CCONJ
cord-326631-7gd3hjc3	110	11	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	110	12	(	(	PUNCT
cord-326631-7gd3hjc3	110	13	1927	1927	NUM
cord-326631-7gd3hjc3	110	14	)	)	PUNCT
cord-326631-7gd3hjc3	110	15	derived	derive	VERB
cord-326631-7gd3hjc3	110	16	the	the	DET
cord-326631-7gd3hjc3	110	17	final	final	ADJ
cord-326631-7gd3hjc3	110	18	size	size	NOUN
cord-326631-7gd3hjc3	110	19	formula	formula	NOUN
cord-326631-7gd3hjc3	110	20	(	(	PUNCT
cord-326631-7gd3hjc3	110	21	5	5	NUM
cord-326631-7gd3hjc3	110	22	)	)	PUNCT
cord-326631-7gd3hjc3	110	23	and	and	CCONJ
cord-326631-7gd3hjc3	110	24	showed	show	VERB
cord-326631-7gd3hjc3	110	25	that	that	SCONJ
cord-326631-7gd3hjc3	110	26	its	its	PRON
cord-326631-7gd3hjc3	110	27	form	form	NOUN
cord-326631-7gd3hjc3	110	28	is	be	AUX
cord-326631-7gd3hjc3	110	29	independent	independent	ADJ
cord-326631-7gd3hjc3	110	30	of	of	ADP
cord-326631-7gd3hjc3	110	31	how	how	SCONJ
cord-326631-7gd3hjc3	110	32	the	the	DET
cord-326631-7gd3hjc3	110	33	transmission	transmission	NOUN
cord-326631-7gd3hjc3	110	34	rate	rate	NOUN
cord-326631-7gd3hjc3	110	35	depends	depend	VERB
cord-326631-7gd3hjc3	110	36	on	on	ADP
cord-326631-7gd3hjc3	110	37	stage	stage	NOUN
cord-326631-7gd3hjc3	110	38	-	-	PUNCT
cord-326631-7gd3hjc3	110	39	age	age	NOUN
cord-326631-7gd3hjc3	110	40	.	.	PUNCT
cord-326631-7gd3hjc3	111	1	we	we	PRON
cord-326631-7gd3hjc3	111	2	have	have	AUX
cord-326631-7gd3hjc3	111	3	seen	see	VERB
cord-326631-7gd3hjc3	111	4	that	that	SCONJ
cord-326631-7gd3hjc3	111	5	the	the	DET
cord-326631-7gd3hjc3	111	6	final	final	ADJ
cord-326631-7gd3hjc3	111	7	size	size	NOUN
cord-326631-7gd3hjc3	111	8	formula	formula	NOUN
cord-326631-7gd3hjc3	111	9	(	(	PUNCT
cord-326631-7gd3hjc3	111	10	5	5	NUM
cord-326631-7gd3hjc3	111	11	)	)	PUNCT
cord-326631-7gd3hjc3	111	12	is	be	AUX
cord-326631-7gd3hjc3	111	13	the	the	DET
cord-326631-7gd3hjc3	111	14	same	same	ADJ
cord-326631-7gd3hjc3	111	15	if	if	SCONJ
cord-326631-7gd3hjc3	111	16	stage	stage	NOUN
cord-326631-7gd3hjc3	111	17	durations	duration	NOUN
cord-326631-7gd3hjc3	111	18	are	be	AUX
cord-326631-7gd3hjc3	111	19	distributed	distribute	VERB
cord-326631-7gd3hjc3	111	20	according	accord	VERB
cord-326631-7gd3hjc3	111	21	to	to	ADP
cord-326631-7gd3hjc3	111	22	any	any	DET
cord-326631-7gd3hjc3	111	23	member	member	NOUN
cord-326631-7gd3hjc3	111	24	of	of	ADP
cord-326631-7gd3hjc3	111	25	the	the	DET
cord-326631-7gd3hjc3	111	26	family	family	NOUN
cord-326631-7gd3hjc3	111	27	of	of	ADP
cord-326631-7gd3hjc3	111	28	the	the	DET
cord-326631-7gd3hjc3	111	29	gamma	gamma	NOUN
cord-326631-7gd3hjc3	111	30	distributions	distribution	NOUN
cord-326631-7gd3hjc3	111	31	(	(	PUNCT
cord-326631-7gd3hjc3	111	32	10	10	NUM
cord-326631-7gd3hjc3	111	33	)	)	PUNCT
cord-326631-7gd3hjc3	111	34	.	.	PUNCT
cord-326631-7gd3hjc3	112	1	this	this	PRON
cord-326631-7gd3hjc3	112	2	suggests	suggest	VERB
cord-326631-7gd3hjc3	112	3	that	that	SCONJ
cord-326631-7gd3hjc3	112	4	any	any	DET
cord-326631-7gd3hjc3	112	5	distribution	distribution	NOUN
cord-326631-7gd3hjc3	112	6	of	of	ADP
cord-326631-7gd3hjc3	112	7	stage	stage	NOUN
cord-326631-7gd3hjc3	112	8	durations	duration	NOUN
cord-326631-7gd3hjc3	112	9	will	will	AUX
cord-326631-7gd3hjc3	112	10	yield	yield	VERB
cord-326631-7gd3hjc3	112	11	the	the	DET
cord-326631-7gd3hjc3	112	12	same	same	ADJ
cord-326631-7gd3hjc3	112	13	final	final	ADJ
cord-326631-7gd3hjc3	112	14	size	size	NOUN
cord-326631-7gd3hjc3	112	15	.	.	PUNCT
cord-326631-7gd3hjc3	113	1	unlike	unlike	ADP
cord-326631-7gd3hjc3	113	2	the	the	DET
cord-326631-7gd3hjc3	113	3	situation	situation	NOUN
cord-326631-7gd3hjc3	113	4	for	for	ADP
cord-326631-7gd3hjc3	113	5	gamma	gamma	NOUN
cord-326631-7gd3hjc3	113	6	distributed	distribute	VERB
cord-326631-7gd3hjc3	113	7	infectious	infectious	ADJ
cord-326631-7gd3hjc3	113	8	periods	period	NOUN
cord-326631-7gd3hjc3	113	9	,	,	PUNCT
cord-326631-7gd3hjc3	113	10	with	with	ADP
cord-326631-7gd3hjc3	113	11	an	an	DET
cord-326631-7gd3hjc3	113	12	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	113	13	distribution	distribution	NOUN
cord-326631-7gd3hjc3	113	14	the	the	DET
cord-326631-7gd3hjc3	113	15	time	time	NOUN
cord-326631-7gd3hjc3	113	16	-	-	PUNCT
cord-326631-7gd3hjc3	113	17	evolution	evolution	NOUN
cord-326631-7gd3hjc3	113	18	of	of	ADP
cord-326631-7gd3hjc3	113	19	the	the	DET
cord-326631-7gd3hjc3	113	20	infectious	infectious	ADJ
cord-326631-7gd3hjc3	113	21	class	class	NOUN
cord-326631-7gd3hjc3	113	22	can	can	AUX
cord-326631-7gd3hjc3	113	23	no	no	ADV
cord-326631-7gd3hjc3	113	24	longer	long	ADV
cord-326631-7gd3hjc3	113	25	be	be	AUX
cord-326631-7gd3hjc3	113	26	expressed	express	VERB
cord-326631-7gd3hjc3	113	27	using	use	VERB
cord-326631-7gd3hjc3	113	28	ordinary	ordinary	ADJ
cord-326631-7gd3hjc3	113	29	differential	differential	ADJ
cord-326631-7gd3hjc3	113	30	equations	equation	NOUN
cord-326631-7gd3hjc3	113	31	(	(	PUNCT
cord-326631-7gd3hjc3	113	32	odes	ode	NOUN
cord-326631-7gd3hjc3	113	33	)	)	PUNCT
cord-326631-7gd3hjc3	113	34	.	.	PUNCT
cord-326631-7gd3hjc3	114	1	instead	instead	ADV
cord-326631-7gd3hjc3	114	2	,	,	PUNCT
cord-326631-7gd3hjc3	114	3	we	we	PRON
cord-326631-7gd3hjc3	114	4	must	must	AUX
cord-326631-7gd3hjc3	114	5	construct	construct	VERB
cord-326631-7gd3hjc3	114	6	a	a	DET
cord-326631-7gd3hjc3	114	7	system	system	NOUN
cord-326631-7gd3hjc3	114	8	of	of	ADP
cord-326631-7gd3hjc3	114	9	integro	integro	NOUN
cord-326631-7gd3hjc3	114	10	-	-	PUNCT
cord-326631-7gd3hjc3	114	11	differential	differential	ADJ
cord-326631-7gd3hjc3	114	12	equations	equation	NOUN
cord-326631-7gd3hjc3	114	13	(	(	PUNCT
cord-326631-7gd3hjc3	114	14	feng	feng	PROPN
cord-326631-7gd3hjc3	114	15	and	and	CCONJ
cord-326631-7gd3hjc3	114	16	thieme	thieme	PROPN
cord-326631-7gd3hjc3	114	17	,	,	PUNCT
cord-326631-7gd3hjc3	114	18	2000	2000	NUM
cord-326631-7gd3hjc3	114	19	)	)	PUNCT
cord-326631-7gd3hjc3	114	20	.	.	PUNCT
cord-326631-7gd3hjc3	115	1	let	let	VERB
cord-326631-7gd3hjc3	115	2	u(t	u(t	PROPN
cord-326631-7gd3hjc3	115	3	)	)	PUNCT
cord-326631-7gd3hjc3	115	4	be	be	AUX
cord-326631-7gd3hjc3	115	5	the	the	DET
cord-326631-7gd3hjc3	115	6	rate	rate	NOUN
cord-326631-7gd3hjc3	115	7	at	at	ADP
cord-326631-7gd3hjc3	115	8	which	which	PRON
cord-326631-7gd3hjc3	115	9	individuals	individual	NOUN
cord-326631-7gd3hjc3	115	10	become	become	VERB
cord-326631-7gd3hjc3	115	11	infectious	infectious	ADJ
cord-326631-7gd3hjc3	115	12	(	(	PUNCT
cord-326631-7gd3hjc3	115	13	enter	enter	VERB
cord-326631-7gd3hjc3	115	14	class	class	NOUN
cord-326631-7gd3hjc3	115	15	i	i	NOUN
cord-326631-7gd3hjc3	115	16	)	)	PUNCT
cord-326631-7gd3hjc3	115	17	at	at	ADP
cord-326631-7gd3hjc3	115	18	time	time	NOUN
cord-326631-7gd3hjc3	115	19	t	t	NOUN
cord-326631-7gd3hjc3	115	20	≥	≥	NOUN
cord-326631-7gd3hjc3	115	21	0	0	NUM
cord-326631-7gd3hjc3	115	22	,	,	PUNCT
cord-326631-7gd3hjc3	115	23	i.e.	i.e.	X
cord-326631-7gd3hjc3	115	24	,	,	PUNCT
cord-326631-7gd3hjc3	115	25	the	the	DET
cord-326631-7gd3hjc3	115	26	equation	equation	NOUN
cord-326631-7gd3hjc3	115	27	for	for	ADP
cord-326631-7gd3hjc3	115	28	the	the	DET
cord-326631-7gd3hjc3	115	29	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	115	30	class	class	NOUN
cord-326631-7gd3hjc3	115	31	is	be	AUX
cord-326631-7gd3hjc3	115	32	the	the	DET
cord-326631-7gd3hjc3	115	33	same	same	ADJ
cord-326631-7gd3hjc3	115	34	as	as	ADP
cord-326631-7gd3hjc3	115	35	in	in	ADP
cord-326631-7gd3hjc3	115	36	the	the	DET
cord-326631-7gd3hjc3	115	37	standard	standard	ADJ
cord-326631-7gd3hjc3	115	38	sir	sir	PROPN
cord-326631-7gd3hjc3	115	39	model	model	NOUN
cord-326631-7gd3hjc3	115	40	,	,	PUNCT
cord-326631-7gd3hjc3	115	41	we	we	PRON
cord-326631-7gd3hjc3	115	42	also	also	ADV
cord-326631-7gd3hjc3	115	43	define	define	VERB
cord-326631-7gd3hjc3	115	44	u(t	u(t	ADJ
cord-326631-7gd3hjc3	115	45	)	)	PUNCT
cord-326631-7gd3hjc3	115	46	for	for	ADP
cord-326631-7gd3hjc3	115	47	t	t	NOUN
cord-326631-7gd3hjc3	115	48	<	<	X
cord-326631-7gd3hjc3	115	49	0	0	NUM
cord-326631-7gd3hjc3	115	50	since	since	SCONJ
cord-326631-7gd3hjc3	115	51	this	this	PRON
cord-326631-7gd3hjc3	115	52	will	will	AUX
cord-326631-7gd3hjc3	115	53	allow	allow	VERB
cord-326631-7gd3hjc3	115	54	us	we	PRON
cord-326631-7gd3hjc3	115	55	to	to	PART
cord-326631-7gd3hjc3	115	56	specify	specify	VERB
cord-326631-7gd3hjc3	115	57	the	the	DET
cord-326631-7gd3hjc3	115	58	initial	initial	ADJ
cord-326631-7gd3hjc3	115	59	conditions	condition	NOUN
cord-326631-7gd3hjc3	115	60	.	.	PUNCT
cord-326631-7gd3hjc3	116	1	for	for	ADP
cord-326631-7gd3hjc3	116	2	t	t	NOUN
cord-326631-7gd3hjc3	116	3	<	<	X
cord-326631-7gd3hjc3	116	4	0	0	NUM
cord-326631-7gd3hjc3	116	5	,	,	PUNCT
cord-326631-7gd3hjc3	116	6	u(t	u(t	PROPN
cord-326631-7gd3hjc3	116	7	)	)	PUNCT
cord-326631-7gd3hjc3	116	8	is	be	AUX
cord-326631-7gd3hjc3	116	9	the	the	DET
cord-326631-7gd3hjc3	116	10	rate	rate	NOUN
cord-326631-7gd3hjc3	116	11	at	at	ADP
cord-326631-7gd3hjc3	116	12	which	which	PRON
cord-326631-7gd3hjc3	116	13	individuals	individual	NOUN
cord-326631-7gd3hjc3	116	14	who	who	PRON
cord-326631-7gd3hjc3	116	15	were	be	AUX
cord-326631-7gd3hjc3	116	16	still	still	ADV
cord-326631-7gd3hjc3	116	17	infectious	infectious	ADJ
cord-326631-7gd3hjc3	116	18	at	at	ADP
cord-326631-7gd3hjc3	116	19	the	the	DET
cord-326631-7gd3hjc3	116	20	initial	initial	ADJ
cord-326631-7gd3hjc3	116	21	time	time	NOUN
cord-326631-7gd3hjc3	116	22	(	(	PUNCT
cord-326631-7gd3hjc3	116	23	time	time	NOUN
cord-326631-7gd3hjc3	116	24	0	0	NUM
cord-326631-7gd3hjc3	116	25	)	)	PUNCT
cord-326631-7gd3hjc3	116	26	became	become	VERB
cord-326631-7gd3hjc3	116	27	infectious	infectious	ADJ
cord-326631-7gd3hjc3	116	28	at	at	ADP
cord-326631-7gd3hjc3	116	29	time	time	NOUN
cord-326631-7gd3hjc3	116	30	t.	t.	PROPN
cord-326631-7gd3hjc3	116	31	hence	hence	ADV
cord-326631-7gd3hjc3	116	32	,	,	PUNCT
cord-326631-7gd3hjc3	116	33	the	the	DET
cord-326631-7gd3hjc3	116	34	number	number	NOUN
cord-326631-7gd3hjc3	116	35	of	of	ADP
cord-326631-7gd3hjc3	116	36	infectious	infectious	ADJ
cord-326631-7gd3hjc3	116	37	individuals	individual	NOUN
cord-326631-7gd3hjc3	116	38	at	at	ADP
cord-326631-7gd3hjc3	116	39	time	time	NOUN
cord-326631-7gd3hjc3	116	40	t	t	PROPN
cord-326631-7gd3hjc3	116	41	=	=	NOUN
cord-326631-7gd3hjc3	116	42	0	0	NUM
cord-326631-7gd3hjc3	116	43	is	be	AUX
cord-326631-7gd3hjc3	116	44	let	let	VERB
cord-326631-7gd3hjc3	116	45	f	f	X
cord-326631-7gd3hjc3	116	46	(	(	PUNCT
cord-326631-7gd3hjc3	116	47	t	t	NOUN
cord-326631-7gd3hjc3	116	48	)	)	PUNCT
cord-326631-7gd3hjc3	116	49	be	be	AUX
cord-326631-7gd3hjc3	116	50	the	the	DET
cord-326631-7gd3hjc3	116	51	probability	probability	NOUN
cord-326631-7gd3hjc3	116	52	density	density	NOUN
cord-326631-7gd3hjc3	116	53	of	of	ADP
cord-326631-7gd3hjc3	116	54	the	the	DET
cord-326631-7gd3hjc3	116	55	infectious	infectious	ADJ
cord-326631-7gd3hjc3	116	56	period	period	NOUN
cord-326631-7gd3hjc3	116	57	(	(	PUNCT
cord-326631-7gd3hjc3	116	58	so	so	ADV
cord-326631-7gd3hjc3	116	59	,	,	PUNCT
cord-326631-7gd3hjc3	116	60	for	for	SCONJ
cord-326631-7gd3hjc3	116	61	the	the	DET
cord-326631-7gd3hjc3	116	62	special	special	ADJ
cord-326631-7gd3hjc3	116	63	case	case	NOUN
cord-326631-7gd3hjc3	116	64	of	of	ADP
cord-326631-7gd3hjc3	116	65	a	a	DET
cord-326631-7gd3hjc3	116	66	gamma	gamma	NOUN
cord-326631-7gd3hjc3	116	67	distribution	distribution	NOUN
cord-326631-7gd3hjc3	116	68	,	,	PUNCT
cord-326631-7gd3hjc3	116	69	f	f	PROPN
cord-326631-7gd3hjc3	116	70	(	(	PUNCT
cord-326631-7gd3hjc3	116	71	t	t	NOUN
cord-326631-7gd3hjc3	116	72	)	)	PUNCT
cord-326631-7gd3hjc3	116	73	is	be	AUX
cord-326631-7gd3hjc3	116	74	given	give	VERB
cord-326631-7gd3hjc3	116	75	by	by	ADP
cord-326631-7gd3hjc3	116	76	g	g	PROPN
cord-326631-7gd3hjc3	116	77	k	k	PROPN
cord-326631-7gd3hjc3	116	78	,	,	PUNCT
cord-326631-7gd3hjc3	116	79	φ	φ	NOUN
cord-326631-7gd3hjc3	116	80	(	(	PUNCT
cord-326631-7gd3hjc3	116	81	t	t	NOUN
cord-326631-7gd3hjc3	116	82	)	)	PUNCT
cord-326631-7gd3hjc3	116	83	in	in	ADP
cord-326631-7gd3hjc3	116	84	eq	eq	PROPN
cord-326631-7gd3hjc3	116	85	.	.	PROPN
cord-326631-7gd3hjc3	116	86	10	10	NUM
cord-326631-7gd3hjc3	116	87	)	)	PUNCT
cord-326631-7gd3hjc3	116	88	.	.	PUNCT
cord-326631-7gd3hjc3	117	1	for	for	ADP
cord-326631-7gd3hjc3	117	2	an	an	DET
cord-326631-7gd3hjc3	117	3	individual	individual	NOUN
cord-326631-7gd3hjc3	117	4	who	who	PRON
cord-326631-7gd3hjc3	117	5	becomes	become	VERB
cord-326631-7gd3hjc3	117	6	infectious	infectious	ADJ
cord-326631-7gd3hjc3	117	7	at	at	ADP
cord-326631-7gd3hjc3	117	8	time	time	NOUN
cord-326631-7gd3hjc3	117	9	τ	τ	NOUN
cord-326631-7gd3hjc3	117	10	≥	≥	PUNCT
cord-326631-7gd3hjc3	117	11	0	0	NUM
cord-326631-7gd3hjc3	117	12	,	,	PUNCT
cord-326631-7gd3hjc3	117	13	the	the	DET
cord-326631-7gd3hjc3	117	14	probability	probability	NOUN
cord-326631-7gd3hjc3	117	15	density	density	NOUN
cord-326631-7gd3hjc3	117	16	that	that	PRON
cord-326631-7gd3hjc3	117	17	s	s	X
cord-326631-7gd3hjc3	117	18	/	/	SYM
cord-326631-7gd3hjc3	117	19	he	he	PRON
cord-326631-7gd3hjc3	117	20	recovers	recover	VERB
cord-326631-7gd3hjc3	117	21	(	(	PUNCT
cord-326631-7gd3hjc3	117	22	leaves	leave	VERB
cord-326631-7gd3hjc3	117	23	the	the	DET
cord-326631-7gd3hjc3	117	24	i	i	NOUN
cord-326631-7gd3hjc3	117	25	class	class	NOUN
cord-326631-7gd3hjc3	117	26	)	)	PUNCT
cord-326631-7gd3hjc3	117	27	at	at	ADP
cord-326631-7gd3hjc3	117	28	time	time	NOUN
cord-326631-7gd3hjc3	117	29	t	t	PROPN
cord-326631-7gd3hjc3	117	30	>	>	X
cord-326631-7gd3hjc3	118	1	τ	τ	PROPN
cord-326631-7gd3hjc3	118	2	is	be	AUX
cord-326631-7gd3hjc3	118	3	however	however	ADV
cord-326631-7gd3hjc3	118	4	,	,	PUNCT
cord-326631-7gd3hjc3	118	5	for	for	ADP
cord-326631-7gd3hjc3	118	6	individuals	individual	NOUN
cord-326631-7gd3hjc3	118	7	who	who	PRON
cord-326631-7gd3hjc3	118	8	became	become	VERB
cord-326631-7gd3hjc3	118	9	infectious	infectious	ADJ
cord-326631-7gd3hjc3	118	10	at	at	ADP
cord-326631-7gd3hjc3	118	11	time	time	NOUN
cord-326631-7gd3hjc3	118	12	τ	τ	NOUN
cord-326631-7gd3hjc3	118	13	<	<	X
cord-326631-7gd3hjc3	118	14	0	0	NUM
cord-326631-7gd3hjc3	118	15	,	,	PUNCT
cord-326631-7gd3hjc3	118	16	the	the	DET
cord-326631-7gd3hjc3	118	17	probability	probability	NOUN
cord-326631-7gd3hjc3	118	18	density	density	NOUN
cord-326631-7gd3hjc3	118	19	to	to	PART
cord-326631-7gd3hjc3	118	20	leave	leave	VERB
cord-326631-7gd3hjc3	118	21	class	class	NOUN
cord-326631-7gd3hjc3	118	22	i	i	PRON
cord-326631-7gd3hjc3	118	23	at	at	ADP
cord-326631-7gd3hjc3	118	24	time	time	NOUN
cord-326631-7gd3hjc3	118	25	t	t	PRON
cord-326631-7gd3hjc3	118	26	must	must	AUX
cord-326631-7gd3hjc3	118	27	be	be	AUX
cord-326631-7gd3hjc3	118	28	conditioned	condition	VERB
cord-326631-7gd3hjc3	118	29	by	by	ADP
cord-326631-7gd3hjc3	118	30	still	still	ADV
cord-326631-7gd3hjc3	118	31	being	be	AUX
cord-326631-7gd3hjc3	118	32	infectious	infectious	ADJ
cord-326631-7gd3hjc3	118	33	at	at	ADP
cord-326631-7gd3hjc3	118	34	time	time	NOUN
cord-326631-7gd3hjc3	118	35	0	0	NUM
cord-326631-7gd3hjc3	118	36	,	,	PUNCT
cord-326631-7gd3hjc3	118	37	hence	hence	ADV
cord-326631-7gd3hjc3	118	38	,	,	PUNCT
cord-326631-7gd3hjc3	118	39	the	the	DET
cord-326631-7gd3hjc3	118	40	rate	rate	NOUN
cord-326631-7gd3hjc3	118	41	of	of	ADP
cord-326631-7gd3hjc3	118	42	change	change	NOUN
cord-326631-7gd3hjc3	118	43	of	of	ADP
cord-326631-7gd3hjc3	118	44	the	the	DET
cord-326631-7gd3hjc3	118	45	number	number	NOUN
cord-326631-7gd3hjc3	118	46	of	of	ADP
cord-326631-7gd3hjc3	118	47	infectious	infectious	ADJ
cord-326631-7gd3hjc3	118	48	individuals	individual	NOUN
cord-326631-7gd3hjc3	118	49	at	at	ADP
cord-326631-7gd3hjc3	118	50	time	time	NOUN
cord-326631-7gd3hjc3	118	51	t	t	PROPN
cord-326631-7gd3hjc3	118	52	is	be	AUX
cord-326631-7gd3hjc3	118	53	those	those	PRON
cord-326631-7gd3hjc3	118	54	who	who	PRON
cord-326631-7gd3hjc3	118	55	leave	leave	VERB
cord-326631-7gd3hjc3	118	56	class	class	NOUN
cord-326631-7gd3hjc3	118	57	i	i	PRON
cord-326631-7gd3hjc3	118	58	enter	enter	VERB
cord-326631-7gd3hjc3	118	59	class	class	NOUN
cord-326631-7gd3hjc3	118	60	r	r	NOUN
cord-326631-7gd3hjc3	118	61	,	,	PUNCT
cord-326631-7gd3hjc3	118	62	hence	hence	ADV
cord-326631-7gd3hjc3	118	63	in	in	ADP
cord-326631-7gd3hjc3	118	64	appendix	appendix	PROPN
cord-326631-7gd3hjc3	118	65	b	b	PROPN
cord-326631-7gd3hjc3	118	66	,	,	PUNCT
cord-326631-7gd3hjc3	118	67	we	we	PRON
cord-326631-7gd3hjc3	118	68	show	show	VERB
cord-326631-7gd3hjc3	118	69	that	that	SCONJ
cord-326631-7gd3hjc3	118	70	if	if	SCONJ
cord-326631-7gd3hjc3	118	71	the	the	DET
cord-326631-7gd3hjc3	118	72	infectious	infectious	ADJ
cord-326631-7gd3hjc3	118	73	period	period	NOUN
cord-326631-7gd3hjc3	118	74	is	be	AUX
cord-326631-7gd3hjc3	118	75	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	118	76	distributed	distribute	VERB
cord-326631-7gd3hjc3	118	77	then	then	ADV
cord-326631-7gd3hjc3	118	78	eqs	eqs	PROPN
cord-326631-7gd3hjc3	118	79	.	.	PUNCT
cord-326631-7gd3hjc3	119	1	(	(	PUNCT
cord-326631-7gd3hjc3	119	2	11	11	NUM
cord-326631-7gd3hjc3	119	3	)	)	PUNCT
cord-326631-7gd3hjc3	119	4	reduce	reduce	VERB
cord-326631-7gd3hjc3	119	5	to	to	ADP
cord-326631-7gd3hjc3	119	6	the	the	DET
cord-326631-7gd3hjc3	119	7	the	the	DET
cord-326631-7gd3hjc3	119	8	standard	standard	ADJ
cord-326631-7gd3hjc3	119	9	sir	sir	PROPN
cord-326631-7gd3hjc3	119	10	model	model	NOUN
cord-326631-7gd3hjc3	119	11	(	(	PUNCT
cord-326631-7gd3hjc3	119	12	1	1	NUM
cord-326631-7gd3hjc3	119	13	)	)	PUNCT
cord-326631-7gd3hjc3	119	14	.	.	PUNCT
cord-326631-7gd3hjc3	120	1	as	as	ADP
cord-326631-7gd3hjc3	120	2	in	in	ADP
cord-326631-7gd3hjc3	120	3	the	the	DET
cord-326631-7gd3hjc3	120	4	standard	standard	ADJ
cord-326631-7gd3hjc3	120	5	sir	sir	PROPN
cord-326631-7gd3hjc3	120	6	model	model	NOUN
cord-326631-7gd3hjc3	120	7	(	(	PUNCT
cord-326631-7gd3hjc3	120	8	1	1	NUM
cord-326631-7gd3hjc3	120	9	)	)	PUNCT
cord-326631-7gd3hjc3	120	10	,	,	PUNCT
cord-326631-7gd3hjc3	120	11	the	the	DET
cord-326631-7gd3hjc3	120	12	population	population	NOUN
cord-326631-7gd3hjc3	120	13	size	size	NOUN
cord-326631-7gd3hjc3	120	14	is	be	AUX
cord-326631-7gd3hjc3	120	15	invariant	invariant	ADJ
cord-326631-7gd3hjc3	120	16	(	(	PUNCT
cord-326631-7gd3hjc3	120	17	s	s	X
cord-326631-7gd3hjc3	120	18	+	+	CCONJ
cord-326631-7gd3hjc3	120	19	i	i	NOUN
cord-326631-7gd3hjc3	120	20	+	+	CCONJ
cord-326631-7gd3hjc3	121	1	r	r	NOUN
cord-326631-7gd3hjc3	121	2	=	=	SYM
cord-326631-7gd3hjc3	121	3	1	1	NUM
cord-326631-7gd3hjc3	121	4	)	)	PUNCT
cord-326631-7gd3hjc3	121	5	,	,	PUNCT
cord-326631-7gd3hjc3	121	6	s	s	X
cord-326631-7gd3hjc3	121	7	≥	≥	NOUN
cord-326631-7gd3hjc3	121	8	0	0	NUM
cord-326631-7gd3hjc3	121	9	,	,	PUNCT
cord-326631-7gd3hjc3	121	10	and	and	CCONJ
cord-326631-7gd3hjc3	121	11	s(∞	s(∞	PROPN
cord-326631-7gd3hjc3	121	12	)	)	PUNCT
cord-326631-7gd3hjc3	121	13	exists	exist	VERB
cord-326631-7gd3hjc3	121	14	.	.	PUNCT
cord-326631-7gd3hjc3	122	1	establishing	establish	VERB
cord-326631-7gd3hjc3	122	2	that	that	DET
cord-326631-7gd3hjc3	122	3	i(∞	i(∞	PROPN
cord-326631-7gd3hjc3	122	4	)	)	PUNCT
cord-326631-7gd3hjc3	122	5	=	=	NOUN
cord-326631-7gd3hjc3	122	6	0	0	NUM
cord-326631-7gd3hjc3	122	7	(	(	PUNCT
cord-326631-7gd3hjc3	122	8	so	so	ADV
cord-326631-7gd3hjc3	122	9	the	the	DET
cord-326631-7gd3hjc3	122	10	disease	disease	NOUN
cord-326631-7gd3hjc3	122	11	will	will	AUX
cord-326631-7gd3hjc3	122	12	burn	burn	VERB
cord-326631-7gd3hjc3	122	13	out	out	ADP
cord-326631-7gd3hjc3	122	14	regardless	regardless	ADV
cord-326631-7gd3hjc3	122	15	of	of	ADP
cord-326631-7gd3hjc3	122	16	the	the	DET
cord-326631-7gd3hjc3	122	17	infectious	infectious	ADJ
cord-326631-7gd3hjc3	122	18	period	period	NOUN
cord-326631-7gd3hjc3	122	19	distribution	distribution	NOUN
cord-326631-7gd3hjc3	122	20	)	)	PUNCT
cord-326631-7gd3hjc3	122	21	requires	require	VERB
cord-326631-7gd3hjc3	122	22	a	a	DET
cord-326631-7gd3hjc3	122	23	little	little	ADJ
cord-326631-7gd3hjc3	122	24	more	more	ADJ
cord-326631-7gd3hjc3	122	25	work	work	NOUN
cord-326631-7gd3hjc3	122	26	.	.	PUNCT
cord-326631-7gd3hjc3	123	1	since	since	SCONJ
cord-326631-7gd3hjc3	123	2	f	f	PROPN
cord-326631-7gd3hjc3	123	3	(	(	PUNCT
cord-326631-7gd3hjc3	123	4	t	t	NOUN
cord-326631-7gd3hjc3	123	5	)	)	PUNCT
cord-326631-7gd3hjc3	123	6	and	and	CCONJ
cord-326631-7gd3hjc3	123	7	l(τ	l(τ	PROPN
cord-326631-7gd3hjc3	123	8	,	,	PUNCT
cord-326631-7gd3hjc3	123	9	t	t	NOUN
cord-326631-7gd3hjc3	123	10	)	)	PUNCT
cord-326631-7gd3hjc3	123	11	are	be	AUX
cord-326631-7gd3hjc3	123	12	probability	probability	NOUN
cord-326631-7gd3hjc3	123	13	densities	density	NOUN
cord-326631-7gd3hjc3	123	14	,	,	PUNCT
cord-326631-7gd3hjc3	123	15	∞	∞	NUM
cord-326631-7gd3hjc3	123	16	0	0	PUNCT
cord-326631-7gd3hjc3	124	1	f	f	PROPN
cord-326631-7gd3hjc3	124	2	(	(	PUNCT
cord-326631-7gd3hjc3	124	3	t	t	PROPN
cord-326631-7gd3hjc3	124	4	)	)	PUNCT
cord-326631-7gd3hjc3	124	5	dt	dt	PROPN
cord-326631-7gd3hjc3	124	6	=	=	SYM
cord-326631-7gd3hjc3	124	7	∞	∞	NUM
cord-326631-7gd3hjc3	124	8	0	0	NUM
cord-326631-7gd3hjc3	124	9	l(τ	l(τ	NOUN
cord-326631-7gd3hjc3	124	10	,	,	PUNCT
cord-326631-7gd3hjc3	124	11	t	t	PROPN
cord-326631-7gd3hjc3	124	12	)	)	PUNCT
cord-326631-7gd3hjc3	124	13	dt	dt	PROPN
cord-326631-7gd3hjc3	124	14	=	=	SYM
cord-326631-7gd3hjc3	124	15	1	1	NUM
cord-326631-7gd3hjc3	124	16	;	;	PUNCT
cord-326631-7gd3hjc3	124	17	consequently	consequently	ADV
cord-326631-7gd3hjc3	124	18	,	,	PUNCT
cord-326631-7gd3hjc3	124	19	switching	switch	VERB
cord-326631-7gd3hjc3	124	20	the	the	DET
cord-326631-7gd3hjc3	124	21	order	order	NOUN
cord-326631-7gd3hjc3	124	22	of	of	ADP
cord-326631-7gd3hjc3	124	23	integrations	integration	NOUN
cord-326631-7gd3hjc3	124	24	,	,	PUNCT
cord-326631-7gd3hjc3	124	25	we	we	PRON
cord-326631-7gd3hjc3	124	26	find	find	VERB
cord-326631-7gd3hjc3	124	27	next	next	ADV
cord-326631-7gd3hjc3	124	28	,	,	PUNCT
cord-326631-7gd3hjc3	124	29	integrating	integrate	VERB
cord-326631-7gd3hjc3	124	30	from	from	ADP
cord-326631-7gd3hjc3	124	31	0	0	NUM
cord-326631-7gd3hjc3	124	32	to	to	ADP
cord-326631-7gd3hjc3	124	33	∞	∞	NUM
cord-326631-7gd3hjc3	124	34	on	on	ADP
cord-326631-7gd3hjc3	124	35	both	both	DET
cord-326631-7gd3hjc3	124	36	sides	side	NOUN
cord-326631-7gd3hjc3	124	37	of	of	ADP
cord-326631-7gd3hjc3	124	38	eq	eq	PROPN
cord-326631-7gd3hjc3	124	39	.	.	PUNCT
cord-326631-7gd3hjc3	125	1	(	(	PUNCT
cord-326631-7gd3hjc3	125	2	11f	11f	NUM
cord-326631-7gd3hjc3	125	3	)	)	PUNCT
cord-326631-7gd3hjc3	125	4	,	,	PUNCT
cord-326631-7gd3hjc3	125	5	we	we	PRON
cord-326631-7gd3hjc3	125	6	have	have	VERB
cord-326631-7gd3hjc3	125	7	i(∞	i(∞	PROPN
cord-326631-7gd3hjc3	125	8	)	)	PUNCT
cord-326631-7gd3hjc3	125	9	=	=	SYM
cord-326631-7gd3hjc3	125	10	0	0	NUM
cord-326631-7gd3hjc3	125	11	.	.	PUNCT
cord-326631-7gd3hjc3	126	1	to	to	PART
cord-326631-7gd3hjc3	126	2	relate	relate	VERB
cord-326631-7gd3hjc3	126	3	the	the	DET
cord-326631-7gd3hjc3	126	4	final	final	ADJ
cord-326631-7gd3hjc3	126	5	size	size	NOUN
cord-326631-7gd3hjc3	126	6	in	in	ADP
cord-326631-7gd3hjc3	126	7	the	the	DET
cord-326631-7gd3hjc3	126	8	present	present	ADJ
cord-326631-7gd3hjc3	126	9	model	model	NOUN
cord-326631-7gd3hjc3	126	10	to	to	ADP
cord-326631-7gd3hjc3	126	11	the	the	DET
cord-326631-7gd3hjc3	126	12	usual	usual	ADJ
cord-326631-7gd3hjc3	126	13	formula	formula	NOUN
cord-326631-7gd3hjc3	126	14	(	(	PUNCT
cord-326631-7gd3hjc3	126	15	5	5	NUM
cord-326631-7gd3hjc3	126	16	)	)	PUNCT
cord-326631-7gd3hjc3	126	17	,	,	PUNCT
cord-326631-7gd3hjc3	126	18	we	we	PRON
cord-326631-7gd3hjc3	126	19	need	need	VERB
cord-326631-7gd3hjc3	126	20	an	an	DET
cord-326631-7gd3hjc3	126	21	expression	expression	NOUN
cord-326631-7gd3hjc3	126	22	for	for	ADP
cord-326631-7gd3hjc3	126	23	the	the	DET
cord-326631-7gd3hjc3	126	24	basic	basic	ADJ
cord-326631-7gd3hjc3	126	25	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	126	26	number	number	NOUN
cord-326631-7gd3hjc3	126	27	r	r	NOUN
cord-326631-7gd3hjc3	126	28	0	0	NUM
cord-326631-7gd3hjc3	126	29	.	.	PUNCT
cord-326631-7gd3hjc3	127	1	feng	feng	PROPN
cord-326631-7gd3hjc3	127	2	and	and	CCONJ
cord-326631-7gd3hjc3	127	3	thieme	thieme	PROPN
cord-326631-7gd3hjc3	127	4	(	(	PUNCT
cord-326631-7gd3hjc3	127	5	2000	2000	NUM
cord-326631-7gd3hjc3	127	6	)	)	PUNCT
cord-326631-7gd3hjc3	127	7	have	have	VERB
cord-326631-7gd3hjc3	127	8	we	we	PRON
cord-326631-7gd3hjc3	127	9	now	now	ADV
cord-326631-7gd3hjc3	127	10	divide	divide	VERB
cord-326631-7gd3hjc3	127	11	eq	eq	PROPN
cord-326631-7gd3hjc3	127	12	.	.	PUNCT
cord-326631-7gd3hjc3	128	1	(	(	PUNCT
cord-326631-7gd3hjc3	128	2	11b	11b	NUM
cord-326631-7gd3hjc3	128	3	)	)	PUNCT
cord-326631-7gd3hjc3	129	1	by	by	ADP
cord-326631-7gd3hjc3	129	2	s	s	NOUN
cord-326631-7gd3hjc3	129	3	and	and	CCONJ
cord-326631-7gd3hjc3	129	4	integrate	integrate	VERB
cord-326631-7gd3hjc3	129	5	,	,	PUNCT
cord-326631-7gd3hjc3	129	6	yielding	yield	VERB
cord-326631-7gd3hjc3	129	7	therefore	therefore	ADV
cord-326631-7gd3hjc3	129	8	,	,	PUNCT
cord-326631-7gd3hjc3	129	9	the	the	DET
cord-326631-7gd3hjc3	129	10	usual	usual	ADJ
cord-326631-7gd3hjc3	129	11	final	final	ADJ
cord-326631-7gd3hjc3	129	12	size	size	NOUN
cord-326631-7gd3hjc3	129	13	formula	formula	NOUN
cord-326631-7gd3hjc3	129	14	(	(	PUNCT
cord-326631-7gd3hjc3	129	15	5	5	NUM
cord-326631-7gd3hjc3	129	16	)	)	PUNCT
cord-326631-7gd3hjc3	129	17	will	will	AUX
cord-326631-7gd3hjc3	129	18	follow	follow	VERB
cord-326631-7gd3hjc3	129	19	if	if	SCONJ
cord-326631-7gd3hjc3	129	20	∞	∞	NUM
cord-326631-7gd3hjc3	129	21	0	0	NUM
cord-326631-7gd3hjc3	129	22	i(t	i(t	PROPN
cord-326631-7gd3hjc3	129	23	)	)	PUNCT
cord-326631-7gd3hjc3	129	24	dt	dt	PROPN
cord-326631-7gd3hjc3	129	25	=	=	SYM
cord-326631-7gd3hjc3	129	26	t	t	PROPN
cord-326631-7gd3hjc3	129	27	z.	z.	PROPN
cord-326631-7gd3hjc3	130	1	this	this	PRON
cord-326631-7gd3hjc3	130	2	is	be	AUX
cord-326631-7gd3hjc3	130	3	plausible	plausible	ADJ
cord-326631-7gd3hjc3	130	4	,	,	PUNCT
cord-326631-7gd3hjc3	130	5	intuitively	intuitively	ADV
cord-326631-7gd3hjc3	130	6	,	,	PUNCT
cord-326631-7gd3hjc3	130	7	since	since	SCONJ
cord-326631-7gd3hjc3	130	8	the	the	DET
cord-326631-7gd3hjc3	130	9	integral	integral	ADJ
cord-326631-7gd3hjc3	130	10	∞	∞	PROPN
cord-326631-7gd3hjc3	130	11	0	0	NUM
cord-326631-7gd3hjc3	130	12	i(t	i(t	PROPN
cord-326631-7gd3hjc3	130	13	)	)	PUNCT
cord-326631-7gd3hjc3	130	14	dt	dt	PROPN
cord-326631-7gd3hjc3	130	15	sums	sum	VERB
cord-326631-7gd3hjc3	130	16	all	all	DET
cord-326631-7gd3hjc3	130	17	infectious	infectious	ADJ
cord-326631-7gd3hjc3	130	18	individuals	individual	NOUN
cord-326631-7gd3hjc3	130	19	,	,	PUNCT
cord-326631-7gd3hjc3	130	20	weighted	weight	VERB
cord-326631-7gd3hjc3	130	21	by	by	ADP
cord-326631-7gd3hjc3	130	22	the	the	DET
cord-326631-7gd3hjc3	130	23	time	time	NOUN
cord-326631-7gd3hjc3	130	24	they	they	PRON
cord-326631-7gd3hjc3	130	25	are	be	AUX
cord-326631-7gd3hjc3	130	26	infectious	infectious	ADJ
cord-326631-7gd3hjc3	130	27	;	;	PUNCT
cord-326631-7gd3hjc3	130	28	this	this	PRON
cord-326631-7gd3hjc3	130	29	must	must	AUX
cord-326631-7gd3hjc3	130	30	also	also	ADV
cord-326631-7gd3hjc3	130	31	equal	equal	VERB
cord-326631-7gd3hjc3	130	32	the	the	DET
cord-326631-7gd3hjc3	130	33	mean	mean	ADJ
cord-326631-7gd3hjc3	130	34	infectious	infectious	ADJ
cord-326631-7gd3hjc3	130	35	period	period	NOUN
cord-326631-7gd3hjc3	130	36	t	t	PROPN
cord-326631-7gd3hjc3	130	37	times	time	NOUN
cord-326631-7gd3hjc3	130	38	the	the	DET
cord-326631-7gd3hjc3	130	39	number	number	NOUN
cord-326631-7gd3hjc3	130	40	of	of	ADP
cord-326631-7gd3hjc3	130	41	individuals	individual	NOUN
cord-326631-7gd3hjc3	130	42	infected	infect	VERB
cord-326631-7gd3hjc3	130	43	over	over	ADP
cord-326631-7gd3hjc3	130	44	the	the	DET
cord-326631-7gd3hjc3	130	45	course	course	NOUN
cord-326631-7gd3hjc3	130	46	of	of	ADP
cord-326631-7gd3hjc3	130	47	the	the	DET
cord-326631-7gd3hjc3	130	48	entire	entire	ADJ
cord-326631-7gd3hjc3	130	49	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	130	50	(	(	PUNCT
cord-326631-7gd3hjc3	130	51	the	the	DET
cord-326631-7gd3hjc3	130	52	final	final	ADJ
cord-326631-7gd3hjc3	130	53	size	size	NOUN
cord-326631-7gd3hjc3	130	54	z	z	NUM
cord-326631-7gd3hjc3	130	55	)	)	PUNCT
cord-326631-7gd3hjc3	130	56	.	.	PUNCT
cord-326631-7gd3hjc3	131	1	more	more	ADV
cord-326631-7gd3hjc3	131	2	rigorously	rigorously	ADV
cord-326631-7gd3hjc3	131	3	,	,	PUNCT
cord-326631-7gd3hjc3	131	4	in	in	ADP
cord-326631-7gd3hjc3	131	5	appendix	appendix	PROPN
cord-326631-7gd3hjc3	131	6	b	b	PROPN
cord-326631-7gd3hjc3	131	7	we	we	PRON
cord-326631-7gd3hjc3	131	8	prove	prove	VERB
cord-326631-7gd3hjc3	131	9	lemma	lemma	NOUN
cord-326631-7gd3hjc3	131	10	6.1	6.1	NUM
cord-326631-7gd3hjc3	131	11	.	.	PUNCT
cord-326631-7gd3hjc3	132	1	for	for	ADP
cord-326631-7gd3hjc3	132	2	the	the	DET
cord-326631-7gd3hjc3	132	3	model	model	NOUN
cord-326631-7gd3hjc3	132	4	specified	specify	VERB
cord-326631-7gd3hjc3	132	5	by	by	ADP
cord-326631-7gd3hjc3	132	6	eqs	eqs	PROPN
cord-326631-7gd3hjc3	132	7	.	.	PUNCT
cord-326631-7gd3hjc3	133	1	(	(	PUNCT
cord-326631-7gd3hjc3	133	2	11	11	NUM
cord-326631-7gd3hjc3	133	3	)	)	PUNCT
cord-326631-7gd3hjc3	133	4	,	,	PUNCT
cord-326631-7gd3hjc3	133	5	in	in	ADP
cord-326631-7gd3hjc3	133	6	the	the	DET
cord-326631-7gd3hjc3	133	7	limit	limit	NOUN
cord-326631-7gd3hjc3	133	8	(	(	PUNCT
cord-326631-7gd3hjc3	133	9	11	11	NUM
cord-326631-7gd3hjc3	133	10	)	)	PUNCT
cord-326631-7gd3hjc3	133	11	.	.	PUNCT
cord-326631-7gd3hjc3	134	1	if	if	SCONJ
cord-326631-7gd3hjc3	134	2	the	the	DET
cord-326631-7gd3hjc3	134	3	initial	initial	ADJ
cord-326631-7gd3hjc3	134	4	number	number	NOUN
cord-326631-7gd3hjc3	134	5	of	of	ADP
cord-326631-7gd3hjc3	134	6	infectious	infectious	ADJ
cord-326631-7gd3hjc3	134	7	individuals	individual	NOUN
cord-326631-7gd3hjc3	134	8	is	be	AUX
cord-326631-7gd3hjc3	134	9	small	small	ADJ
cord-326631-7gd3hjc3	134	10	(	(	PUNCT
cord-326631-7gd3hjc3	134	11	i(0	i(0	NOUN
cord-326631-7gd3hjc3	134	12	)	)	PUNCT
cord-326631-7gd3hjc3	134	13	→	→	NUM
cord-326631-7gd3hjc3	134	14	0	0	NUM
cord-326631-7gd3hjc3	134	15	)	)	PUNCT
cord-326631-7gd3hjc3	134	16	,	,	PUNCT
cord-326631-7gd3hjc3	134	17	then	then	ADV
cord-326631-7gd3hjc3	134	18	the	the	DET
cord-326631-7gd3hjc3	134	19	final	final	ADJ
cord-326631-7gd3hjc3	134	20	size	size	NOUN
cord-326631-7gd3hjc3	134	21	of	of	ADP
cord-326631-7gd3hjc3	134	22	the	the	DET
cord-326631-7gd3hjc3	134	23	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	134	24	(	(	PUNCT
cord-326631-7gd3hjc3	134	25	z	z	NOUN
cord-326631-7gd3hjc3	134	26	)	)	PUNCT
cord-326631-7gd3hjc3	134	27	is	be	AUX
cord-326631-7gd3hjc3	134	28	given	give	VERB
cord-326631-7gd3hjc3	134	29	by	by	ADP
cord-326631-7gd3hjc3	134	30	the	the	DET
cord-326631-7gd3hjc3	134	31	classical	classical	ADJ
cord-326631-7gd3hjc3	134	32	formula	formula	NOUN
cord-326631-7gd3hjc3	134	33	(	(	PUNCT
cord-326631-7gd3hjc3	134	34	5	5	NUM
cord-326631-7gd3hjc3	134	35	)	)	PUNCT
cord-326631-7gd3hjc3	134	36	.	.	PUNCT
cord-326631-7gd3hjc3	135	1	in	in	ADP
cord-326631-7gd3hjc3	135	2	this	this	DET
cord-326631-7gd3hjc3	135	3	formula	formula	NOUN
cord-326631-7gd3hjc3	135	4	,	,	PUNCT
cord-326631-7gd3hjc3	135	5	the	the	DET
cord-326631-7gd3hjc3	135	6	basic	basic	ADJ
cord-326631-7gd3hjc3	135	7	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	135	8	number	number	NOUN
cord-326631-7gd3hjc3	135	9	is	be	AUX
cord-326631-7gd3hjc3	135	10	r	r	NOUN
cord-326631-7gd3hjc3	135	11	0	0	NUM
cord-326631-7gd3hjc3	135	12	=	=	NOUN
cord-326631-7gd3hjc3	135	13	βt	βt	INTJ
cord-326631-7gd3hjc3	135	14	,	,	PUNCT
cord-326631-7gd3hjc3	135	15	where	where	SCONJ
cord-326631-7gd3hjc3	135	16	t	t	PROPN
cord-326631-7gd3hjc3	135	17	is	be	AUX
cord-326631-7gd3hjc3	135	18	the	the	DET
cord-326631-7gd3hjc3	135	19	mean	mean	ADJ
cord-326631-7gd3hjc3	135	20	infectious	infectious	ADJ
cord-326631-7gd3hjc3	135	21	period	period	NOUN
cord-326631-7gd3hjc3	135	22	.	.	PUNCT
cord-326631-7gd3hjc3	136	1	with	with	ADP
cord-326631-7gd3hjc3	136	2	modest	modest	ADJ
cord-326631-7gd3hjc3	136	3	additional	additional	ADJ
cord-326631-7gd3hjc3	136	4	effort	effort	NOUN
cord-326631-7gd3hjc3	136	5	,	,	PUNCT
cord-326631-7gd3hjc3	136	6	we	we	PRON
cord-326631-7gd3hjc3	136	7	can	can	AUX
cord-326631-7gd3hjc3	136	8	generalize	generalize	VERB
cord-326631-7gd3hjc3	136	9	theorem	theorem	NOUN
cord-326631-7gd3hjc3	136	10	6.1	6.1	NUM
cord-326631-7gd3hjc3	136	11	to	to	ADP
cord-326631-7gd3hjc3	136	12	the	the	DET
cord-326631-7gd3hjc3	136	13	multiple	multiple	ADJ
cord-326631-7gd3hjc3	136	14	stage	stage	NOUN
cord-326631-7gd3hjc3	136	15	si	si	PROPN
cord-326631-7gd3hjc3	136	16	n	n	NOUN
cord-326631-7gd3hjc3	136	17	r	r	NOUN
cord-326631-7gd3hjc3	136	18	model	model	NOUN
cord-326631-7gd3hjc3	136	19	,	,	PUNCT
cord-326631-7gd3hjc3	136	20	i.e.	i.e.	X
cord-326631-7gd3hjc3	136	21	,	,	PUNCT
cord-326631-7gd3hjc3	136	22	the	the	DET
cord-326631-7gd3hjc3	136	23	usual	usual	ADJ
cord-326631-7gd3hjc3	136	24	final	final	ADJ
cord-326631-7gd3hjc3	136	25	size	size	NOUN
cord-326631-7gd3hjc3	136	26	formula	formula	NOUN
cord-326631-7gd3hjc3	136	27	(	(	PUNCT
cord-326631-7gd3hjc3	136	28	5	5	NUM
cord-326631-7gd3hjc3	136	29	)	)	PUNCT
cord-326631-7gd3hjc3	136	30	is	be	AUX
cord-326631-7gd3hjc3	136	31	still	still	ADV
cord-326631-7gd3hjc3	136	32	valid	valid	ADJ
cord-326631-7gd3hjc3	136	33	if	if	SCONJ
cord-326631-7gd3hjc3	136	34	there	there	PRON
cord-326631-7gd3hjc3	136	35	are	be	VERB
cord-326631-7gd3hjc3	136	36	multiple	multiple	ADJ
cord-326631-7gd3hjc3	136	37	infectious	infectious	ADJ
cord-326631-7gd3hjc3	136	38	stages	stage	NOUN
cord-326631-7gd3hjc3	136	39	and	and	CCONJ
cord-326631-7gd3hjc3	136	40	the	the	DET
cord-326631-7gd3hjc3	136	41	durations	duration	NOUN
cord-326631-7gd3hjc3	136	42	of	of	ADP
cord-326631-7gd3hjc3	136	43	each	each	DET
cord-326631-7gd3hjc3	136	44	stage	stage	NOUN
cord-326631-7gd3hjc3	136	45	are	be	AUX
cord-326631-7gd3hjc3	136	46	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	136	47	distributed	distribute	VERB
cord-326631-7gd3hjc3	136	48	.	.	PUNCT
cord-326631-7gd3hjc3	137	1	recall	recall	VERB
cord-326631-7gd3hjc3	137	2	that	that	SCONJ
cord-326631-7gd3hjc3	137	3	latent	latent	ADJ
cord-326631-7gd3hjc3	137	4	stages	stage	NOUN
cord-326631-7gd3hjc3	137	5	can	can	AUX
cord-326631-7gd3hjc3	137	6	be	be	AUX
cord-326631-7gd3hjc3	137	7	considered	consider	VERB
cord-326631-7gd3hjc3	137	8	infectious	infectious	ADJ
cord-326631-7gd3hjc3	137	9	stages	stage	NOUN
cord-326631-7gd3hjc3	137	10	with	with	ADP
cord-326631-7gd3hjc3	137	11	zero	zero	NUM
cord-326631-7gd3hjc3	137	12	transmission	transmission	NOUN
cord-326631-7gd3hjc3	137	13	rate	rate	NOUN
cord-326631-7gd3hjc3	137	14	,	,	PUNCT
cord-326631-7gd3hjc3	137	15	so	so	SCONJ
cord-326631-7gd3hjc3	137	16	we	we	PRON
cord-326631-7gd3hjc3	137	17	do	do	AUX
cord-326631-7gd3hjc3	137	18	not	not	PART
cord-326631-7gd3hjc3	137	19	make	make	VERB
cord-326631-7gd3hjc3	137	20	any	any	DET
cord-326631-7gd3hjc3	137	21	explicit	explicit	ADJ
cord-326631-7gd3hjc3	137	22	reference	reference	NOUN
cord-326631-7gd3hjc3	137	23	to	to	ADP
cord-326631-7gd3hjc3	137	24	latency	latency	NOUN
cord-326631-7gd3hjc3	137	25	.	.	PUNCT
cord-326631-7gd3hjc3	138	1	as	as	ADP
cord-326631-7gd3hjc3	138	2	in	in	ADP
cord-326631-7gd3hjc3	138	3	all	all	DET
cord-326631-7gd3hjc3	138	4	the	the	DET
cord-326631-7gd3hjc3	138	5	situations	situation	NOUN
cord-326631-7gd3hjc3	138	6	considered	consider	VERB
cord-326631-7gd3hjc3	138	7	above	above	ADV
cord-326631-7gd3hjc3	138	8	,	,	PUNCT
cord-326631-7gd3hjc3	138	9	we	we	PRON
cord-326631-7gd3hjc3	138	10	assume	assume	VERB
cord-326631-7gd3hjc3	138	11	that	that	SCONJ
cord-326631-7gd3hjc3	138	12	vital	vital	ADJ
cord-326631-7gd3hjc3	138	13	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	138	14	(	(	PUNCT
cord-326631-7gd3hjc3	138	15	births	birth	NOUN
cord-326631-7gd3hjc3	138	16	and	and	CCONJ
cord-326631-7gd3hjc3	138	17	deaths	death	NOUN
cord-326631-7gd3hjc3	138	18	)	)	PUNCT
cord-326631-7gd3hjc3	138	19	can	can	AUX
cord-326631-7gd3hjc3	138	20	be	be	AUX
cord-326631-7gd3hjc3	138	21	ignored	ignore	VERB
cord-326631-7gd3hjc3	138	22	and	and	CCONJ
cord-326631-7gd3hjc3	138	23	that	that	SCONJ
cord-326631-7gd3hjc3	138	24	recovery	recovery	NOUN
cord-326631-7gd3hjc3	138	25	entails	entail	VERB
cord-326631-7gd3hjc3	138	26	lifelong	lifelong	ADJ
cord-326631-7gd3hjc3	138	27	immunity	immunity	NOUN
cord-326631-7gd3hjc3	138	28	.	.	PUNCT
cord-326631-7gd3hjc3	139	1	suppose	suppose	VERB
cord-326631-7gd3hjc3	139	2	the	the	DET
cord-326631-7gd3hjc3	139	3	ith	ith	PROPN
cord-326631-7gd3hjc3	139	4	infectious	infectious	ADJ
cord-326631-7gd3hjc3	139	5	stage	stage	NOUN
cord-326631-7gd3hjc3	139	6	has	have	VERB
cord-326631-7gd3hjc3	139	7	duration	duration	NOUN
cord-326631-7gd3hjc3	139	8	distribution	distribution	NOUN
cord-326631-7gd3hjc3	139	9	with	with	ADP
cord-326631-7gd3hjc3	139	10	probability	probability	NOUN
cord-326631-7gd3hjc3	139	11	density	density	NOUN
cord-326631-7gd3hjc3	140	1	f	f	X
cord-326631-7gd3hjc3	140	2	i	i	PROPN
cord-326631-7gd3hjc3	140	3	(	(	PUNCT
cord-326631-7gd3hjc3	140	4	t	t	NOUN
cord-326631-7gd3hjc3	140	5	)	)	PUNCT
cord-326631-7gd3hjc3	140	6	and	and	CCONJ
cord-326631-7gd3hjc3	140	7	mean	mean	VERB
cord-326631-7gd3hjc3	140	8	t	t	PROPN
cord-326631-7gd3hjc3	140	9	i	i	PRON
cord-326631-7gd3hjc3	140	10	.	.	PUNCT
cord-326631-7gd3hjc3	141	1	thus	thus	ADV
cord-326631-7gd3hjc3	141	2	,	,	PUNCT
cord-326631-7gd3hjc3	141	3	in	in	ADP
cord-326631-7gd3hjc3	141	4	the	the	DET
cord-326631-7gd3hjc3	141	5	special	special	ADJ
cord-326631-7gd3hjc3	141	6	case	case	NOUN
cord-326631-7gd3hjc3	141	7	that	that	SCONJ
cord-326631-7gd3hjc3	141	8	durations	duration	NOUN
cord-326631-7gd3hjc3	141	9	in	in	ADP
cord-326631-7gd3hjc3	141	10	each	each	DET
cord-326631-7gd3hjc3	141	11	stage	stage	NOUN
cord-326631-7gd3hjc3	141	12	follow	follow	VERB
cord-326631-7gd3hjc3	141	13	gamma	gamma	PROPN
cord-326631-7gd3hjc3	141	14	distributions	distribution	NOUN
cord-326631-7gd3hjc3	141	15	(	(	PUNCT
cord-326631-7gd3hjc3	141	16	10	10	NUM
cord-326631-7gd3hjc3	141	17	)	)	PUNCT
cord-326631-7gd3hjc3	141	18	,	,	PUNCT
cord-326631-7gd3hjc3	141	19	we	we	PRON
cord-326631-7gd3hjc3	141	20	have	have	VERB
cord-326631-7gd3hjc3	141	21	f	f	PROPN
cord-326631-7gd3hjc3	141	22	i	i	PROPN
cord-326631-7gd3hjc3	141	23	(	(	PUNCT
cord-326631-7gd3hjc3	141	24	t	t	NOUN
cord-326631-7gd3hjc3	141	25	)	)	PUNCT
cord-326631-7gd3hjc3	141	26	=	=	NOUN
cord-326631-7gd3hjc3	141	27	g	g	PROPN
cord-326631-7gd3hjc3	141	28	ki	ki	PROPN
cord-326631-7gd3hjc3	141	29	φi	φi	PROPN
cord-326631-7gd3hjc3	141	30	(	(	PUNCT
cord-326631-7gd3hjc3	141	31	t	t	NOUN
cord-326631-7gd3hjc3	141	32	)	)	PUNCT
cord-326631-7gd3hjc3	141	33	and	and	CCONJ
cord-326631-7gd3hjc3	141	34	the	the	DET
cord-326631-7gd3hjc3	141	35	the	the	DET
cord-326631-7gd3hjc3	141	36	rate	rate	NOUN
cord-326631-7gd3hjc3	141	37	of	of	ADP
cord-326631-7gd3hjc3	141	38	change	change	NOUN
cord-326631-7gd3hjc3	141	39	of	of	ADP
cord-326631-7gd3hjc3	141	40	the	the	DET
cord-326631-7gd3hjc3	141	41	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	141	42	class	class	NOUN
cord-326631-7gd3hjc3	141	43	is	be	AUX
cord-326631-7gd3hjc3	141	44	given	give	VERB
cord-326631-7gd3hjc3	141	45	by	by	ADP
cord-326631-7gd3hjc3	141	46	eq	eq	PROPN
cord-326631-7gd3hjc3	141	47	.	.	PUNCT
cord-326631-7gd3hjc3	142	1	(	(	PUNCT
cord-326631-7gd3hjc3	142	2	6a	6a	NOUN
cord-326631-7gd3hjc3	142	3	)	)	PUNCT
cord-326631-7gd3hjc3	142	4	,	,	PUNCT
cord-326631-7gd3hjc3	142	5	as	as	ADP
cord-326631-7gd3hjc3	142	6	when	when	SCONJ
cord-326631-7gd3hjc3	142	7	all	all	DET
cord-326631-7gd3hjc3	142	8	stage	stage	NOUN
cord-326631-7gd3hjc3	142	9	durations	duration	NOUN
cord-326631-7gd3hjc3	142	10	are	be	AUX
cord-326631-7gd3hjc3	142	11	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	142	12	distributed	distribute	VERB
cord-326631-7gd3hjc3	142	13	.	.	PUNCT
cord-326631-7gd3hjc3	143	1	similar	similar	ADJ
cord-326631-7gd3hjc3	143	2	to	to	ADP
cord-326631-7gd3hjc3	143	3	section	section	NOUN
cord-326631-7gd3hjc3	143	4	6	6	NUM
cord-326631-7gd3hjc3	143	5	,	,	PUNCT
cord-326631-7gd3hjc3	143	6	the	the	DET
cord-326631-7gd3hjc3	143	7	equation	equation	NOUN
cord-326631-7gd3hjc3	143	8	for	for	ADP
cord-326631-7gd3hjc3	143	9	each	each	DET
cord-326631-7gd3hjc3	143	10	infectious	infectious	ADJ
cord-326631-7gd3hjc3	143	11	stage	stage	NOUN
cord-326631-7gd3hjc3	143	12	can	can	AUX
cord-326631-7gd3hjc3	143	13	be	be	AUX
cord-326631-7gd3hjc3	143	14	writteṅ	writteṅ	PROPN
cord-326631-7gd3hjc3	143	15	where	where	SCONJ
cord-326631-7gd3hjc3	143	16	u	u	PROPN
cord-326631-7gd3hjc3	143	17	i	i	NOUN
cord-326631-7gd3hjc3	143	18	(	(	PUNCT
cord-326631-7gd3hjc3	143	19	t	t	NOUN
cord-326631-7gd3hjc3	143	20	)	)	PUNCT
cord-326631-7gd3hjc3	143	21	is	be	AUX
cord-326631-7gd3hjc3	143	22	the	the	DET
cord-326631-7gd3hjc3	143	23	number	number	NOUN
cord-326631-7gd3hjc3	143	24	of	of	ADP
cord-326631-7gd3hjc3	143	25	individuals	individual	NOUN
cord-326631-7gd3hjc3	143	26	entering	enter	VERB
cord-326631-7gd3hjc3	143	27	class	class	NOUN
cord-326631-7gd3hjc3	144	1	i	i	PRON
cord-326631-7gd3hjc3	144	2	i	i	PRON
cord-326631-7gd3hjc3	144	3	at	at	ADP
cord-326631-7gd3hjc3	144	4	time	time	NOUN
cord-326631-7gd3hjc3	144	5	t	t	PROPN
cord-326631-7gd3hjc3	144	6	,	,	PUNCT
cord-326631-7gd3hjc3	144	7	and	and	CCONJ
cord-326631-7gd3hjc3	144	8	the	the	DET
cord-326631-7gd3hjc3	144	9	initial	initial	ADJ
cord-326631-7gd3hjc3	144	10	conditions	condition	NOUN
cord-326631-7gd3hjc3	144	11	are	be	AUX
cord-326631-7gd3hjc3	144	12	specified	specify	VERB
cord-326631-7gd3hjc3	144	13	by	by	ADP
cord-326631-7gd3hjc3	144	14	individuals	individual	NOUN
cord-326631-7gd3hjc3	144	15	who	who	PRON
cord-326631-7gd3hjc3	144	16	leave	leave	VERB
cord-326631-7gd3hjc3	144	17	the	the	DET
cord-326631-7gd3hjc3	144	18	last	last	ADJ
cord-326631-7gd3hjc3	144	19	infectious	infectious	ADJ
cord-326631-7gd3hjc3	144	20	stage	stage	NOUN
cord-326631-7gd3hjc3	144	21	recover	recover	NOUN
cord-326631-7gd3hjc3	144	22	(	(	PUNCT
cord-326631-7gd3hjc3	144	23	into	into	ADP
cord-326631-7gd3hjc3	144	24	class	class	NOUN
cord-326631-7gd3hjc3	144	25	r	r	NOUN
cord-326631-7gd3hjc3	144	26	)	)	PUNCT
cord-326631-7gd3hjc3	144	27	,	,	PUNCT
cord-326631-7gd3hjc3	144	28	hencė	hencė	PROPN
cord-326631-7gd3hjc3	144	29	when	when	SCONJ
cord-326631-7gd3hjc3	144	30	the	the	DET
cord-326631-7gd3hjc3	144	31	infectious	infectious	ADJ
cord-326631-7gd3hjc3	144	32	periods	period	NOUN
cord-326631-7gd3hjc3	144	33	and	and	CCONJ
cord-326631-7gd3hjc3	144	34	the	the	DET
cord-326631-7gd3hjc3	144	35	latent	latent	ADJ
cord-326631-7gd3hjc3	144	36	period	period	NOUN
cord-326631-7gd3hjc3	144	37	are	be	AUX
cord-326631-7gd3hjc3	144	38	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	144	39	distributed	distribute	VERB
cord-326631-7gd3hjc3	144	40	,	,	PUNCT
cord-326631-7gd3hjc3	144	41	i.e.	i.e.	X
cord-326631-7gd3hjc3	144	42	,	,	PUNCT
cord-326631-7gd3hjc3	144	43	f	f	PROPN
cord-326631-7gd3hjc3	144	44	i	i	PROPN
cord-326631-7gd3hjc3	144	45	(	(	PUNCT
cord-326631-7gd3hjc3	144	46	t	t	NOUN
cord-326631-7gd3hjc3	144	47	)	)	PUNCT
cord-326631-7gd3hjc3	144	48	=	=	PRON
cord-326631-7gd3hjc3	145	1	γ	γ	PROPN
cord-326631-7gd3hjc3	145	2	i	i	PROPN
cord-326631-7gd3hjc3	145	3	e	e	X
cord-326631-7gd3hjc3	145	4	−γi	−γi	PROPN
cord-326631-7gd3hjc3	145	5	t	t	PROPN
cord-326631-7gd3hjc3	145	6	,	,	PUNCT
cord-326631-7gd3hjc3	145	7	the	the	DET
cord-326631-7gd3hjc3	145	8	technique	technique	NOUN
cord-326631-7gd3hjc3	145	9	introduced	introduce	VERB
cord-326631-7gd3hjc3	145	10	in	in	ADP
cord-326631-7gd3hjc3	145	11	appendix	appendix	PROPN
cord-326631-7gd3hjc3	145	12	b	b	PROPN
cord-326631-7gd3hjc3	145	13	can	can	AUX
cord-326631-7gd3hjc3	145	14	be	be	AUX
cord-326631-7gd3hjc3	145	15	applied	apply	VERB
cord-326631-7gd3hjc3	145	16	to	to	PART
cord-326631-7gd3hjc3	145	17	show	show	VERB
cord-326631-7gd3hjc3	145	18	that	that	SCONJ
cord-326631-7gd3hjc3	145	19	the	the	DET
cord-326631-7gd3hjc3	145	20	model	model	NOUN
cord-326631-7gd3hjc3	145	21	(	(	PUNCT
cord-326631-7gd3hjc3	145	22	13	13	NUM
cord-326631-7gd3hjc3	145	23	)	)	PUNCT
cord-326631-7gd3hjc3	145	24	is	be	AUX
cord-326631-7gd3hjc3	145	25	indeed	indeed	ADV
cord-326631-7gd3hjc3	145	26	the	the	DET
cord-326631-7gd3hjc3	145	27	standard	standard	ADJ
cord-326631-7gd3hjc3	145	28	multiple	multiple	ADJ
cord-326631-7gd3hjc3	145	29	-	-	PUNCT
cord-326631-7gd3hjc3	145	30	stage	stage	NOUN
cord-326631-7gd3hjc3	145	31	sir	sir	PROPN
cord-326631-7gd3hjc3	145	32	model	model	NOUN
cord-326631-7gd3hjc3	145	33	.	.	PUNCT
cord-326631-7gd3hjc3	146	1	in	in	ADP
cord-326631-7gd3hjc3	146	2	their	their	PRON
cord-326631-7gd3hjc3	146	3	analysis	analysis	NOUN
cord-326631-7gd3hjc3	146	4	of	of	ADP
cord-326631-7gd3hjc3	146	5	the	the	DET
cord-326631-7gd3hjc3	146	6	si	si	PROPN
cord-326631-7gd3hjc3	146	7	n	n	NOUN
cord-326631-7gd3hjc3	146	8	r	r	NOUN
cord-326631-7gd3hjc3	146	9	model	model	NOUN
cord-326631-7gd3hjc3	146	10	with	with	ADP
cord-326631-7gd3hjc3	146	11	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	146	12	distributed	distribute	VERB
cord-326631-7gd3hjc3	146	13	stage	stage	NOUN
cord-326631-7gd3hjc3	146	14	durations	duration	NOUN
cord-326631-7gd3hjc3	146	15	(	(	PUNCT
cord-326631-7gd3hjc3	146	16	13	13	NUM
cord-326631-7gd3hjc3	146	17	)	)	PUNCT
cord-326631-7gd3hjc3	146	18	,	,	PUNCT
cord-326631-7gd3hjc3	146	19	feng	feng	PROPN
cord-326631-7gd3hjc3	146	20	and	and	CCONJ
cord-326631-7gd3hjc3	146	21	thieme	thieme	NOUN
cord-326631-7gd3hjc3	146	22	(	(	PUNCT
cord-326631-7gd3hjc3	146	23	2000	2000	NUM
cord-326631-7gd3hjc3	146	24	)	)	PUNCT
cord-326631-7gd3hjc3	146	25	have	have	AUX
cord-326631-7gd3hjc3	146	26	shown	show	VERB
cord-326631-7gd3hjc3	146	27	that	that	SCONJ
cord-326631-7gd3hjc3	146	28	the	the	DET
cord-326631-7gd3hjc3	146	29	basic	basic	ADJ
cord-326631-7gd3hjc3	146	30	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	146	31	number	number	NOUN
cord-326631-7gd3hjc3	146	32	is	be	AUX
cord-326631-7gd3hjc3	146	33	and	and	CCONJ
cord-326631-7gd3hjc3	146	34	that	that	SCONJ
cord-326631-7gd3hjc3	146	35	the	the	DET
cord-326631-7gd3hjc3	146	36	disease	disease	NOUN
cord-326631-7gd3hjc3	146	37	free	free	ADJ
cord-326631-7gd3hjc3	146	38	equilibrium	equilibrium	NOUN
cord-326631-7gd3hjc3	146	39	is	be	AUX
cord-326631-7gd3hjc3	146	40	unstable	unstable	ADJ
cord-326631-7gd3hjc3	146	41	if	if	SCONJ
cord-326631-7gd3hjc3	146	42	and	and	CCONJ
cord-326631-7gd3hjc3	146	43	only	only	ADV
cord-326631-7gd3hjc3	146	44	if	if	SCONJ
cord-326631-7gd3hjc3	146	45	r	r	NOUN
cord-326631-7gd3hjc3	146	46	0	0	PUNCT
cord-326631-7gd3hjc3	146	47	>	>	SYM
cord-326631-7gd3hjc3	146	48	1	1	NUM
cord-326631-7gd3hjc3	146	49	.	.	PUNCT
cord-326631-7gd3hjc3	147	1	similar	similar	ADJ
cord-326631-7gd3hjc3	147	2	to	to	ADP
cord-326631-7gd3hjc3	147	3	previous	previous	ADJ
cord-326631-7gd3hjc3	147	4	sections	section	NOUN
cord-326631-7gd3hjc3	147	5	,	,	PUNCT
cord-326631-7gd3hjc3	147	6	we	we	PRON
cord-326631-7gd3hjc3	147	7	find	find	VERB
cord-326631-7gd3hjc3	147	8	that	that	SCONJ
cord-326631-7gd3hjc3	147	9	s	s	X
cord-326631-7gd3hjc3	148	1	+	+	ADV
cord-326631-7gd3hjc3	149	1	i	i	PRON
cord-326631-7gd3hjc3	150	1	i	i	PRON
cord-326631-7gd3hjc3	150	2	i	i	PRON
cord-326631-7gd3hjc3	151	1	+	+	CCONJ
cord-326631-7gd3hjc3	151	2	r	r	NOUN
cord-326631-7gd3hjc3	151	3	=	=	NOUN
cord-326631-7gd3hjc3	151	4	1	1	NUM
cord-326631-7gd3hjc3	151	5	is	be	AUX
cord-326631-7gd3hjc3	151	6	invariant	invariant	ADJ
cord-326631-7gd3hjc3	151	7	,	,	PUNCT
cord-326631-7gd3hjc3	151	8	s	s	NOUN
cord-326631-7gd3hjc3	151	9	≥	≥	NOUN
cord-326631-7gd3hjc3	151	10	0	0	NUM
cord-326631-7gd3hjc3	151	11	,	,	PUNCT
cord-326631-7gd3hjc3	151	12	and	and	CCONJ
cord-326631-7gd3hjc3	151	13	s(∞	s(∞	PROPN
cord-326631-7gd3hjc3	151	14	)	)	PUNCT
cord-326631-7gd3hjc3	151	15	exists	exist	VERB
cord-326631-7gd3hjc3	151	16	.	.	PUNCT
cord-326631-7gd3hjc3	152	1	integrating	integrate	VERB
cord-326631-7gd3hjc3	152	2	eq	eq	PROPN
cord-326631-7gd3hjc3	152	3	.	.	PUNCT
cord-326631-7gd3hjc3	153	1	(	(	PUNCT
cord-326631-7gd3hjc3	153	2	13a	13a	NUM
cord-326631-7gd3hjc3	153	3	)	)	PUNCT
cord-326631-7gd3hjc3	153	4	from	from	ADP
cord-326631-7gd3hjc3	153	5	0	0	NUM
cord-326631-7gd3hjc3	153	6	to	to	ADP
cord-326631-7gd3hjc3	153	7	t	t	NOUN
cord-326631-7gd3hjc3	153	8	and	and	CCONJ
cord-326631-7gd3hjc3	153	9	and	and	CCONJ
cord-326631-7gd3hjc3	153	10	switching	switch	VERB
cord-326631-7gd3hjc3	153	11	the	the	DET
cord-326631-7gd3hjc3	153	12	order	order	NOUN
cord-326631-7gd3hjc3	153	13	of	of	ADP
cord-326631-7gd3hjc3	153	14	integrations	integration	NOUN
cord-326631-7gd3hjc3	153	15	,	,	PUNCT
cord-326631-7gd3hjc3	153	16	we	we	PRON
cord-326631-7gd3hjc3	153	17	have	have	VERB
cord-326631-7gd3hjc3	153	18	i(t	i(t	PROPN
cord-326631-7gd3hjc3	153	19	)	)	PUNCT
cord-326631-7gd3hjc3	153	20	≥	≥	NOUN
cord-326631-7gd3hjc3	153	21	0	0	NUM
cord-326631-7gd3hjc3	153	22	;	;	PUNCT
cord-326631-7gd3hjc3	153	23	similarly	similarly	ADV
cord-326631-7gd3hjc3	153	24	,	,	PUNCT
cord-326631-7gd3hjc3	153	25	integrating	integrate	VERB
cord-326631-7gd3hjc3	153	26	from	from	ADP
cord-326631-7gd3hjc3	153	27	0	0	NUM
cord-326631-7gd3hjc3	153	28	to	to	ADP
cord-326631-7gd3hjc3	153	29	∞	∞	NUM
cord-326631-7gd3hjc3	153	30	,	,	PUNCT
cord-326631-7gd3hjc3	153	31	we	we	PRON
cord-326631-7gd3hjc3	153	32	have	have	VERB
cord-326631-7gd3hjc3	153	33	i(∞	i(∞	PROPN
cord-326631-7gd3hjc3	153	34	)	)	PUNCT
cord-326631-7gd3hjc3	153	35	=	=	NOUN
cord-326631-7gd3hjc3	153	36	0	0	X
cord-326631-7gd3hjc3	153	37	.	.	PUNCT
cord-326631-7gd3hjc3	154	1	thus	thus	ADV
cord-326631-7gd3hjc3	154	2	,	,	PUNCT
cord-326631-7gd3hjc3	154	3	the	the	DET
cord-326631-7gd3hjc3	154	4	disease	disease	NOUN
cord-326631-7gd3hjc3	154	5	will	will	AUX
cord-326631-7gd3hjc3	154	6	also	also	ADV
cord-326631-7gd3hjc3	154	7	eventually	eventually	ADV
cord-326631-7gd3hjc3	154	8	burn	burn	VERB
cord-326631-7gd3hjc3	154	9	out	out	ADP
cord-326631-7gd3hjc3	154	10	.	.	PUNCT
cord-326631-7gd3hjc3	155	1	theorem	theorem	VERB
cord-326631-7gd3hjc3	155	2	7.1	7.1	NUM
cord-326631-7gd3hjc3	155	3	.	.	PUNCT
cord-326631-7gd3hjc3	156	1	consider	consider	VERB
cord-326631-7gd3hjc3	156	2	the	the	DET
cord-326631-7gd3hjc3	156	3	multiple	multiple	ADJ
cord-326631-7gd3hjc3	156	4	stage	stage	NOUN
cord-326631-7gd3hjc3	156	5	si	si	PROPN
cord-326631-7gd3hjc3	156	6	n	n	NOUN
cord-326631-7gd3hjc3	156	7	r	r	PROPN
cord-326631-7gd3hjc3	156	8	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	156	9	model	model	NOUN
cord-326631-7gd3hjc3	156	10	with	with	ADP
cord-326631-7gd3hjc3	156	11	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	156	12	distributed	distribute	VERB
cord-326631-7gd3hjc3	156	13	stage	stage	NOUN
cord-326631-7gd3hjc3	156	14	durations	duration	NOUN
cord-326631-7gd3hjc3	156	15	,	,	PUNCT
cord-326631-7gd3hjc3	156	16	specified	specify	VERB
cord-326631-7gd3hjc3	156	17	by	by	ADP
cord-326631-7gd3hjc3	156	18	eqs	eqs	PROPN
cord-326631-7gd3hjc3	156	19	.	.	PUNCT
cord-326631-7gd3hjc3	157	1	(	(	PUNCT
cord-326631-7gd3hjc3	157	2	13	13	NUM
cord-326631-7gd3hjc3	157	3	)	)	PUNCT
cord-326631-7gd3hjc3	157	4	.	.	PUNCT
cord-326631-7gd3hjc3	158	1	if	if	SCONJ
cord-326631-7gd3hjc3	158	2	the	the	DET
cord-326631-7gd3hjc3	158	3	initial	initial	ADJ
cord-326631-7gd3hjc3	158	4	number	number	NOUN
cord-326631-7gd3hjc3	158	5	of	of	ADP
cord-326631-7gd3hjc3	158	6	infectious	infectious	ADJ
cord-326631-7gd3hjc3	158	7	individuals	individual	NOUN
cord-326631-7gd3hjc3	158	8	is	be	AUX
cord-326631-7gd3hjc3	158	9	suffciently	suffciently	ADV
cord-326631-7gd3hjc3	158	10	small	small	ADJ
cord-326631-7gd3hjc3	158	11	,	,	PUNCT
cord-326631-7gd3hjc3	158	12	i.e.	i.e.	X
cord-326631-7gd3hjc3	158	13	,	,	PUNCT
cord-326631-7gd3hjc3	158	14	in	in	ADP
cord-326631-7gd3hjc3	158	15	the	the	DET
cord-326631-7gd3hjc3	158	16	limit	limit	NOUN
cord-326631-7gd3hjc3	158	17	i	i	PRON
cord-326631-7gd3hjc3	158	18	i	i	PRON
cord-326631-7gd3hjc3	158	19	i	i	NOUN
cord-326631-7gd3hjc3	158	20	(	(	PUNCT
cord-326631-7gd3hjc3	158	21	0	0	NUM
cord-326631-7gd3hjc3	158	22	)	)	PUNCT
cord-326631-7gd3hjc3	158	23	→	→	PUNCT
cord-326631-7gd3hjc3	158	24	0	0	NUM
cord-326631-7gd3hjc3	158	25	,	,	PUNCT
cord-326631-7gd3hjc3	158	26	the	the	DET
cord-326631-7gd3hjc3	158	27	final	final	ADJ
cord-326631-7gd3hjc3	158	28	size	size	NOUN
cord-326631-7gd3hjc3	158	29	z	z	NOUN
cord-326631-7gd3hjc3	158	30	is	be	AUX
cord-326631-7gd3hjc3	158	31	given	give	VERB
cord-326631-7gd3hjc3	158	32	by	by	ADP
cord-326631-7gd3hjc3	158	33	the	the	DET
cord-326631-7gd3hjc3	158	34	unique	unique	ADJ
cord-326631-7gd3hjc3	158	35	solution	solution	NOUN
cord-326631-7gd3hjc3	158	36	of	of	ADP
cord-326631-7gd3hjc3	158	37	eq	eq	PROPN
cord-326631-7gd3hjc3	158	38	.	.	PUNCT
cord-326631-7gd3hjc3	159	1	(	(	PUNCT
cord-326631-7gd3hjc3	159	2	5	5	NUM
cord-326631-7gd3hjc3	159	3	)	)	PUNCT
cord-326631-7gd3hjc3	159	4	,	,	PUNCT
cord-326631-7gd3hjc3	159	5	or	or	CCONJ
cord-326631-7gd3hjc3	159	6	explicitly	explicitly	ADV
cord-326631-7gd3hjc3	159	7	by	by	ADP
cord-326631-7gd3hjc3	159	8	eq	eq	PROPN
cord-326631-7gd3hjc3	159	9	.	.	PUNCT
cord-326631-7gd3hjc3	159	10	(	(	PUNCT
cord-326631-7gd3hjc3	159	11	a.2	a.2	NOUN
cord-326631-7gd3hjc3	159	12	)	)	PUNCT
cord-326631-7gd3hjc3	159	13	,	,	PUNCT
cord-326631-7gd3hjc3	159	14	in	in	ADP
cord-326631-7gd3hjc3	159	15	which	which	PRON
cord-326631-7gd3hjc3	159	16	r	r	NOUN
cord-326631-7gd3hjc3	159	17	0	0	NUM
cord-326631-7gd3hjc3	159	18	is	be	AUX
cord-326631-7gd3hjc3	159	19	given	give	VERB
cord-326631-7gd3hjc3	159	20	by	by	ADP
cord-326631-7gd3hjc3	159	21	eq	eq	PROPN
cord-326631-7gd3hjc3	159	22	.	.	PUNCT
cord-326631-7gd3hjc3	159	23	(	(	PUNCT
cord-326631-7gd3hjc3	159	24	14	14	NUM
cord-326631-7gd3hjc3	159	25	)	)	PUNCT
cord-326631-7gd3hjc3	159	26	.	.	PUNCT
cord-326631-7gd3hjc3	160	1	proof	proof	NOUN
cord-326631-7gd3hjc3	160	2	.	.	PUNCT
cord-326631-7gd3hjc3	161	1	to	to	PART
cord-326631-7gd3hjc3	161	2	prove	prove	VERB
cord-326631-7gd3hjc3	161	3	this	this	PRON
cord-326631-7gd3hjc3	161	4	,	,	PUNCT
cord-326631-7gd3hjc3	161	5	we	we	PRON
cord-326631-7gd3hjc3	161	6	divide	divide	VERB
cord-326631-7gd3hjc3	161	7	by	by	ADP
cord-326631-7gd3hjc3	161	8	s	s	NOUN
cord-326631-7gd3hjc3	161	9	on	on	ADP
cord-326631-7gd3hjc3	161	10	both	both	DET
cord-326631-7gd3hjc3	161	11	sides	side	NOUN
cord-326631-7gd3hjc3	161	12	of	of	ADP
cord-326631-7gd3hjc3	161	13	(	(	PUNCT
cord-326631-7gd3hjc3	161	14	6a	6a	NUM
cord-326631-7gd3hjc3	161	15	)	)	PUNCT
cord-326631-7gd3hjc3	161	16	and	and	CCONJ
cord-326631-7gd3hjc3	161	17	integrate	integrate	VERB
cord-326631-7gd3hjc3	161	18	with	with	ADP
cord-326631-7gd3hjc3	161	19	respect	respect	NOUN
cord-326631-7gd3hjc3	161	20	to	to	ADP
cord-326631-7gd3hjc3	161	21	time	time	NOUN
cord-326631-7gd3hjc3	161	22	,	,	PUNCT
cord-326631-7gd3hjc3	161	23	using	use	VERB
cord-326631-7gd3hjc3	161	24	lemma	lemma	NOUN
cord-326631-7gd3hjc3	161	25	6.1	6.1	NUM
cord-326631-7gd3hjc3	161	26	,	,	PUNCT
cord-326631-7gd3hjc3	161	27	eq	eq	PROPN
cord-326631-7gd3hjc3	161	28	.	.	PUNCT
cord-326631-7gd3hjc3	161	29	(	(	PUNCT
cord-326631-7gd3hjc3	161	30	15	15	NUM
cord-326631-7gd3hjc3	161	31	)	)	PUNCT
cord-326631-7gd3hjc3	161	32	becomes	become	VERB
cord-326631-7gd3hjc3	161	33	suppose	suppose	VERB
cord-326631-7gd3hjc3	161	34	i	i	PRON
cord-326631-7gd3hjc3	161	35	i	i	PRON
cord-326631-7gd3hjc3	161	36	(	(	PUNCT
cord-326631-7gd3hjc3	161	37	0	0	NUM
cord-326631-7gd3hjc3	161	38	)	)	PUNCT
cord-326631-7gd3hjc3	161	39	=	=	NOUN
cord-326631-7gd3hjc3	161	40	i	i	NOUN
cord-326631-7gd3hjc3	161	41	1	1	X
cord-326631-7gd3hjc3	161	42	.	.	PUNCT
cord-326631-7gd3hjc3	162	1	switching	switch	VERB
cord-326631-7gd3hjc3	162	2	the	the	DET
cord-326631-7gd3hjc3	162	3	order	order	NOUN
cord-326631-7gd3hjc3	162	4	of	of	ADP
cord-326631-7gd3hjc3	162	5	integration	integration	NOUN
cord-326631-7gd3hjc3	162	6	,	,	PUNCT
cord-326631-7gd3hjc3	162	7	also	also	ADV
cord-326631-7gd3hjc3	162	8	,	,	PUNCT
cord-326631-7gd3hjc3	162	9	integrating	integrate	VERB
cord-326631-7gd3hjc3	162	10	eq	eq	PROPN
cord-326631-7gd3hjc3	162	11	.	.	PUNCT
cord-326631-7gd3hjc3	163	1	(	(	PUNCT
cord-326631-7gd3hjc3	163	2	13d	13d	NUM
cord-326631-7gd3hjc3	163	3	)	)	PUNCT
cord-326631-7gd3hjc3	163	4	and	and	CCONJ
cord-326631-7gd3hjc3	163	5	switching	switch	VERB
cord-326631-7gd3hjc3	163	6	the	the	DET
cord-326631-7gd3hjc3	163	7	order	order	NOUN
cord-326631-7gd3hjc3	163	8	of	of	ADP
cord-326631-7gd3hjc3	163	9	integrations	integration	NOUN
cord-326631-7gd3hjc3	163	10	,	,	PUNCT
cord-326631-7gd3hjc3	163	11	we	we	PRON
cord-326631-7gd3hjc3	163	12	have	have	AUX
cord-326631-7gd3hjc3	163	13	i.e.	i.e.	ADV
cord-326631-7gd3hjc3	163	14	,	,	PUNCT
cord-326631-7gd3hjc3	163	15	summed	sum	VERB
cord-326631-7gd3hjc3	163	16	over	over	ADP
cord-326631-7gd3hjc3	163	17	all	all	DET
cord-326631-7gd3hjc3	163	18	time	time	NOUN
cord-326631-7gd3hjc3	163	19	,	,	PUNCT
cord-326631-7gd3hjc3	163	20	the	the	DET
cord-326631-7gd3hjc3	163	21	number	number	NOUN
cord-326631-7gd3hjc3	163	22	of	of	ADP
cord-326631-7gd3hjc3	163	23	individuals	individual	NOUN
cord-326631-7gd3hjc3	163	24	who	who	PRON
cord-326631-7gd3hjc3	163	25	enter	enter	VERB
cord-326631-7gd3hjc3	163	26	the	the	DET
cord-326631-7gd3hjc3	163	27	(	(	PUNCT
cord-326631-7gd3hjc3	163	28	i	i	PRON
cord-326631-7gd3hjc3	163	29	+	+	SYM
cord-326631-7gd3hjc3	163	30	1)th	1)th	NUM
cord-326631-7gd3hjc3	163	31	stage	stage	NOUN
cord-326631-7gd3hjc3	163	32	is	be	AUX
cord-326631-7gd3hjc3	163	33	the	the	DET
cord-326631-7gd3hjc3	163	34	same	same	ADJ
cord-326631-7gd3hjc3	163	35	as	as	ADP
cord-326631-7gd3hjc3	163	36	the	the	DET
cord-326631-7gd3hjc3	163	37	number	number	NOUN
cord-326631-7gd3hjc3	163	38	who	who	PRON
cord-326631-7gd3hjc3	163	39	enter	enter	VERB
cord-326631-7gd3hjc3	163	40	the	the	DET
cord-326631-7gd3hjc3	163	41	ith	ith	PROPN
cord-326631-7gd3hjc3	163	42	stage	stage	NOUN
cord-326631-7gd3hjc3	163	43	.	.	PUNCT
cord-326631-7gd3hjc3	164	1	we	we	PRON
cord-326631-7gd3hjc3	164	2	then	then	ADV
cord-326631-7gd3hjc3	164	3	integrate	integrate	VERB
cord-326631-7gd3hjc3	164	4	eq	eq	PROPN
cord-326631-7gd3hjc3	164	5	.	.	PUNCT
cord-326631-7gd3hjc3	165	1	(	(	PUNCT
cord-326631-7gd3hjc3	165	2	6a	6a	NOUN
cord-326631-7gd3hjc3	165	3	)	)	PUNCT
cord-326631-7gd3hjc3	165	4	.	.	PUNCT
cord-326631-7gd3hjc3	166	1	from	from	ADP
cord-326631-7gd3hjc3	166	2	the	the	DET
cord-326631-7gd3hjc3	166	3	definition	definition	NOUN
cord-326631-7gd3hjc3	166	4	of	of	ADP
cord-326631-7gd3hjc3	166	5	u	u	NOUN
cord-326631-7gd3hjc3	166	6	1	1	NUM
cord-326631-7gd3hjc3	166	7	(	(	PUNCT
cord-326631-7gd3hjc3	166	8	t	t	NOUN
cord-326631-7gd3hjc3	166	9	)	)	PUNCT
cord-326631-7gd3hjc3	166	10	in	in	ADP
cord-326631-7gd3hjc3	166	11	eq	eq	PROPN
cord-326631-7gd3hjc3	166	12	.	.	PUNCT
cord-326631-7gd3hjc3	166	13	(	(	PUNCT
cord-326631-7gd3hjc3	166	14	13c	13c	NUM
cord-326631-7gd3hjc3	166	15	)	)	PUNCT
cord-326631-7gd3hjc3	166	16	,	,	PUNCT
cord-326631-7gd3hjc3	166	17	we	we	PRON
cord-326631-7gd3hjc3	166	18	have	have	VERB
cord-326631-7gd3hjc3	166	19	for	for	ADP
cord-326631-7gd3hjc3	166	20	all	all	PRON
cord-326631-7gd3hjc3	166	21	i	i	PRON
cord-326631-7gd3hjc3	166	22	=	=	NOUN
cord-326631-7gd3hjc3	166	23	1	1	NUM
cord-326631-7gd3hjc3	166	24	,	,	PUNCT
cord-326631-7gd3hjc3	166	25	.	.	PUNCT
cord-326631-7gd3hjc3	166	26	.	.	PUNCT
cord-326631-7gd3hjc3	166	27	.	.	PUNCT
cord-326631-7gd3hjc3	167	1	,	,	PUNCT
cord-326631-7gd3hjc3	167	2	n.	n.	PROPN
cord-326631-7gd3hjc3	167	3	notice	notice	VERB
cord-326631-7gd3hjc3	167	4	that	that	SCONJ
cord-326631-7gd3hjc3	167	5	the	the	DET
cord-326631-7gd3hjc3	167	6	final	final	ADJ
cord-326631-7gd3hjc3	167	7	size	size	NOUN
cord-326631-7gd3hjc3	167	8	z	z	NOUN
cord-326631-7gd3hjc3	167	9	=	=	NOUN
cord-326631-7gd3hjc3	167	10	s(0	s(0	PROPN
cord-326631-7gd3hjc3	167	11	)	)	PUNCT
cord-326631-7gd3hjc3	167	12	−	−	PROPN
cord-326631-7gd3hjc3	167	13	s(∞	s(∞	PROPN
cord-326631-7gd3hjc3	167	14	)	)	PUNCT
cord-326631-7gd3hjc3	167	15	,	,	PUNCT
cord-326631-7gd3hjc3	167	16	so	so	ADV
cord-326631-7gd3hjc3	167	17	eq	eq	PROPN
cord-326631-7gd3hjc3	167	18	.	.	PUNCT
cord-326631-7gd3hjc3	167	19	(	(	PUNCT
cord-326631-7gd3hjc3	167	20	16	16	NUM
cord-326631-7gd3hjc3	167	21	)	)	PUNCT
cord-326631-7gd3hjc3	167	22	becomes	become	VERB
cord-326631-7gd3hjc3	167	23	during	during	ADP
cord-326631-7gd3hjc3	167	24	the	the	DET
cord-326631-7gd3hjc3	167	25	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	167	26	of	of	ADP
cord-326631-7gd3hjc3	167	27	severe	severe	ADJ
cord-326631-7gd3hjc3	167	28	acute	acute	ADJ
cord-326631-7gd3hjc3	167	29	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	167	30	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	167	31	(	(	PUNCT
cord-326631-7gd3hjc3	167	32	sars	sar	NOUN
cord-326631-7gd3hjc3	167	33	)	)	PUNCT
cord-326631-7gd3hjc3	167	34	in	in	ADP
cord-326631-7gd3hjc3	167	35	2003	2003	NUM
cord-326631-7gd3hjc3	167	36	(	(	PUNCT
cord-326631-7gd3hjc3	167	37	poutanen	poutanen	PROPN
cord-326631-7gd3hjc3	167	38	et	et	X
cord-326631-7gd3hjc3	167	39	al	al	PROPN
cord-326631-7gd3hjc3	167	40	.	.	PROPN
cord-326631-7gd3hjc3	167	41	,	,	PUNCT
cord-326631-7gd3hjc3	167	42	2003	2003	NUM
cord-326631-7gd3hjc3	167	43	;	;	PUNCT
cord-326631-7gd3hjc3	167	44	low	low	ADJ
cord-326631-7gd3hjc3	167	45	and	and	CCONJ
cord-326631-7gd3hjc3	167	46	mcgeer	mcgeer	PROPN
cord-326631-7gd3hjc3	167	47	,	,	PUNCT
cord-326631-7gd3hjc3	167	48	2003	2003	NUM
cord-326631-7gd3hjc3	167	49	)	)	PUNCT
cord-326631-7gd3hjc3	167	50	,	,	PUNCT
cord-326631-7gd3hjc3	167	51	one	one	NUM
cord-326631-7gd3hjc3	167	52	aspect	aspect	NOUN
cord-326631-7gd3hjc3	167	53	of	of	ADP
cord-326631-7gd3hjc3	167	54	observed	observe	VERB
cord-326631-7gd3hjc3	167	55	transmission	transmission	NOUN
cord-326631-7gd3hjc3	167	56	that	that	PRON
cord-326631-7gd3hjc3	167	57	received	receive	VERB
cord-326631-7gd3hjc3	167	58	a	a	DET
cord-326631-7gd3hjc3	167	59	great	great	ADJ
cord-326631-7gd3hjc3	167	60	deal	deal	NOUN
cord-326631-7gd3hjc3	167	61	of	of	ADP
cord-326631-7gd3hjc3	167	62	attention	attention	NOUN
cord-326631-7gd3hjc3	167	63	was	be	AUX
cord-326631-7gd3hjc3	167	64	the	the	DET
cord-326631-7gd3hjc3	167	65	existence	existence	NOUN
cord-326631-7gd3hjc3	167	66	of	of	ADP
cord-326631-7gd3hjc3	167	67	super	super	NOUN
cord-326631-7gd3hjc3	167	68	-	-	NOUN
cord-326631-7gd3hjc3	167	69	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	167	70	(	(	PUNCT
cord-326631-7gd3hjc3	167	71	who	who	PRON
cord-326631-7gd3hjc3	167	72	sars	sar	VERB
cord-326631-7gd3hjc3	167	73	update	update	VERB
cord-326631-7gd3hjc3	167	74	27	27	NUM
cord-326631-7gd3hjc3	167	75	,	,	PUNCT
cord-326631-7gd3hjc3	167	76	2003	2003	NUM
cord-326631-7gd3hjc3	167	77	)	)	PUNCT
cord-326631-7gd3hjc3	167	78	,	,	PUNCT
cord-326631-7gd3hjc3	167	79	i.e.	i.e.	X
cord-326631-7gd3hjc3	167	80	,	,	PUNCT
cord-326631-7gd3hjc3	167	81	individuals	individual	NOUN
cord-326631-7gd3hjc3	167	82	who	who	PRON
cord-326631-7gd3hjc3	167	83	infect	infect	VERB
cord-326631-7gd3hjc3	167	84	many	many	ADJ
cord-326631-7gd3hjc3	167	85	more	more	ADJ
cord-326631-7gd3hjc3	167	86	people	people	NOUN
cord-326631-7gd3hjc3	167	87	than	than	ADP
cord-326631-7gd3hjc3	167	88	the	the	DET
cord-326631-7gd3hjc3	167	89	average	average	NOUN
cord-326631-7gd3hjc3	167	90	(	(	PUNCT
cord-326631-7gd3hjc3	167	91	e.g.	e.g.	ADV
cord-326631-7gd3hjc3	167	92	,	,	PUNCT
cord-326631-7gd3hjc3	167	93	at	at	ADP
cord-326631-7gd3hjc3	167	94	least	least	ADJ
cord-326631-7gd3hjc3	167	95	an	an	DET
cord-326631-7gd3hjc3	167	96	order	order	NOUN
cord-326631-7gd3hjc3	167	97	of	of	ADP
cord-326631-7gd3hjc3	167	98	magnitude	magnitude	NOUN
cord-326631-7gd3hjc3	167	99	greater	great	ADJ
cord-326631-7gd3hjc3	167	100	than	than	ADP
cord-326631-7gd3hjc3	167	101	r	r	NOUN
cord-326631-7gd3hjc3	167	102	0	0	NUM
cord-326631-7gd3hjc3	167	103	)	)	PUNCT
cord-326631-7gd3hjc3	167	104	.	.	PUNCT
cord-326631-7gd3hjc3	168	1	in	in	ADP
cord-326631-7gd3hjc3	168	2	this	this	DET
cord-326631-7gd3hjc3	168	3	section	section	NOUN
cord-326631-7gd3hjc3	168	4	,	,	PUNCT
cord-326631-7gd3hjc3	168	5	we	we	PRON
cord-326631-7gd3hjc3	168	6	prove	prove	VERB
cord-326631-7gd3hjc3	168	7	that	that	SCONJ
cord-326631-7gd3hjc3	168	8	the	the	DET
cord-326631-7gd3hjc3	168	9	existence	existence	NOUN
cord-326631-7gd3hjc3	168	10	of	of	ADP
cord-326631-7gd3hjc3	168	11	the	the	DET
cord-326631-7gd3hjc3	168	12	type	type	NOUN
cord-326631-7gd3hjc3	168	13	of	of	ADP
cord-326631-7gd3hjc3	168	14	super	super	NOUN
cord-326631-7gd3hjc3	168	15	-	-	NOUN
cord-326631-7gd3hjc3	168	16	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	168	17	that	that	PRON
cord-326631-7gd3hjc3	168	18	occurred	occur	VERB
cord-326631-7gd3hjc3	168	19	during	during	ADP
cord-326631-7gd3hjc3	168	20	the	the	DET
cord-326631-7gd3hjc3	168	21	sars	sar	NOUN
cord-326631-7gd3hjc3	168	22	outbreak	outbreak	NOUN
cord-326631-7gd3hjc3	168	23	in	in	ADP
cord-326631-7gd3hjc3	168	24	2003	2003	NUM
cord-326631-7gd3hjc3	168	25	has	have	VERB
cord-326631-7gd3hjc3	168	26	no	no	DET
cord-326631-7gd3hjc3	168	27	effect	effect	NOUN
cord-326631-7gd3hjc3	168	28	on	on	ADP
cord-326631-7gd3hjc3	168	29	the	the	DET
cord-326631-7gd3hjc3	168	30	final	final	ADJ
cord-326631-7gd3hjc3	168	31	size	size	NOUN
cord-326631-7gd3hjc3	168	32	formula	formula	NOUN
cord-326631-7gd3hjc3	168	33	.	.	PUNCT
cord-326631-7gd3hjc3	169	1	one	one	NUM
cord-326631-7gd3hjc3	169	2	mechanism	mechanism	NOUN
cord-326631-7gd3hjc3	169	3	for	for	ADP
cord-326631-7gd3hjc3	169	4	the	the	DET
cord-326631-7gd3hjc3	169	5	generation	generation	NOUN
cord-326631-7gd3hjc3	169	6	of	of	ADP
cord-326631-7gd3hjc3	169	7	super	super	NOUN
cord-326631-7gd3hjc3	169	8	-	-	NOUN
cord-326631-7gd3hjc3	169	9	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	169	10	is	be	AUX
cord-326631-7gd3hjc3	169	11	that	that	SCONJ
cord-326631-7gd3hjc3	169	12	the	the	DET
cord-326631-7gd3hjc3	169	13	infectious	infectious	ADJ
cord-326631-7gd3hjc3	169	14	period	period	NOUN
cord-326631-7gd3hjc3	169	15	distribution	distribution	NOUN
cord-326631-7gd3hjc3	169	16	could	could	AUX
cord-326631-7gd3hjc3	169	17	be	be	AUX
cord-326631-7gd3hjc3	169	18	bimodal	bimodal	ADJ
cord-326631-7gd3hjc3	169	19	,	,	PUNCT
cord-326631-7gd3hjc3	169	20	such	such	ADJ
cord-326631-7gd3hjc3	169	21	that	that	SCONJ
cord-326631-7gd3hjc3	169	22	a	a	DET
cord-326631-7gd3hjc3	169	23	small	small	ADJ
cord-326631-7gd3hjc3	169	24	proportion	proportion	NOUN
cord-326631-7gd3hjc3	169	25	of	of	ADP
cord-326631-7gd3hjc3	169	26	individuals	individual	NOUN
cord-326631-7gd3hjc3	169	27	are	be	AUX
cord-326631-7gd3hjc3	169	28	infectious	infectious	ADJ
cord-326631-7gd3hjc3	169	29	much	much	ADV
cord-326631-7gd3hjc3	169	30	longer	long	ADV
cord-326631-7gd3hjc3	169	31	than	than	ADP
cord-326631-7gd3hjc3	169	32	average	average	ADJ
cord-326631-7gd3hjc3	169	33	.	.	PUNCT
cord-326631-7gd3hjc3	170	1	this	this	DET
cord-326631-7gd3hjc3	170	2	situation	situation	NOUN
cord-326631-7gd3hjc3	170	3	is	be	AUX
cord-326631-7gd3hjc3	170	4	already	already	ADV
cord-326631-7gd3hjc3	170	5	covered	cover	VERB
cord-326631-7gd3hjc3	170	6	by	by	ADP
cord-326631-7gd3hjc3	170	7	theorem	theorem	NOUN
cord-326631-7gd3hjc3	170	8	7.1	7.1	NUM
cord-326631-7gd3hjc3	170	9	,	,	PUNCT
cord-326631-7gd3hjc3	170	10	which	which	PRON
cord-326631-7gd3hjc3	170	11	deals	deal	VERB
cord-326631-7gd3hjc3	170	12	with	with	ADP
cord-326631-7gd3hjc3	170	13	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	170	14	distributions	distribution	NOUN
cord-326631-7gd3hjc3	170	15	of	of	ADP
cord-326631-7gd3hjc3	170	16	stage	stage	NOUN
cord-326631-7gd3hjc3	170	17	durations	duration	NOUN
cord-326631-7gd3hjc3	170	18	.	.	PUNCT
cord-326631-7gd3hjc3	171	1	in	in	ADP
cord-326631-7gd3hjc3	171	2	this	this	DET
cord-326631-7gd3hjc3	171	3	section	section	NOUN
cord-326631-7gd3hjc3	171	4	,	,	PUNCT
cord-326631-7gd3hjc3	171	5	we	we	PRON
cord-326631-7gd3hjc3	171	6	consider	consider	VERB
cord-326631-7gd3hjc3	171	7	a	a	DET
cord-326631-7gd3hjc3	171	8	different	different	ADJ
cord-326631-7gd3hjc3	171	9	type	type	NOUN
cord-326631-7gd3hjc3	171	10	of	of	ADP
cord-326631-7gd3hjc3	171	11	generalization	generalization	NOUN
cord-326631-7gd3hjc3	171	12	of	of	ADP
cord-326631-7gd3hjc3	171	13	the	the	DET
cord-326631-7gd3hjc3	171	14	sir	sir	PROPN
cord-326631-7gd3hjc3	171	15	model	model	NOUN
cord-326631-7gd3hjc3	171	16	.	.	PUNCT
cord-326631-7gd3hjc3	172	1	in	in	ADP
cord-326631-7gd3hjc3	172	2	all	all	PRON
cord-326631-7gd3hjc3	172	3	of	of	ADP
cord-326631-7gd3hjc3	172	4	the	the	DET
cord-326631-7gd3hjc3	172	5	models	model	NOUN
cord-326631-7gd3hjc3	172	6	we	we	PRON
cord-326631-7gd3hjc3	172	7	have	have	AUX
cord-326631-7gd3hjc3	172	8	considered	consider	VERB
cord-326631-7gd3hjc3	172	9	thus	thus	ADV
cord-326631-7gd3hjc3	172	10	far	far	ADV
cord-326631-7gd3hjc3	172	11	,	,	PUNCT
cord-326631-7gd3hjc3	172	12	it	it	PRON
cord-326631-7gd3hjc3	172	13	has	have	AUX
cord-326631-7gd3hjc3	172	14	been	be	AUX
cord-326631-7gd3hjc3	172	15	assumed	assume	VERB
cord-326631-7gd3hjc3	172	16	implicitly	implicitly	ADV
cord-326631-7gd3hjc3	172	17	that	that	SCONJ
cord-326631-7gd3hjc3	172	18	all	all	DET
cord-326631-7gd3hjc3	172	19	infectious	infectious	ADJ
cord-326631-7gd3hjc3	172	20	individuals	individual	NOUN
cord-326631-7gd3hjc3	172	21	have	have	VERB
cord-326631-7gd3hjc3	172	22	the	the	DET
cord-326631-7gd3hjc3	172	23	same	same	ADJ
cord-326631-7gd3hjc3	172	24	transmission	transmission	NOUN
cord-326631-7gd3hjc3	172	25	rate	rate	NOUN
cord-326631-7gd3hjc3	172	26	.	.	PUNCT
cord-326631-7gd3hjc3	173	1	if	if	SCONJ
cord-326631-7gd3hjc3	173	2	some	some	DET
cord-326631-7gd3hjc3	173	3	individuals	individual	NOUN
cord-326631-7gd3hjc3	173	4	actually	actually	ADV
cord-326631-7gd3hjc3	173	5	have	have	VERB
cord-326631-7gd3hjc3	173	6	a	a	PRON
cord-326631-7gd3hjc3	173	7	much	much	ADV
cord-326631-7gd3hjc3	173	8	higher	high	ADJ
cord-326631-7gd3hjc3	173	9	than	than	ADP
cord-326631-7gd3hjc3	173	10	average	average	ADJ
cord-326631-7gd3hjc3	173	11	transmission	transmission	NOUN
cord-326631-7gd3hjc3	173	12	rate	rate	NOUN
cord-326631-7gd3hjc3	173	13	then	then	ADV
cord-326631-7gd3hjc3	173	14	they	they	PRON
cord-326631-7gd3hjc3	173	15	will	will	AUX
cord-326631-7gd3hjc3	173	16	be	be	AUX
cord-326631-7gd3hjc3	173	17	super	super	ADJ
cord-326631-7gd3hjc3	173	18	-	-	NOUN
cord-326631-7gd3hjc3	173	19	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	173	20	.	.	PUNCT
cord-326631-7gd3hjc3	174	1	this	this	PRON
cord-326631-7gd3hjc3	174	2	could	could	AUX
cord-326631-7gd3hjc3	174	3	arise	arise	VERB
cord-326631-7gd3hjc3	174	4	,	,	PUNCT
cord-326631-7gd3hjc3	174	5	for	for	ADP
cord-326631-7gd3hjc3	174	6	example	example	NOUN
cord-326631-7gd3hjc3	174	7	,	,	PUNCT
cord-326631-7gd3hjc3	174	8	because	because	SCONJ
cord-326631-7gd3hjc3	174	9	of	of	ADP
cord-326631-7gd3hjc3	174	10	individual	individual	ADJ
cord-326631-7gd3hjc3	174	11	variation	variation	NOUN
cord-326631-7gd3hjc3	174	12	in	in	ADP
cord-326631-7gd3hjc3	174	13	viral	viral	ADJ
cord-326631-7gd3hjc3	174	14	load	load	NOUN
cord-326631-7gd3hjc3	174	15	(	(	PUNCT
cord-326631-7gd3hjc3	174	16	reflecting	reflect	VERB
cord-326631-7gd3hjc3	174	17	variation	variation	NOUN
cord-326631-7gd3hjc3	174	18	in	in	ADP
cord-326631-7gd3hjc3	174	19	immune	immune	ADJ
cord-326631-7gd3hjc3	174	20	response	response	NOUN
cord-326631-7gd3hjc3	174	21	)	)	PUNCT
cord-326631-7gd3hjc3	174	22	or	or	CCONJ
cord-326631-7gd3hjc3	174	23	as	as	ADP
cord-326631-7gd3hjc3	174	24	the	the	DET
cord-326631-7gd3hjc3	174	25	result	result	NOUN
cord-326631-7gd3hjc3	174	26	of	of	ADP
cord-326631-7gd3hjc3	174	27	chance	chance	NOUN
cord-326631-7gd3hjc3	174	28	occurence	occurence	NOUN
cord-326631-7gd3hjc3	174	29	of	of	ADP
cord-326631-7gd3hjc3	174	30	environmental	environmental	ADJ
cord-326631-7gd3hjc3	174	31	circumstances	circumstance	NOUN
cord-326631-7gd3hjc3	174	32	that	that	PRON
cord-326631-7gd3hjc3	174	33	promote	promote	VERB
cord-326631-7gd3hjc3	174	34	disease	disease	NOUN
cord-326631-7gd3hjc3	174	35	spread	spread	VERB
cord-326631-7gd3hjc3	174	36	(	(	PUNCT
cord-326631-7gd3hjc3	174	37	as	as	SCONJ
cord-326631-7gd3hjc3	174	38	apparently	apparently	ADV
cord-326631-7gd3hjc3	174	39	occurred	occur	VERB
cord-326631-7gd3hjc3	174	40	during	during	ADP
cord-326631-7gd3hjc3	174	41	the	the	DET
cord-326631-7gd3hjc3	174	42	sars	sar	NOUN
cord-326631-7gd3hjc3	174	43	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	174	44	(	(	PUNCT
cord-326631-7gd3hjc3	174	45	who	who	PRON
cord-326631-7gd3hjc3	174	46	sars	sar	VERB
cord-326631-7gd3hjc3	174	47	update	update	VERB
cord-326631-7gd3hjc3	174	48	33	33	NUM
cord-326631-7gd3hjc3	174	49	,	,	PUNCT
cord-326631-7gd3hjc3	174	50	2003	2003	NUM
cord-326631-7gd3hjc3	174	51	)	)	PUNCT
cord-326631-7gd3hjc3	174	52	)	)	PUNCT
cord-326631-7gd3hjc3	174	53	.	.	PUNCT
cord-326631-7gd3hjc3	175	1	whatever	whatever	PRON
cord-326631-7gd3hjc3	175	2	the	the	DET
cord-326631-7gd3hjc3	175	3	origin	origin	NOUN
cord-326631-7gd3hjc3	175	4	,	,	PUNCT
cord-326631-7gd3hjc3	175	5	we	we	PRON
cord-326631-7gd3hjc3	175	6	focus	focus	VERB
cord-326631-7gd3hjc3	175	7	here	here	ADV
cord-326631-7gd3hjc3	175	8	on	on	ADP
cord-326631-7gd3hjc3	175	9	variation	variation	NOUN
cord-326631-7gd3hjc3	175	10	in	in	ADP
cord-326631-7gd3hjc3	175	11	transmission	transmission	NOUN
cord-326631-7gd3hjc3	175	12	rate	rate	NOUN
cord-326631-7gd3hjc3	175	13	that	that	PRON
cord-326631-7gd3hjc3	175	14	is	be	AUX
cord-326631-7gd3hjc3	175	15	manifested	manifest	VERB
cord-326631-7gd3hjc3	175	16	only	only	ADV
cord-326631-7gd3hjc3	175	17	after	after	SCONJ
cord-326631-7gd3hjc3	175	18	an	an	DET
cord-326631-7gd3hjc3	175	19	individual	individual	NOUN
cord-326631-7gd3hjc3	175	20	is	be	AUX
cord-326631-7gd3hjc3	175	21	infected	infect	VERB
cord-326631-7gd3hjc3	175	22	.	.	PUNCT
cord-326631-7gd3hjc3	176	1	in	in	ADP
cord-326631-7gd3hjc3	176	2	the	the	DET
cord-326631-7gd3hjc3	176	3	following	following	ADJ
cord-326631-7gd3hjc3	176	4	sections	section	NOUN
cord-326631-7gd3hjc3	176	5	we	we	PRON
cord-326631-7gd3hjc3	176	6	consider	consider	VERB
cord-326631-7gd3hjc3	176	7	the	the	DET
cord-326631-7gd3hjc3	176	8	effects	effect	NOUN
cord-326631-7gd3hjc3	176	9	of	of	ADP
cord-326631-7gd3hjc3	176	10	intrinsic	intrinsic	ADJ
cord-326631-7gd3hjc3	176	11	variation	variation	NOUN
cord-326631-7gd3hjc3	176	12	in	in	ADP
cord-326631-7gd3hjc3	176	13	contact	contact	NOUN
cord-326631-7gd3hjc3	176	14	rates	rate	NOUN
cord-326631-7gd3hjc3	176	15	among	among	ADP
cord-326631-7gd3hjc3	176	16	individuals	individual	NOUN
cord-326631-7gd3hjc3	176	17	,	,	PUNCT
cord-326631-7gd3hjc3	176	18	which	which	PRON
cord-326631-7gd3hjc3	176	19	results	result	VERB
cord-326631-7gd3hjc3	176	20	from	from	ADP
cord-326631-7gd3hjc3	176	21	inhomogeneous	inhomogeneous	ADJ
cord-326631-7gd3hjc3	176	22	contact	contact	NOUN
cord-326631-7gd3hjc3	176	23	network	network	NOUN
cord-326631-7gd3hjc3	176	24	structure	structure	NOUN
cord-326631-7gd3hjc3	176	25	in	in	ADP
cord-326631-7gd3hjc3	176	26	the	the	DET
cord-326631-7gd3hjc3	176	27	host	host	NOUN
cord-326631-7gd3hjc3	176	28	population	population	NOUN
cord-326631-7gd3hjc3	176	29	.	.	PUNCT
cord-326631-7gd3hjc3	177	1	we	we	PRON
cord-326631-7gd3hjc3	177	2	now	now	ADV
cord-326631-7gd3hjc3	177	3	proceed	proceed	VERB
cord-326631-7gd3hjc3	177	4	to	to	PART
cord-326631-7gd3hjc3	177	5	develop	develop	VERB
cord-326631-7gd3hjc3	177	6	and	and	CCONJ
cord-326631-7gd3hjc3	177	7	analyze	analyze	VERB
cord-326631-7gd3hjc3	177	8	an	an	DET
cord-326631-7gd3hjc3	177	9	sir	sir	NOUN
cord-326631-7gd3hjc3	177	10	model	model	NOUN
cord-326631-7gd3hjc3	177	11	with	with	ADP
cord-326631-7gd3hjc3	177	12	a	a	DET
cord-326631-7gd3hjc3	177	13	distribution	distribution	NOUN
cord-326631-7gd3hjc3	177	14	of	of	ADP
cord-326631-7gd3hjc3	177	15	transmission	transmission	NOUN
cord-326631-7gd3hjc3	177	16	rates	rate	NOUN
cord-326631-7gd3hjc3	177	17	and	and	CCONJ
cord-326631-7gd3hjc3	177	18	show	show	VERB
cord-326631-7gd3hjc3	177	19	that	that	SCONJ
cord-326631-7gd3hjc3	177	20	the	the	DET
cord-326631-7gd3hjc3	177	21	usual	usual	ADJ
cord-326631-7gd3hjc3	177	22	final	final	ADJ
cord-326631-7gd3hjc3	177	23	size	size	NOUN
cord-326631-7gd3hjc3	177	24	formula	formula	NOUN
cord-326631-7gd3hjc3	177	25	(	(	PUNCT
cord-326631-7gd3hjc3	177	26	5	5	NUM
cord-326631-7gd3hjc3	177	27	)	)	PUNCT
cord-326631-7gd3hjc3	177	28	applies	apply	VERB
cord-326631-7gd3hjc3	177	29	.	.	PUNCT
cord-326631-7gd3hjc3	178	1	extension	extension	NOUN
cord-326631-7gd3hjc3	178	2	of	of	ADP
cord-326631-7gd3hjc3	178	3	our	our	PRON
cord-326631-7gd3hjc3	178	4	results	result	NOUN
cord-326631-7gd3hjc3	178	5	to	to	ADP
cord-326631-7gd3hjc3	178	6	a	a	DET
cord-326631-7gd3hjc3	178	7	multiple	multiple	ADJ
cord-326631-7gd3hjc3	178	8	stage	stage	NOUN
cord-326631-7gd3hjc3	178	9	si	si	PROPN
cord-326631-7gd3hjc3	178	10	n	n	NOUN
cord-326631-7gd3hjc3	178	11	r	r	PROPN
cord-326631-7gd3hjc3	178	12	model	model	NOUN
cord-326631-7gd3hjc3	178	13	is	be	AUX
cord-326631-7gd3hjc3	178	14	straightfoward	straightfoward	ADJ
cord-326631-7gd3hjc3	178	15	and	and	CCONJ
cord-326631-7gd3hjc3	178	16	similar	similar	ADJ
cord-326631-7gd3hjc3	178	17	to	to	ADP
cord-326631-7gd3hjc3	178	18	the	the	DET
cord-326631-7gd3hjc3	178	19	way	way	NOUN
cord-326631-7gd3hjc3	178	20	we	we	PRON
cord-326631-7gd3hjc3	178	21	generalized	generalize	VERB
cord-326631-7gd3hjc3	178	22	our	our	PRON
cord-326631-7gd3hjc3	178	23	results	result	NOUN
cord-326631-7gd3hjc3	178	24	for	for	ADP
cord-326631-7gd3hjc3	178	25	the	the	DET
cord-326631-7gd3hjc3	178	26	sir	sir	NOUN
cord-326631-7gd3hjc3	178	27	with	with	ADP
cord-326631-7gd3hjc3	178	28	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	178	29	infectious	infectious	ADJ
cord-326631-7gd3hjc3	178	30	period	period	NOUN
cord-326631-7gd3hjc3	178	31	distribution	distribution	NOUN
cord-326631-7gd3hjc3	178	32	to	to	ADP
cord-326631-7gd3hjc3	178	33	an	an	DET
cord-326631-7gd3hjc3	178	34	si	si	PROPN
cord-326631-7gd3hjc3	178	35	n	n	NOUN
cord-326631-7gd3hjc3	178	36	r	r	NOUN
cord-326631-7gd3hjc3	178	37	model	model	NOUN
cord-326631-7gd3hjc3	178	38	with	with	ADP
cord-326631-7gd3hjc3	178	39	arbitrary	arbitrary	ADJ
cord-326631-7gd3hjc3	178	40	stage	stage	NOUN
cord-326631-7gd3hjc3	178	41	duration	duration	NOUN
cord-326631-7gd3hjc3	178	42	distributions	distribution	NOUN
cord-326631-7gd3hjc3	178	43	.	.	PUNCT
cord-326631-7gd3hjc3	179	1	let	let	VERB
cord-326631-7gd3hjc3	179	2	i(β	i(β	PROPN
cord-326631-7gd3hjc3	179	3	,	,	PUNCT
cord-326631-7gd3hjc3	179	4	t	t	PROPN
cord-326631-7gd3hjc3	179	5	)	)	PUNCT
cord-326631-7gd3hjc3	179	6	be	be	AUX
cord-326631-7gd3hjc3	179	7	the	the	DET
cord-326631-7gd3hjc3	179	8	distribution	distribution	NOUN
cord-326631-7gd3hjc3	179	9	(	(	PUNCT
cord-326631-7gd3hjc3	179	10	at	at	ADP
cord-326631-7gd3hjc3	179	11	time	time	NOUN
cord-326631-7gd3hjc3	179	12	t	t	NOUN
cord-326631-7gd3hjc3	179	13	)	)	PUNCT
cord-326631-7gd3hjc3	179	14	of	of	ADP
cord-326631-7gd3hjc3	179	15	infectious	infectious	ADJ
cord-326631-7gd3hjc3	179	16	individuals	individual	NOUN
cord-326631-7gd3hjc3	179	17	that	that	PRON
cord-326631-7gd3hjc3	179	18	have	have	VERB
cord-326631-7gd3hjc3	179	19	transmission	transmission	NOUN
cord-326631-7gd3hjc3	179	20	rate	rate	NOUN
cord-326631-7gd3hjc3	179	21	β	β	NOUN
cord-326631-7gd3hjc3	179	22	.	.	PUNCT
cord-326631-7gd3hjc3	180	1	note	note	VERB
cord-326631-7gd3hjc3	180	2	that	that	SCONJ
cord-326631-7gd3hjc3	180	3	we	we	PRON
cord-326631-7gd3hjc3	180	4	assume	assume	VERB
cord-326631-7gd3hjc3	180	5	implicitly	implicitly	ADV
cord-326631-7gd3hjc3	180	6	that	that	SCONJ
cord-326631-7gd3hjc3	180	7	a	a	DET
cord-326631-7gd3hjc3	180	8	given	give	VERB
cord-326631-7gd3hjc3	180	9	individual	individual	NOUN
cord-326631-7gd3hjc3	180	10	retains	retain	VERB
cord-326631-7gd3hjc3	180	11	the	the	DET
cord-326631-7gd3hjc3	180	12	same	same	ADJ
cord-326631-7gd3hjc3	180	13	transmission	transmission	NOUN
cord-326631-7gd3hjc3	180	14	rate	rate	NOUN
cord-326631-7gd3hjc3	180	15	throughout	throughout	ADP
cord-326631-7gd3hjc3	180	16	his	his	PRON
cord-326631-7gd3hjc3	180	17	/	/	SYM
cord-326631-7gd3hjc3	180	18	her	her	PRON
cord-326631-7gd3hjc3	180	19	infectious	infectious	ADJ
cord-326631-7gd3hjc3	180	20	period	period	NOUN
cord-326631-7gd3hjc3	180	21	,	,	PUNCT
cord-326631-7gd3hjc3	180	22	and	and	CCONJ
cord-326631-7gd3hjc3	180	23	hence	hence	ADV
cord-326631-7gd3hjc3	180	24	that	that	SCONJ
cord-326631-7gd3hjc3	180	25	this	this	DET
cord-326631-7gd3hjc3	180	26	transmission	transmission	NOUN
cord-326631-7gd3hjc3	180	27	rate	rate	NOUN
cord-326631-7gd3hjc3	180	28	is	be	AUX
cord-326631-7gd3hjc3	180	29	determined	determine	VERB
cord-326631-7gd3hjc3	180	30	as	as	ADV
cord-326631-7gd3hjc3	180	31	soon	soon	ADV
cord-326631-7gd3hjc3	180	32	as	as	SCONJ
cord-326631-7gd3hjc3	180	33	infection	infection	NOUN
cord-326631-7gd3hjc3	180	34	occurs	occur	VERB
cord-326631-7gd3hjc3	180	35	.	.	PUNCT
cord-326631-7gd3hjc3	181	1	let	let	VERB
cord-326631-7gd3hjc3	181	2	q(β	q(β	PROPN
cord-326631-7gd3hjc3	181	3	)	)	PUNCT
cord-326631-7gd3hjc3	181	4	be	be	AUX
cord-326631-7gd3hjc3	181	5	the	the	DET
cord-326631-7gd3hjc3	181	6	probability	probability	NOUN
cord-326631-7gd3hjc3	181	7	that	that	SCONJ
cord-326631-7gd3hjc3	181	8	a	a	DET
cord-326631-7gd3hjc3	181	9	newly	newly	ADV
cord-326631-7gd3hjc3	181	10	infectious	infectious	ADJ
cord-326631-7gd3hjc3	181	11	individual	individual	NOUN
cord-326631-7gd3hjc3	181	12	has	have	AUX
cord-326631-7gd3hjc3	181	13	transmission	transmission	NOUN
cord-326631-7gd3hjc3	181	14	rate	rate	NOUN
cord-326631-7gd3hjc3	181	15	β	β	NOUN
cord-326631-7gd3hjc3	181	16	.	.	PUNCT
cord-326631-7gd3hjc3	182	1	thus	thus	ADV
cord-326631-7gd3hjc3	182	2	,	,	PUNCT
cord-326631-7gd3hjc3	182	3	the	the	DET
cord-326631-7gd3hjc3	182	4	mean	mean	ADJ
cord-326631-7gd3hjc3	182	5	transmission	transmission	NOUN
cord-326631-7gd3hjc3	182	6	rate	rate	NOUN
cord-326631-7gd3hjc3	182	7	is	be	AUX
cord-326631-7gd3hjc3	182	8	the	the	DET
cord-326631-7gd3hjc3	182	9	rate	rate	NOUN
cord-326631-7gd3hjc3	182	10	of	of	ADP
cord-326631-7gd3hjc3	182	11	change	change	NOUN
cord-326631-7gd3hjc3	182	12	of	of	ADP
cord-326631-7gd3hjc3	182	13	the	the	DET
cord-326631-7gd3hjc3	182	14	proportion	proportion	NOUN
cord-326631-7gd3hjc3	182	15	of	of	ADP
cord-326631-7gd3hjc3	182	16	the	the	DET
cord-326631-7gd3hjc3	182	17	population	population	NOUN
cord-326631-7gd3hjc3	182	18	that	that	PRON
cord-326631-7gd3hjc3	182	19	is	be	AUX
cord-326631-7gd3hjc3	182	20	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	182	21	iṡ	iṡ	PROPN
cord-326631-7gd3hjc3	182	22	upon	upon	SCONJ
cord-326631-7gd3hjc3	182	23	infection	infection	NOUN
cord-326631-7gd3hjc3	182	24	,	,	PUNCT
cord-326631-7gd3hjc3	182	25	individuals	individual	NOUN
cord-326631-7gd3hjc3	182	26	leave	leave	VERB
cord-326631-7gd3hjc3	182	27	the	the	DET
cord-326631-7gd3hjc3	182	28	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	182	29	class	class	NOUN
cord-326631-7gd3hjc3	182	30	s	s	NOUN
cord-326631-7gd3hjc3	182	31	and	and	CCONJ
cord-326631-7gd3hjc3	182	32	enter	enter	VERB
cord-326631-7gd3hjc3	182	33	the	the	DET
cord-326631-7gd3hjc3	182	34	infectious	infectious	ADJ
cord-326631-7gd3hjc3	182	35	class	class	NOUN
cord-326631-7gd3hjc3	182	36	i	i	PROPN
cord-326631-7gd3hjc3	182	37	,	,	PUNCT
cord-326631-7gd3hjc3	182	38	a	a	DET
cord-326631-7gd3hjc3	182	39	proportion	proportion	NOUN
cord-326631-7gd3hjc3	182	40	q(β	q(β	PROPN
cord-326631-7gd3hjc3	182	41	)	)	PUNCT
cord-326631-7gd3hjc3	182	42	of	of	ADP
cord-326631-7gd3hjc3	182	43	them	they	PRON
cord-326631-7gd3hjc3	182	44	having	have	VERB
cord-326631-7gd3hjc3	182	45	a	a	DET
cord-326631-7gd3hjc3	182	46	transmission	transmission	NOUN
cord-326631-7gd3hjc3	182	47	rate	rate	NOUN
cord-326631-7gd3hjc3	182	48	β	β	NOUN
cord-326631-7gd3hjc3	182	49	.	.	PUNCT
cord-326631-7gd3hjc3	183	1	upon	upon	SCONJ
cord-326631-7gd3hjc3	183	2	recovery	recovery	NOUN
cord-326631-7gd3hjc3	183	3	,	,	PUNCT
cord-326631-7gd3hjc3	183	4	they	they	PRON
cord-326631-7gd3hjc3	183	5	leave	leave	VERB
cord-326631-7gd3hjc3	183	6	the	the	DET
cord-326631-7gd3hjc3	183	7	infectious	infectious	ADJ
cord-326631-7gd3hjc3	183	8	class	class	NOUN
cord-326631-7gd3hjc3	183	9	at	at	ADP
cord-326631-7gd3hjc3	183	10	rate	rate	NOUN
cord-326631-7gd3hjc3	183	11	γ	γ	PROPN
cord-326631-7gd3hjc3	183	12	.	.	PUNCT
cord-326631-7gd3hjc3	184	1	thus	thus	ADV
cord-326631-7gd3hjc3	184	2	,	,	PUNCT
cord-326631-7gd3hjc3	184	3	in	in	ADP
cord-326631-7gd3hjc3	184	4	order	order	NOUN
cord-326631-7gd3hjc3	184	5	to	to	PART
cord-326631-7gd3hjc3	184	6	ensure	ensure	VERB
cord-326631-7gd3hjc3	184	7	that	that	SCONJ
cord-326631-7gd3hjc3	184	8	the	the	DET
cord-326631-7gd3hjc3	184	9	model	model	NOUN
cord-326631-7gd3hjc3	184	10	is	be	AUX
cord-326631-7gd3hjc3	184	11	well	well	ADV
cord-326631-7gd3hjc3	184	12	posed	pose	VERB
cord-326631-7gd3hjc3	184	13	,	,	PUNCT
cord-326631-7gd3hjc3	184	14	we	we	PRON
cord-326631-7gd3hjc3	184	15	must	must	AUX
cord-326631-7gd3hjc3	184	16	establish	establish	VERB
cord-326631-7gd3hjc3	184	17	that	that	SCONJ
cord-326631-7gd3hjc3	184	18	if	if	SCONJ
cord-326631-7gd3hjc3	184	19	i(β	i(β	PROPN
cord-326631-7gd3hjc3	184	20	,	,	PUNCT
cord-326631-7gd3hjc3	184	21	0	0	NUM
cord-326631-7gd3hjc3	184	22	)	)	PUNCT
cord-326631-7gd3hjc3	184	23	>	>	PUNCT
cord-326631-7gd3hjc3	184	24	0	0	NUM
cord-326631-7gd3hjc3	184	25	then	then	ADV
cord-326631-7gd3hjc3	184	26	i(β	i(β	PROPN
cord-326631-7gd3hjc3	184	27	,	,	PUNCT
cord-326631-7gd3hjc3	184	28	t	t	PROPN
cord-326631-7gd3hjc3	184	29	)	)	PUNCT
cord-326631-7gd3hjc3	184	30	>	>	PUNCT
cord-326631-7gd3hjc3	184	31	0	0	NUM
cord-326631-7gd3hjc3	185	1	for	for	ADP
cord-326631-7gd3hjc3	185	2	all	all	DET
cord-326631-7gd3hjc3	185	3	time	time	NOUN
cord-326631-7gd3hjc3	185	4	.	.	PUNCT
cord-326631-7gd3hjc3	186	1	suppose	suppose	VERB
cord-326631-7gd3hjc3	186	2	this	this	PRON
cord-326631-7gd3hjc3	186	3	is	be	AUX
cord-326631-7gd3hjc3	186	4	not	not	PART
cord-326631-7gd3hjc3	186	5	true	true	ADJ
cord-326631-7gd3hjc3	186	6	.	.	PUNCT
cord-326631-7gd3hjc3	187	1	then	then	ADV
cord-326631-7gd3hjc3	187	2	there	there	ADV
cord-326631-7gd3hjc3	187	3	existsβ	existsβ	NOUN
cord-326631-7gd3hjc3	187	4	and	and	CCONJ
cord-326631-7gd3hjc3	187	5	t	t	PROPN
cord-326631-7gd3hjc3	187	6	such	such	ADJ
cord-326631-7gd3hjc3	187	7	that	that	SCONJ
cord-326631-7gd3hjc3	187	8	∞	∞	NUM
cord-326631-7gd3hjc3	187	9	0	0	NUM
cord-326631-7gd3hjc3	187	10	i(β	i(β	PROPN
cord-326631-7gd3hjc3	187	11	,	,	PUNCT
cord-326631-7gd3hjc3	187	12	t	t	PROPN
cord-326631-7gd3hjc3	187	13	)	)	PUNCT
cord-326631-7gd3hjc3	187	14	dβ	dβ	PROPN
cord-326631-7gd3hjc3	187	15	>	>	SYM
cord-326631-7gd3hjc3	187	16	0	0	NUM
cord-326631-7gd3hjc3	187	17	,	,	PUNCT
cord-326631-7gd3hjc3	187	18	i(β	i(β	PROPN
cord-326631-7gd3hjc3	187	19	,	,	PUNCT
cord-326631-7gd3hjc3	187	20	t	t	PROPN
cord-326631-7gd3hjc3	187	21	)	)	PUNCT
cord-326631-7gd3hjc3	187	22	>	>	PUNCT
cord-326631-7gd3hjc3	187	23	0	0	NUM
cord-326631-7gd3hjc3	187	24	for	for	ADP
cord-326631-7gd3hjc3	187	25	t	t	PROPN
cord-326631-7gd3hjc3	187	26	<	<	X
cord-326631-7gd3hjc3	187	27	t	t	PROPN
cord-326631-7gd3hjc3	187	28	,	,	PUNCT
cord-326631-7gd3hjc3	187	29	but	but	CCONJ
cord-326631-7gd3hjc3	187	30	i(β	i(β	PROPN
cord-326631-7gd3hjc3	187	31	,	,	PUNCT
cord-326631-7gd3hjc3	187	32	t	t	PROPN
cord-326631-7gd3hjc3	187	33	)	)	PUNCT
cord-326631-7gd3hjc3	187	34	=	=	NOUN
cord-326631-7gd3hjc3	187	35	0	0	X
cord-326631-7gd3hjc3	187	36	.	.	PUNCT
cord-326631-7gd3hjc3	188	1	substituting	substitute	VERB
cord-326631-7gd3hjc3	188	2	these	these	DET
cord-326631-7gd3hjc3	188	3	conditions	condition	NOUN
cord-326631-7gd3hjc3	188	4	into	into	ADP
cord-326631-7gd3hjc3	188	5	eq	eq	PROPN
cord-326631-7gd3hjc3	188	6	.	.	PUNCT
cord-326631-7gd3hjc3	188	7	(	(	PUNCT
cord-326631-7gd3hjc3	188	8	21b	21b	NUM
cord-326631-7gd3hjc3	188	9	)	)	PUNCT
cord-326631-7gd3hjc3	188	10	,	,	PUNCT
cord-326631-7gd3hjc3	188	11	we	we	PRON
cord-326631-7gd3hjc3	188	12	obtaini̇(β	obtaini̇(β	PROPN
cord-326631-7gd3hjc3	188	13	,	,	PUNCT
cord-326631-7gd3hjc3	188	14	t	t	NOUN
cord-326631-7gd3hjc3	188	15	)	)	PUNCT
cord-326631-7gd3hjc3	188	16	>	>	PUNCT
cord-326631-7gd3hjc3	188	17	0	0	NUM
cord-326631-7gd3hjc3	188	18	.	.	PUNCT
cord-326631-7gd3hjc3	189	1	but	but	CCONJ
cord-326631-7gd3hjc3	189	2	this	this	PRON
cord-326631-7gd3hjc3	189	3	contradicts	contradict	VERB
cord-326631-7gd3hjc3	189	4	the	the	DET
cord-326631-7gd3hjc3	189	5	hypothesis	hypothesis	NOUN
cord-326631-7gd3hjc3	189	6	that	that	SCONJ
cord-326631-7gd3hjc3	189	7	i(β	i(β	PROPN
cord-326631-7gd3hjc3	189	8	,	,	PUNCT
cord-326631-7gd3hjc3	189	9	t	t	PROPN
cord-326631-7gd3hjc3	189	10	)	)	PUNCT
cord-326631-7gd3hjc3	189	11	decreases	decrease	VERB
cord-326631-7gd3hjc3	189	12	from	from	ADP
cord-326631-7gd3hjc3	189	13	i(β	i(β	PROPN
cord-326631-7gd3hjc3	189	14	,	,	PUNCT
cord-326631-7gd3hjc3	189	15	0	0	NUM
cord-326631-7gd3hjc3	189	16	)	)	PUNCT
cord-326631-7gd3hjc3	189	17	>	>	PUNCT
cord-326631-7gd3hjc3	189	18	0	0	NUM
cord-326631-7gd3hjc3	189	19	to	to	AUX
cord-326631-7gd3hjc3	189	20	i(β	i(β	PROPN
cord-326631-7gd3hjc3	189	21	,	,	PUNCT
cord-326631-7gd3hjc3	189	22	t	t	PROPN
cord-326631-7gd3hjc3	189	23	)	)	PUNCT
cord-326631-7gd3hjc3	189	24	=	=	NOUN
cord-326631-7gd3hjc3	189	25	0	0	X
cord-326631-7gd3hjc3	189	26	.	.	PUNCT
cord-326631-7gd3hjc3	190	1	hence	hence	ADV
cord-326631-7gd3hjc3	190	2	i(β	i(β	PROPN
cord-326631-7gd3hjc3	190	3	,	,	PUNCT
cord-326631-7gd3hjc3	190	4	t	t	PROPN
cord-326631-7gd3hjc3	190	5	)	)	PUNCT
cord-326631-7gd3hjc3	190	6	>	>	PUNCT
cord-326631-7gd3hjc3	190	7	0	0	NUM
cord-326631-7gd3hjc3	190	8	for	for	ADP
cord-326631-7gd3hjc3	190	9	all	all	DET
cord-326631-7gd3hjc3	190	10	t	t	NOUN
cord-326631-7gd3hjc3	190	11	≥	≥	NOUN
cord-326631-7gd3hjc3	190	12	0	0	NUM
cord-326631-7gd3hjc3	190	13	.	.	PUNCT
cord-326631-7gd3hjc3	191	1	we	we	PRON
cord-326631-7gd3hjc3	191	2	now	now	ADV
cord-326631-7gd3hjc3	191	3	check	check	VERB
cord-326631-7gd3hjc3	191	4	that	that	SCONJ
cord-326631-7gd3hjc3	191	5	the	the	DET
cord-326631-7gd3hjc3	191	6	disease	disease	NOUN
cord-326631-7gd3hjc3	191	7	will	will	AUX
cord-326631-7gd3hjc3	191	8	always	always	ADV
cord-326631-7gd3hjc3	191	9	burn	burn	VERB
cord-326631-7gd3hjc3	191	10	out	out	ADP
cord-326631-7gd3hjc3	191	11	in	in	ADP
cord-326631-7gd3hjc3	191	12	this	this	DET
cord-326631-7gd3hjc3	191	13	model	model	NOUN
cord-326631-7gd3hjc3	191	14	,	,	PUNCT
cord-326631-7gd3hjc3	191	15	as	as	SCONJ
cord-326631-7gd3hjc3	191	16	expected	expect	VERB
cord-326631-7gd3hjc3	191	17	.	.	PUNCT
cord-326631-7gd3hjc3	192	1	which	which	PRON
cord-326631-7gd3hjc3	192	2	is	be	AUX
cord-326631-7gd3hjc3	192	3	strictly	strictly	ADV
cord-326631-7gd3hjc3	192	4	negative	negative	ADJ
cord-326631-7gd3hjc3	192	5	.	.	PUNCT
cord-326631-7gd3hjc3	193	1	hence	hence	ADV
cord-326631-7gd3hjc3	193	2	,	,	PUNCT
cord-326631-7gd3hjc3	193	3	s	s	PROPN
cord-326631-7gd3hjc3	194	1	+	+	CCONJ
cord-326631-7gd3hjc3	194	2	i	i	PRON
cord-326631-7gd3hjc3	194	3	tot	tot	VERB
cord-326631-7gd3hjc3	194	4	is	be	AUX
cord-326631-7gd3hjc3	194	5	decreasing	decrease	VERB
cord-326631-7gd3hjc3	194	6	and	and	CCONJ
cord-326631-7gd3hjc3	194	7	bounded	bound	VERB
cord-326631-7gd3hjc3	194	8	below	below	ADV
cord-326631-7gd3hjc3	194	9	by	by	ADP
cord-326631-7gd3hjc3	194	10	zero	zero	NUM
cord-326631-7gd3hjc3	194	11	.	.	PUNCT
cord-326631-7gd3hjc3	195	1	hence	hence	ADV
cord-326631-7gd3hjc3	195	2	lim	lim	PROPN
cord-326631-7gd3hjc3	195	3	t→∞	t→∞	PRON
cord-326631-7gd3hjc3	195	4	d	d	X
cord-326631-7gd3hjc3	195	5	dt	dt	PROPN
cord-326631-7gd3hjc3	195	6	(	(	PUNCT
cord-326631-7gd3hjc3	195	7	s	s	PROPN
cord-326631-7gd3hjc3	195	8	+	+	CCONJ
cord-326631-7gd3hjc3	195	9	i	i	PRON
cord-326631-7gd3hjc3	195	10	tot	tot	VERB
cord-326631-7gd3hjc3	195	11	)	)	PUNCT
cord-326631-7gd3hjc3	196	1	=	=	NOUN
cord-326631-7gd3hjc3	196	2	0	0	NUM
cord-326631-7gd3hjc3	196	3	,	,	PUNCT
cord-326631-7gd3hjc3	196	4	i.e.	i.e.	X
cord-326631-7gd3hjc3	196	5	,	,	PUNCT
cord-326631-7gd3hjc3	196	6	i	i	PRON
cord-326631-7gd3hjc3	196	7	tot	tot	NOUN
cord-326631-7gd3hjc3	196	8	(	(	PUNCT
cord-326631-7gd3hjc3	196	9	∞	∞	NUM
cord-326631-7gd3hjc3	196	10	)	)	PUNCT
cord-326631-7gd3hjc3	196	11	=	=	NOUN
cord-326631-7gd3hjc3	196	12	0	0	X
cord-326631-7gd3hjc3	196	13	.	.	PUNCT
cord-326631-7gd3hjc3	197	1	for	for	ADP
cord-326631-7gd3hjc3	197	2	the	the	DET
cord-326631-7gd3hjc3	197	3	model	model	NOUN
cord-326631-7gd3hjc3	197	4	specified	specify	VERB
cord-326631-7gd3hjc3	197	5	by	by	ADP
cord-326631-7gd3hjc3	197	6	eqs	eqs	PROPN
cord-326631-7gd3hjc3	197	7	.	.	PUNCT
cord-326631-7gd3hjc3	198	1	(	(	PUNCT
cord-326631-7gd3hjc3	198	2	21	21	NUM
cord-326631-7gd3hjc3	198	3	)	)	PUNCT
cord-326631-7gd3hjc3	198	4	,	,	PUNCT
cord-326631-7gd3hjc3	198	5	the	the	DET
cord-326631-7gd3hjc3	198	6	basic	basic	ADJ
cord-326631-7gd3hjc3	198	7	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	198	8	number	number	NOUN
cord-326631-7gd3hjc3	198	9	is	be	AUX
cord-326631-7gd3hjc3	198	10	in	in	ADP
cord-326631-7gd3hjc3	198	11	appendix	appendix	PROPN
cord-326631-7gd3hjc3	198	12	b	b	PROPN
cord-326631-7gd3hjc3	198	13	,	,	PUNCT
cord-326631-7gd3hjc3	198	14	we	we	PRON
cord-326631-7gd3hjc3	198	15	prove	prove	VERB
cord-326631-7gd3hjc3	198	16	that	that	SCONJ
cord-326631-7gd3hjc3	198	17	the	the	DET
cord-326631-7gd3hjc3	198	18	disease	disease	NOUN
cord-326631-7gd3hjc3	198	19	free	free	ADJ
cord-326631-7gd3hjc3	198	20	equilibrium	equilibrium	NOUN
cord-326631-7gd3hjc3	198	21	(	(	PUNCT
cord-326631-7gd3hjc3	198	22	dfe	dfe	PROPN
cord-326631-7gd3hjc3	198	23	)	)	PUNCT
cord-326631-7gd3hjc3	198	24	is	be	AUX
cord-326631-7gd3hjc3	198	25	unstable	unstable	ADJ
cord-326631-7gd3hjc3	198	26	if	if	SCONJ
cord-326631-7gd3hjc3	198	27	and	and	CCONJ
cord-326631-7gd3hjc3	198	28	only	only	ADV
cord-326631-7gd3hjc3	198	29	if	if	SCONJ
cord-326631-7gd3hjc3	198	30	r	r	NOUN
cord-326631-7gd3hjc3	198	31	0	0	PUNCT
cord-326631-7gd3hjc3	198	32	>	>	SYM
cord-326631-7gd3hjc3	198	33	1	1	NUM
cord-326631-7gd3hjc3	198	34	.	.	PUNCT
cord-326631-7gd3hjc3	199	1	to	to	PART
cord-326631-7gd3hjc3	199	2	find	find	VERB
cord-326631-7gd3hjc3	199	3	the	the	DET
cord-326631-7gd3hjc3	199	4	final	final	ADJ
cord-326631-7gd3hjc3	199	5	size	size	NOUN
cord-326631-7gd3hjc3	199	6	,	,	PUNCT
cord-326631-7gd3hjc3	199	7	we	we	PRON
cord-326631-7gd3hjc3	199	8	divide	divide	VERB
cord-326631-7gd3hjc3	199	9	by	by	ADP
cord-326631-7gd3hjc3	199	10	s	s	NOUN
cord-326631-7gd3hjc3	199	11	on	on	ADP
cord-326631-7gd3hjc3	199	12	both	both	DET
cord-326631-7gd3hjc3	199	13	sides	side	NOUN
cord-326631-7gd3hjc3	199	14	of	of	ADP
cord-326631-7gd3hjc3	199	15	(	(	PUNCT
cord-326631-7gd3hjc3	199	16	21a	21a	NUM
cord-326631-7gd3hjc3	199	17	)	)	PUNCT
cord-326631-7gd3hjc3	199	18	and	and	CCONJ
cord-326631-7gd3hjc3	199	19	integrate	integrate	VERB
cord-326631-7gd3hjc3	199	20	,	,	PUNCT
cord-326631-7gd3hjc3	199	21	substituting	substitute	VERB
cord-326631-7gd3hjc3	199	22	eq	eq	PROPN
cord-326631-7gd3hjc3	199	23	.	.	PUNCT
cord-326631-7gd3hjc3	200	1	(	(	PUNCT
cord-326631-7gd3hjc3	200	2	21a	21a	NUM
cord-326631-7gd3hjc3	200	3	)	)	PUNCT
cord-326631-7gd3hjc3	200	4	in	in	ADP
cord-326631-7gd3hjc3	200	5	eq	eq	PROPN
cord-326631-7gd3hjc3	200	6	.	.	PUNCT
cord-326631-7gd3hjc3	200	7	(	(	PUNCT
cord-326631-7gd3hjc3	200	8	21b	21b	NUM
cord-326631-7gd3hjc3	200	9	)	)	PUNCT
cord-326631-7gd3hjc3	200	10	we	we	PRON
cord-326631-7gd3hjc3	200	11	can	can	AUX
cord-326631-7gd3hjc3	200	12	writė	writė	AUX
cord-326631-7gd3hjc3	200	13	integrating	integrate	VERB
cord-326631-7gd3hjc3	200	14	this	this	PRON
cord-326631-7gd3hjc3	200	15	we	we	PRON
cord-326631-7gd3hjc3	200	16	obtain	obtain	VERB
cord-326631-7gd3hjc3	200	17	since	since	SCONJ
cord-326631-7gd3hjc3	200	18	we	we	PRON
cord-326631-7gd3hjc3	200	19	have	have	AUX
cord-326631-7gd3hjc3	200	20	established	establish	VERB
cord-326631-7gd3hjc3	200	21	that	that	PRON
cord-326631-7gd3hjc3	200	22	i(β	i(β	PROPN
cord-326631-7gd3hjc3	200	23	,	,	PUNCT
cord-326631-7gd3hjc3	200	24	∞	∞	NUM
cord-326631-7gd3hjc3	200	25	)	)	PUNCT
cord-326631-7gd3hjc3	200	26	=	=	NOUN
cord-326631-7gd3hjc3	200	27	0	0	NUM
cord-326631-7gd3hjc3	200	28	,	,	PUNCT
cord-326631-7gd3hjc3	200	29	we	we	PRON
cord-326631-7gd3hjc3	200	30	can	can	AUX
cord-326631-7gd3hjc3	200	31	write	write	VERB
cord-326631-7gd3hjc3	200	32	substituting	substituting	NOUN
cord-326631-7gd3hjc3	200	33	(	(	PUNCT
cord-326631-7gd3hjc3	200	34	25	25	NUM
cord-326631-7gd3hjc3	200	35	)	)	PUNCT
cord-326631-7gd3hjc3	200	36	into	into	ADP
cord-326631-7gd3hjc3	200	37	(	(	PUNCT
cord-326631-7gd3hjc3	200	38	24	24	NUM
cord-326631-7gd3hjc3	200	39	)	)	PUNCT
cord-326631-7gd3hjc3	200	40	and	and	CCONJ
cord-326631-7gd3hjc3	200	41	using	use	VERB
cord-326631-7gd3hjc3	200	42	(	(	PUNCT
cord-326631-7gd3hjc3	200	43	23	23	NUM
cord-326631-7gd3hjc3	200	44	)	)	PUNCT
cord-326631-7gd3hjc3	200	45	,	,	PUNCT
cord-326631-7gd3hjc3	200	46	we	we	PRON
cord-326631-7gd3hjc3	200	47	obtain	obtain	VERB
cord-326631-7gd3hjc3	200	48	hence	hence	ADV
cord-326631-7gd3hjc3	200	49	,	,	PUNCT
cord-326631-7gd3hjc3	200	50	since	since	SCONJ
cord-326631-7gd3hjc3	200	51	the	the	DET
cord-326631-7gd3hjc3	200	52	final	final	ADJ
cord-326631-7gd3hjc3	200	53	size	size	NOUN
cord-326631-7gd3hjc3	200	54	z	z	NOUN
cord-326631-7gd3hjc3	200	55	=	=	NOUN
cord-326631-7gd3hjc3	200	56	s(0	s(0	PROPN
cord-326631-7gd3hjc3	200	57	)	)	PUNCT
cord-326631-7gd3hjc3	200	58	−	−	PROPN
cord-326631-7gd3hjc3	200	59	s(∞	s(∞	PROPN
cord-326631-7gd3hjc3	200	60	)	)	PUNCT
cord-326631-7gd3hjc3	200	61	,	,	PUNCT
cord-326631-7gd3hjc3	200	62	we	we	PRON
cord-326631-7gd3hjc3	200	63	have	have	VERB
cord-326631-7gd3hjc3	200	64	it	it	PRON
cord-326631-7gd3hjc3	200	65	is	be	AUX
cord-326631-7gd3hjc3	200	66	possible	possible	ADJ
cord-326631-7gd3hjc3	200	67	to	to	PART
cord-326631-7gd3hjc3	200	68	generalize	generalize	VERB
cord-326631-7gd3hjc3	200	69	this	this	DET
cord-326631-7gd3hjc3	200	70	theorem	theorem	NOUN
cord-326631-7gd3hjc3	200	71	for	for	ADP
cord-326631-7gd3hjc3	200	72	an	an	DET
cord-326631-7gd3hjc3	200	73	si	si	PROPN
cord-326631-7gd3hjc3	200	74	n	n	NOUN
cord-326631-7gd3hjc3	200	75	r	r	NOUN
cord-326631-7gd3hjc3	200	76	model	model	NOUN
cord-326631-7gd3hjc3	200	77	with	with	ADP
cord-326631-7gd3hjc3	200	78	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	200	79	distributed	distribute	VERB
cord-326631-7gd3hjc3	200	80	stage	stage	NOUN
cord-326631-7gd3hjc3	200	81	durations	duration	NOUN
cord-326631-7gd3hjc3	200	82	and	and	CCONJ
cord-326631-7gd3hjc3	200	83	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	200	84	distributed	distribute	VERB
cord-326631-7gd3hjc3	200	85	transmission	transmission	NOUN
cord-326631-7gd3hjc3	200	86	rates	rate	NOUN
cord-326631-7gd3hjc3	200	87	in	in	ADP
cord-326631-7gd3hjc3	200	88	each	each	DET
cord-326631-7gd3hjc3	200	89	stage	stage	NOUN
cord-326631-7gd3hjc3	200	90	.	.	PUNCT
cord-326631-7gd3hjc3	201	1	we	we	PRON
cord-326631-7gd3hjc3	201	2	do	do	AUX
cord-326631-7gd3hjc3	201	3	not	not	PART
cord-326631-7gd3hjc3	201	4	go	go	VERB
cord-326631-7gd3hjc3	201	5	through	through	ADP
cord-326631-7gd3hjc3	201	6	the	the	DET
cord-326631-7gd3hjc3	201	7	details	detail	NOUN
cord-326631-7gd3hjc3	201	8	because	because	SCONJ
cord-326631-7gd3hjc3	201	9	no	no	DET
cord-326631-7gd3hjc3	201	10	new	new	ADJ
cord-326631-7gd3hjc3	201	11	ideas	idea	NOUN
cord-326631-7gd3hjc3	201	12	are	be	AUX
cord-326631-7gd3hjc3	201	13	required	require	VERB
cord-326631-7gd3hjc3	201	14	.	.	PUNCT
cord-326631-7gd3hjc3	202	1	with	with	ADP
cord-326631-7gd3hjc3	202	2	theorems	theorem	NOUN
cord-326631-7gd3hjc3	202	3	7.1	7.1	NUM
cord-326631-7gd3hjc3	202	4	and	and	CCONJ
cord-326631-7gd3hjc3	202	5	8.1	8.1	NUM
cord-326631-7gd3hjc3	202	6	in	in	ADP
cord-326631-7gd3hjc3	202	7	hand	hand	NOUN
cord-326631-7gd3hjc3	202	8	,	,	PUNCT
cord-326631-7gd3hjc3	202	9	the	the	DET
cord-326631-7gd3hjc3	202	10	extra	extra	ADJ
cord-326631-7gd3hjc3	202	11	effort	effort	NOUN
cord-326631-7gd3hjc3	202	12	required	require	VERB
cord-326631-7gd3hjc3	202	13	for	for	ADP
cord-326631-7gd3hjc3	202	14	the	the	DET
cord-326631-7gd3hjc3	202	15	generalization	generalization	NOUN
cord-326631-7gd3hjc3	202	16	is	be	AUX
cord-326631-7gd3hjc3	202	17	merely	merely	ADV
cord-326631-7gd3hjc3	202	18	one	one	NUM
cord-326631-7gd3hjc3	202	19	of	of	ADP
cord-326631-7gd3hjc3	202	20	keeping	keep	VERB
cord-326631-7gd3hjc3	202	21	track	track	NOUN
cord-326631-7gd3hjc3	202	22	of	of	ADP
cord-326631-7gd3hjc3	202	23	notation	notation	NOUN
cord-326631-7gd3hjc3	202	24	.	.	PUNCT
cord-326631-7gd3hjc3	203	1	in	in	ADP
cord-326631-7gd3hjc3	203	2	all	all	PRON
cord-326631-7gd3hjc3	203	3	of	of	ADP
cord-326631-7gd3hjc3	203	4	the	the	DET
cord-326631-7gd3hjc3	203	5	models	model	NOUN
cord-326631-7gd3hjc3	203	6	that	that	PRON
cord-326631-7gd3hjc3	203	7	we	we	PRON
cord-326631-7gd3hjc3	203	8	have	have	AUX
cord-326631-7gd3hjc3	203	9	discussed	discuss	VERB
cord-326631-7gd3hjc3	203	10	so	so	ADV
cord-326631-7gd3hjc3	203	11	far	far	ADV
cord-326631-7gd3hjc3	203	12	,	,	PUNCT
cord-326631-7gd3hjc3	203	13	we	we	PRON
cord-326631-7gd3hjc3	203	14	have	have	AUX
cord-326631-7gd3hjc3	203	15	assumed	assume	VERB
cord-326631-7gd3hjc3	203	16	that	that	SCONJ
cord-326631-7gd3hjc3	203	17	the	the	DET
cord-326631-7gd3hjc3	203	18	population	population	NOUN
cord-326631-7gd3hjc3	203	19	is	be	AUX
cord-326631-7gd3hjc3	203	20	homogeneously	homogeneously	ADV
cord-326631-7gd3hjc3	203	21	mixed	mixed	ADJ
cord-326631-7gd3hjc3	203	22	.	.	PUNCT
cord-326631-7gd3hjc3	204	1	in	in	ADP
cord-326631-7gd3hjc3	204	2	the	the	DET
cord-326631-7gd3hjc3	204	3	remainder	remainder	NOUN
cord-326631-7gd3hjc3	204	4	of	of	ADP
cord-326631-7gd3hjc3	204	5	this	this	DET
cord-326631-7gd3hjc3	204	6	paper	paper	NOUN
cord-326631-7gd3hjc3	204	7	,	,	PUNCT
cord-326631-7gd3hjc3	204	8	we	we	PRON
cord-326631-7gd3hjc3	204	9	explore	explore	VERB
cord-326631-7gd3hjc3	204	10	the	the	DET
cord-326631-7gd3hjc3	204	11	significance	significance	NOUN
cord-326631-7gd3hjc3	204	12	of	of	ADP
cord-326631-7gd3hjc3	204	13	heterogeneous	heterogeneous	ADJ
cord-326631-7gd3hjc3	204	14	mixing	mixing	NOUN
cord-326631-7gd3hjc3	204	15	for	for	ADP
cord-326631-7gd3hjc3	204	16	the	the	DET
cord-326631-7gd3hjc3	204	17	final	final	ADJ
cord-326631-7gd3hjc3	204	18	size	size	NOUN
cord-326631-7gd3hjc3	204	19	formula	formula	NOUN
cord-326631-7gd3hjc3	204	20	.	.	PUNCT
cord-326631-7gd3hjc3	205	1	in	in	ADP
cord-326631-7gd3hjc3	205	2	the	the	DET
cord-326631-7gd3hjc3	205	3	present	present	ADJ
cord-326631-7gd3hjc3	205	4	section	section	NOUN
cord-326631-7gd3hjc3	205	5	we	we	PRON
cord-326631-7gd3hjc3	205	6	identify	identify	VERB
cord-326631-7gd3hjc3	205	7	an	an	DET
cord-326631-7gd3hjc3	205	8	important	important	ADJ
cord-326631-7gd3hjc3	205	9	class	class	NOUN
cord-326631-7gd3hjc3	205	10	of	of	ADP
cord-326631-7gd3hjc3	205	11	spatially	spatially	ADV
cord-326631-7gd3hjc3	205	12	structured	structured	ADJ
cord-326631-7gd3hjc3	205	13	models	model	NOUN
cord-326631-7gd3hjc3	205	14	for	for	ADP
cord-326631-7gd3hjc3	205	15	which	which	PRON
cord-326631-7gd3hjc3	205	16	the	the	DET
cord-326631-7gd3hjc3	205	17	standard	standard	ADJ
cord-326631-7gd3hjc3	205	18	formula	formula	NOUN
cord-326631-7gd3hjc3	205	19	(	(	PUNCT
cord-326631-7gd3hjc3	205	20	5	5	NUM
cord-326631-7gd3hjc3	205	21	)	)	PUNCT
cord-326631-7gd3hjc3	205	22	remains	remain	VERB
cord-326631-7gd3hjc3	205	23	valid	valid	ADJ
cord-326631-7gd3hjc3	205	24	.	.	PUNCT
cord-326631-7gd3hjc3	206	1	a	a	DET
cord-326631-7gd3hjc3	206	2	simple	simple	ADJ
cord-326631-7gd3hjc3	206	3	but	but	CCONJ
cord-326631-7gd3hjc3	206	4	important	important	ADJ
cord-326631-7gd3hjc3	206	5	example	example	NOUN
cord-326631-7gd3hjc3	206	6	of	of	ADP
cord-326631-7gd3hjc3	206	7	heterogenous	heterogenous	ADJ
cord-326631-7gd3hjc3	206	8	mixing	mixing	NOUN
cord-326631-7gd3hjc3	206	9	occurs	occur	VERB
cord-326631-7gd3hjc3	206	10	if	if	SCONJ
cord-326631-7gd3hjc3	206	11	the	the	DET
cord-326631-7gd3hjc3	206	12	population	population	NOUN
cord-326631-7gd3hjc3	206	13	is	be	AUX
cord-326631-7gd3hjc3	206	14	divided	divide	VERB
cord-326631-7gd3hjc3	206	15	into	into	ADP
cord-326631-7gd3hjc3	206	16	a	a	DET
cord-326631-7gd3hjc3	206	17	number	number	NOUN
cord-326631-7gd3hjc3	206	18	of	of	ADP
cord-326631-7gd3hjc3	206	19	spatially	spatially	ADV
cord-326631-7gd3hjc3	206	20	isolated	isolate	VERB
cord-326631-7gd3hjc3	206	21	patches	patch	NOUN
cord-326631-7gd3hjc3	206	22	(	(	PUNCT
cord-326631-7gd3hjc3	206	23	e.g.	e.g.	ADV
cord-326631-7gd3hjc3	206	24	,	,	PUNCT
cord-326631-7gd3hjc3	206	25	cities	city	NOUN
cord-326631-7gd3hjc3	206	26	)	)	PUNCT
cord-326631-7gd3hjc3	206	27	,	,	PUNCT
cord-326631-7gd3hjc3	206	28	often	often	ADV
cord-326631-7gd3hjc3	206	29	called	call	VERB
cord-326631-7gd3hjc3	206	30	a	a	DET
cord-326631-7gd3hjc3	206	31	metapopulation	metapopulation	NOUN
cord-326631-7gd3hjc3	206	32	(	(	PUNCT
cord-326631-7gd3hjc3	206	33	hanski	hanski	NOUN
cord-326631-7gd3hjc3	206	34	and	and	CCONJ
cord-326631-7gd3hjc3	206	35	gilpin	gilpin	NOUN
cord-326631-7gd3hjc3	206	36	,	,	PUNCT
cord-326631-7gd3hjc3	206	37	1997	1997	NUM
cord-326631-7gd3hjc3	206	38	)	)	PUNCT
cord-326631-7gd3hjc3	206	39	.	.	PUNCT
cord-326631-7gd3hjc3	207	1	in	in	ADP
cord-326631-7gd3hjc3	207	2	ecological	ecological	ADJ
cord-326631-7gd3hjc3	207	3	models	model	NOUN
cord-326631-7gd3hjc3	207	4	,	,	PUNCT
cord-326631-7gd3hjc3	207	5	coupling	couple	VERB
cord-326631-7gd3hjc3	207	6	among	among	ADP
cord-326631-7gd3hjc3	207	7	patches	patch	NOUN
cord-326631-7gd3hjc3	207	8	in	in	ADP
cord-326631-7gd3hjc3	207	9	a	a	DET
cord-326631-7gd3hjc3	207	10	metapopulation	metapopulation	NOUN
cord-326631-7gd3hjc3	207	11	usually	usually	ADV
cord-326631-7gd3hjc3	207	12	occurs	occur	VERB
cord-326631-7gd3hjc3	207	13	as	as	ADP
cord-326631-7gd3hjc3	207	14	a	a	DET
cord-326631-7gd3hjc3	207	15	result	result	NOUN
cord-326631-7gd3hjc3	207	16	of	of	ADP
cord-326631-7gd3hjc3	207	17	migration	migration	NOUN
cord-326631-7gd3hjc3	207	18	(	(	PUNCT
cord-326631-7gd3hjc3	207	19	earn	earn	VERB
cord-326631-7gd3hjc3	207	20	et	et	PROPN
cord-326631-7gd3hjc3	207	21	al	al	PROPN
cord-326631-7gd3hjc3	207	22	.	.	PROPN
cord-326631-7gd3hjc3	207	23	,	,	PUNCT
cord-326631-7gd3hjc3	207	24	2000b	2000b	NUM
cord-326631-7gd3hjc3	207	25	)	)	PUNCT
cord-326631-7gd3hjc3	207	26	.	.	PUNCT
cord-326631-7gd3hjc3	208	1	in	in	ADP
cord-326631-7gd3hjc3	208	2	the	the	DET
cord-326631-7gd3hjc3	208	3	present	present	ADJ
cord-326631-7gd3hjc3	208	4	context	context	NOUN
cord-326631-7gd3hjc3	208	5	,	,	PUNCT
cord-326631-7gd3hjc3	208	6	inter	inter	ADJ
cord-326631-7gd3hjc3	208	7	-	-	ADJ
cord-326631-7gd3hjc3	208	8	patch	patch	ADJ
cord-326631-7gd3hjc3	208	9	coupling	coupling	NOUN
cord-326631-7gd3hjc3	208	10	occurs	occur	VERB
cord-326631-7gd3hjc3	208	11	because	because	SCONJ
cord-326631-7gd3hjc3	208	12	individuals	individual	NOUN
cord-326631-7gd3hjc3	208	13	travel	travel	VERB
cord-326631-7gd3hjc3	208	14	temporarily	temporarily	ADV
cord-326631-7gd3hjc3	208	15	from	from	ADP
cord-326631-7gd3hjc3	208	16	their	their	PRON
cord-326631-7gd3hjc3	208	17	home	home	NOUN
cord-326631-7gd3hjc3	208	18	patch	patch	NOUN
cord-326631-7gd3hjc3	208	19	to	to	ADP
cord-326631-7gd3hjc3	208	20	other	other	ADJ
cord-326631-7gd3hjc3	208	21	patches	patch	NOUN
cord-326631-7gd3hjc3	208	22	.	.	PUNCT
cord-326631-7gd3hjc3	209	1	on	on	ADP
cord-326631-7gd3hjc3	209	2	such	such	ADJ
cord-326631-7gd3hjc3	209	3	journeys	journey	NOUN
cord-326631-7gd3hjc3	209	4	,	,	PUNCT
cord-326631-7gd3hjc3	209	5	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	209	6	individuals	individual	NOUN
cord-326631-7gd3hjc3	209	7	might	might	AUX
cord-326631-7gd3hjc3	209	8	contact	contact	VERB
cord-326631-7gd3hjc3	209	9	infectious	infectious	ADJ
cord-326631-7gd3hjc3	209	10	individuals	individual	NOUN
cord-326631-7gd3hjc3	209	11	and	and	CCONJ
cord-326631-7gd3hjc3	209	12	become	become	VERB
cord-326631-7gd3hjc3	209	13	infected	infected	ADJ
cord-326631-7gd3hjc3	209	14	,	,	PUNCT
cord-326631-7gd3hjc3	209	15	and	and	CCONJ
cord-326631-7gd3hjc3	209	16	infectious	infectious	ADJ
cord-326631-7gd3hjc3	209	17	individuals	individual	NOUN
cord-326631-7gd3hjc3	209	18	might	might	AUX
cord-326631-7gd3hjc3	209	19	contact	contact	VERB
cord-326631-7gd3hjc3	209	20	susceptibles	susceptible	VERB
cord-326631-7gd3hjc3	209	21	and	and	CCONJ
cord-326631-7gd3hjc3	209	22	infect	infect	VERB
cord-326631-7gd3hjc3	209	23	them	they	PRON
cord-326631-7gd3hjc3	209	24	.	.	PUNCT
cord-326631-7gd3hjc3	210	1	if	if	SCONJ
cord-326631-7gd3hjc3	210	2	we	we	PRON
cord-326631-7gd3hjc3	210	3	restrict	restrict	VERB
cord-326631-7gd3hjc3	210	4	attention	attention	NOUN
cord-326631-7gd3hjc3	210	5	to	to	ADP
cord-326631-7gd3hjc3	210	6	a	a	DET
cord-326631-7gd3hjc3	210	7	single	single	ADJ
cord-326631-7gd3hjc3	210	8	infectious	infectious	ADJ
cord-326631-7gd3hjc3	210	9	stage	stage	NOUN
cord-326631-7gd3hjc3	210	10	with	with	ADP
cord-326631-7gd3hjc3	210	11	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	210	12	distributed	distribute	VERB
cord-326631-7gd3hjc3	210	13	infectious	infectious	ADJ
cord-326631-7gd3hjc3	210	14	period	period	NOUN
cord-326631-7gd3hjc3	210	15	then	then	ADV
cord-326631-7gd3hjc3	210	16	the	the	DET
cord-326631-7gd3hjc3	210	17	model	model	NOUN
cord-326631-7gd3hjc3	210	18	is	be	AUX
cord-326631-7gd3hjc3	210	19	specified	specify	VERB
cord-326631-7gd3hjc3	210	20	as	as	ADP
cord-326631-7gd3hjc3	210	21	follows	follow	NOUN
cord-326631-7gd3hjc3	210	22	.	.	PUNCT
cord-326631-7gd3hjc3	211	1	here	here	ADV
cord-326631-7gd3hjc3	211	2	,	,	PUNCT
cord-326631-7gd3hjc3	211	3	s	s	VERB
cord-326631-7gd3hjc3	211	4	i	i	PRON
cord-326631-7gd3hjc3	211	5	,	,	PUNCT
cord-326631-7gd3hjc3	211	6	i	i	PRON
cord-326631-7gd3hjc3	211	7	i	i	NOUN
cord-326631-7gd3hjc3	211	8	,	,	PUNCT
cord-326631-7gd3hjc3	211	9	and	and	CCONJ
cord-326631-7gd3hjc3	211	10	r	r	NOUN
cord-326631-7gd3hjc3	211	11	i	i	NOUN
cord-326631-7gd3hjc3	211	12	(	(	PUNCT
cord-326631-7gd3hjc3	211	13	i	i	NOUN
cord-326631-7gd3hjc3	211	14	=	=	NOUN
cord-326631-7gd3hjc3	211	15	1	1	NUM
cord-326631-7gd3hjc3	211	16	,	,	PUNCT
cord-326631-7gd3hjc3	211	17	.	.	PUNCT
cord-326631-7gd3hjc3	211	18	.	.	PUNCT
cord-326631-7gd3hjc3	211	19	.	.	PUNCT
cord-326631-7gd3hjc3	212	1	,	,	PUNCT
cord-326631-7gd3hjc3	212	2	n	n	X
cord-326631-7gd3hjc3	212	3	)	)	PUNCT
cord-326631-7gd3hjc3	212	4	are	be	AUX
cord-326631-7gd3hjc3	212	5	the	the	DET
cord-326631-7gd3hjc3	212	6	proportions	proportion	NOUN
cord-326631-7gd3hjc3	212	7	of	of	ADP
cord-326631-7gd3hjc3	212	8	the	the	DET
cord-326631-7gd3hjc3	212	9	population	population	NOUN
cord-326631-7gd3hjc3	212	10	in	in	ADP
cord-326631-7gd3hjc3	212	11	patch	patch	NOUN
cord-326631-7gd3hjc3	212	12	i	i	PRON
cord-326631-7gd3hjc3	212	13	that	that	PRON
cord-326631-7gd3hjc3	212	14	are	be	AUX
cord-326631-7gd3hjc3	212	15	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	212	16	,	,	PUNCT
cord-326631-7gd3hjc3	212	17	infectious	infectious	ADJ
cord-326631-7gd3hjc3	212	18	recovered	recover	VERB
cord-326631-7gd3hjc3	212	19	,	,	PUNCT
cord-326631-7gd3hjc3	212	20	respectively	respectively	ADV
cord-326631-7gd3hjc3	212	21	.	.	PUNCT
cord-326631-7gd3hjc3	213	1	summing	sum	VERB
cord-326631-7gd3hjc3	213	2	eqs	eqs	PROPN
cord-326631-7gd3hjc3	213	3	.	.	PUNCT
cord-326631-7gd3hjc3	214	1	(	(	PUNCT
cord-326631-7gd3hjc3	214	2	26	26	NUM
cord-326631-7gd3hjc3	214	3	)	)	PUNCT
cord-326631-7gd3hjc3	214	4	,	,	PUNCT
cord-326631-7gd3hjc3	214	5	we	we	PRON
cord-326631-7gd3hjc3	214	6	see	see	VERB
cord-326631-7gd3hjc3	214	7	that	that	PRON
cord-326631-7gd3hjc3	214	8	s	s	NOUN
cord-326631-7gd3hjc3	214	9	i	i	PRON
cord-326631-7gd3hjc3	214	10	(	(	PUNCT
cord-326631-7gd3hjc3	214	11	t	t	NOUN
cord-326631-7gd3hjc3	214	12	)	)	PUNCT
cord-326631-7gd3hjc3	215	1	+	+	CCONJ
cord-326631-7gd3hjc3	216	1	i	i	PRON
cord-326631-7gd3hjc3	216	2	i	i	NOUN
cord-326631-7gd3hjc3	216	3	(	(	PUNCT
cord-326631-7gd3hjc3	216	4	t	t	NOUN
cord-326631-7gd3hjc3	216	5	)	)	PUNCT
cord-326631-7gd3hjc3	217	1	+	+	CCONJ
cord-326631-7gd3hjc3	218	1	r	r	NOUN
cord-326631-7gd3hjc3	218	2	i	i	NOUN
cord-326631-7gd3hjc3	218	3	(	(	PUNCT
cord-326631-7gd3hjc3	218	4	t	t	NOUN
cord-326631-7gd3hjc3	218	5	)	)	PUNCT
cord-326631-7gd3hjc3	218	6	=	=	PUNCT
cord-326631-7gd3hjc3	218	7	1	1	NUM
cord-326631-7gd3hjc3	218	8	is	be	AUX
cord-326631-7gd3hjc3	218	9	invariant	invariant	ADJ
cord-326631-7gd3hjc3	218	10	in	in	ADP
cord-326631-7gd3hjc3	218	11	all	all	DET
cord-326631-7gd3hjc3	218	12	patches	patch	NOUN
cord-326631-7gd3hjc3	218	13	.	.	PUNCT
cord-326631-7gd3hjc3	219	1	we	we	PRON
cord-326631-7gd3hjc3	219	2	denote	denote	VERB
cord-326631-7gd3hjc3	219	3	by	by	ADP
cord-326631-7gd3hjc3	219	4	n	n	PRON
cord-326631-7gd3hjc3	219	5	i	i	PRON
cord-326631-7gd3hjc3	219	6	the	the	DET
cord-326631-7gd3hjc3	219	7	number	number	NOUN
cord-326631-7gd3hjc3	219	8	of	of	ADP
cord-326631-7gd3hjc3	219	9	individuals	individual	NOUN
cord-326631-7gd3hjc3	219	10	in	in	ADP
cord-326631-7gd3hjc3	219	11	patch	patch	PROPN
cord-326631-7gd3hjc3	219	12	i	i	PROPN
cord-326631-7gd3hjc3	219	13	,	,	PUNCT
cord-326631-7gd3hjc3	219	14	so	so	CCONJ
cord-326631-7gd3hjc3	219	15	the	the	DET
cord-326631-7gd3hjc3	219	16	total	total	ADJ
cord-326631-7gd3hjc3	219	17	population	population	NOUN
cord-326631-7gd3hjc3	219	18	size	size	NOUN
cord-326631-7gd3hjc3	219	19	is	be	AUX
cord-326631-7gd3hjc3	219	20	n	n	NOUN
cord-326631-7gd3hjc3	219	21	=	=	NOUN
cord-326631-7gd3hjc3	220	1	i	i	PRON
cord-326631-7gd3hjc3	221	1	n	n	NOUN
cord-326631-7gd3hjc3	222	1	i	i	PRON
cord-326631-7gd3hjc3	222	2	.	.	PUNCT
cord-326631-7gd3hjc3	223	1	it	it	PRON
cord-326631-7gd3hjc3	223	2	is	be	AUX
cord-326631-7gd3hjc3	223	3	also	also	ADV
cord-326631-7gd3hjc3	223	4	convenient	convenient	ADJ
cord-326631-7gd3hjc3	223	5	to	to	PART
cord-326631-7gd3hjc3	223	6	use	use	VERB
cord-326631-7gd3hjc3	223	7	b	b	X
cord-326631-7gd3hjc3	223	8	=	=	SYM
cord-326631-7gd3hjc3	223	9	(	(	PUNCT
cord-326631-7gd3hjc3	223	10	β	β	PROPN
cord-326631-7gd3hjc3	223	11	i	i	NOUN
cord-326631-7gd3hjc3	223	12	j	j	NOUN
cord-326631-7gd3hjc3	223	13	)	)	PUNCT
cord-326631-7gd3hjc3	223	14	to	to	PART
cord-326631-7gd3hjc3	223	15	denote	denote	VERB
cord-326631-7gd3hjc3	223	16	the	the	DET
cord-326631-7gd3hjc3	223	17	n	n	PROPN
cord-326631-7gd3hjc3	223	18	×	×	PROPN
cord-326631-7gd3hjc3	223	19	n	n	NOUN
cord-326631-7gd3hjc3	223	20	transmission	transmission	NOUN
cord-326631-7gd3hjc3	223	21	matrix	matrix	NOUN
cord-326631-7gd3hjc3	223	22	.	.	PUNCT
cord-326631-7gd3hjc3	224	1	similar	similar	ADJ
cord-326631-7gd3hjc3	224	2	to	to	ADP
cord-326631-7gd3hjc3	224	3	our	our	PRON
cord-326631-7gd3hjc3	224	4	analysis	analysis	NOUN
cord-326631-7gd3hjc3	224	5	of	of	ADP
cord-326631-7gd3hjc3	224	6	other	other	ADJ
cord-326631-7gd3hjc3	224	7	models	model	NOUN
cord-326631-7gd3hjc3	224	8	in	in	ADP
cord-326631-7gd3hjc3	224	9	previous	previous	ADJ
cord-326631-7gd3hjc3	224	10	sections	section	NOUN
cord-326631-7gd3hjc3	224	11	,	,	PUNCT
cord-326631-7gd3hjc3	224	12	it	it	PRON
cord-326631-7gd3hjc3	224	13	is	be	AUX
cord-326631-7gd3hjc3	224	14	straightforward	straightforward	ADJ
cord-326631-7gd3hjc3	224	15	to	to	PART
cord-326631-7gd3hjc3	224	16	prove	prove	VERB
cord-326631-7gd3hjc3	224	17	that	that	PRON
cord-326631-7gd3hjc3	224	18	s	s	NOUN
cord-326631-7gd3hjc3	224	19	i	i	PRON
cord-326631-7gd3hjc3	224	20	(	(	PUNCT
cord-326631-7gd3hjc3	224	21	∞	∞	NUM
cord-326631-7gd3hjc3	224	22	)	)	PUNCT
cord-326631-7gd3hjc3	224	23	,	,	PUNCT
cord-326631-7gd3hjc3	225	1	r	r	NOUN
cord-326631-7gd3hjc3	225	2	i	i	NOUN
cord-326631-7gd3hjc3	225	3	(	(	PUNCT
cord-326631-7gd3hjc3	225	4	∞	∞	NUM
cord-326631-7gd3hjc3	225	5	)	)	PUNCT
cord-326631-7gd3hjc3	225	6	,	,	PUNCT
cord-326631-7gd3hjc3	225	7	i	i	PRON
cord-326631-7gd3hjc3	225	8	i	i	NOUN
cord-326631-7gd3hjc3	225	9	(	(	PUNCT
cord-326631-7gd3hjc3	225	10	∞	∞	NUM
cord-326631-7gd3hjc3	225	11	)	)	PUNCT
cord-326631-7gd3hjc3	225	12	exist	exist	VERB
cord-326631-7gd3hjc3	225	13	,	,	PUNCT
cord-326631-7gd3hjc3	225	14	that	that	PRON
cord-326631-7gd3hjc3	225	15	s	s	VERB
cord-326631-7gd3hjc3	225	16	i	i	PRON
cord-326631-7gd3hjc3	225	17	(	(	PUNCT
cord-326631-7gd3hjc3	225	18	∞	∞	NUM
cord-326631-7gd3hjc3	225	19	)	)	PUNCT
cord-326631-7gd3hjc3	225	20	+	+	CCONJ
cord-326631-7gd3hjc3	226	1	r	r	NOUN
cord-326631-7gd3hjc3	226	2	i	i	NOUN
cord-326631-7gd3hjc3	226	3	(	(	PUNCT
cord-326631-7gd3hjc3	226	4	∞	∞	NUM
cord-326631-7gd3hjc3	226	5	)	)	PUNCT
cord-326631-7gd3hjc3	226	6	=	=	SYM
cord-326631-7gd3hjc3	226	7	1	1	NUM
cord-326631-7gd3hjc3	226	8	and	and	CCONJ
cord-326631-7gd3hjc3	226	9	that	that	SCONJ
cord-326631-7gd3hjc3	227	1	i	i	PRON
cord-326631-7gd3hjc3	228	1	i	i	NOUN
cord-326631-7gd3hjc3	228	2	(	(	PUNCT
cord-326631-7gd3hjc3	228	3	∞	∞	NUM
cord-326631-7gd3hjc3	228	4	)	)	PUNCT
cord-326631-7gd3hjc3	228	5	=	=	NOUN
cord-326631-7gd3hjc3	228	6	0	0	X
cord-326631-7gd3hjc3	228	7	.	.	PUNCT
cord-326631-7gd3hjc3	229	1	since	since	SCONJ
cord-326631-7gd3hjc3	229	2	β	β	PROPN
cord-326631-7gd3hjc3	229	3	i	i	NOUN
cord-326631-7gd3hjc3	229	4	j	j	NOUN
cord-326631-7gd3hjc3	229	5	≥	≥	PUNCT
cord-326631-7gd3hjc3	229	6	0	0	NUM
cord-326631-7gd3hjc3	229	7	,	,	PUNCT
cord-326631-7gd3hjc3	229	8	the	the	DET
cord-326631-7gd3hjc3	229	9	dominant	dominant	ADJ
cord-326631-7gd3hjc3	229	10	eigenvalue	eigenvalue	NOUN
cord-326631-7gd3hjc3	229	11	λ	λ	PROPN
cord-326631-7gd3hjc3	229	12	of	of	ADP
cord-326631-7gd3hjc3	229	13	b	b	PROPN
cord-326631-7gd3hjc3	229	14	is	be	AUX
cord-326631-7gd3hjc3	229	15	real	real	ADJ
cord-326631-7gd3hjc3	229	16	and	and	CCONJ
cord-326631-7gd3hjc3	229	17	positive	positive	ADJ
cord-326631-7gd3hjc3	229	18	(	(	PUNCT
cord-326631-7gd3hjc3	229	19	horn	horn	NOUN
cord-326631-7gd3hjc3	229	20	and	and	CCONJ
cord-326631-7gd3hjc3	229	21	johnson	johnson	PROPN
cord-326631-7gd3hjc3	229	22	,	,	PUNCT
cord-326631-7gd3hjc3	229	23	1985	1985	NUM
cord-326631-7gd3hjc3	229	24	)	)	PUNCT
cord-326631-7gd3hjc3	229	25	.	.	PUNCT
cord-326631-7gd3hjc3	230	1	if	if	SCONJ
cord-326631-7gd3hjc3	230	2	we	we	PRON
cord-326631-7gd3hjc3	230	3	linearize	linearize	VERB
cord-326631-7gd3hjc3	230	4	the	the	DET
cord-326631-7gd3hjc3	230	5	model	model	NOUN
cord-326631-7gd3hjc3	230	6	(	(	PUNCT
cord-326631-7gd3hjc3	230	7	26	26	NUM
cord-326631-7gd3hjc3	230	8	)	)	PUNCT
cord-326631-7gd3hjc3	230	9	at	at	ADP
cord-326631-7gd3hjc3	230	10	the	the	DET
cord-326631-7gd3hjc3	230	11	disease	disease	NOUN
cord-326631-7gd3hjc3	230	12	free	free	ADJ
cord-326631-7gd3hjc3	230	13	equilibrium	equilibrium	NOUN
cord-326631-7gd3hjc3	230	14	(	(	PUNCT
cord-326631-7gd3hjc3	230	15	dfe	dfe	PROPN
cord-326631-7gd3hjc3	230	16	)	)	PUNCT
cord-326631-7gd3hjc3	230	17	(	(	PUNCT
cord-326631-7gd3hjc3	230	18	s	s	PROPN
cord-326631-7gd3hjc3	230	19	i	i	NOUN
cord-326631-7gd3hjc3	230	20	=	=	NOUN
cord-326631-7gd3hjc3	230	21	1	1	NUM
cord-326631-7gd3hjc3	230	22	,	,	PUNCT
cord-326631-7gd3hjc3	230	23	i	i	PRON
cord-326631-7gd3hjc3	230	24	i	i	NOUN
cord-326631-7gd3hjc3	230	25	=	=	NOUN
cord-326631-7gd3hjc3	230	26	0	0	NUM
cord-326631-7gd3hjc3	230	27	,	,	PUNCT
cord-326631-7gd3hjc3	230	28	r	r	NOUN
cord-326631-7gd3hjc3	230	29	i	i	NOUN
cord-326631-7gd3hjc3	230	30	=	=	NOUN
cord-326631-7gd3hjc3	230	31	0	0	NUM
cord-326631-7gd3hjc3	230	32	)	)	PUNCT
cord-326631-7gd3hjc3	230	33	,	,	PUNCT
cord-326631-7gd3hjc3	230	34	we	we	PRON
cord-326631-7gd3hjc3	230	35	see	see	VERB
cord-326631-7gd3hjc3	230	36	that	that	SCONJ
cord-326631-7gd3hjc3	230	37	the	the	DET
cord-326631-7gd3hjc3	230	38	stability	stability	NOUN
cord-326631-7gd3hjc3	230	39	of	of	ADP
cord-326631-7gd3hjc3	230	40	the	the	DET
cord-326631-7gd3hjc3	230	41	dfe	dfe	PROPN
cord-326631-7gd3hjc3	230	42	is	be	AUX
cord-326631-7gd3hjc3	230	43	determined	determine	VERB
cord-326631-7gd3hjc3	230	44	by	by	ADP
cord-326631-7gd3hjc3	230	45	λ	λ	PROPN
cord-326631-7gd3hjc3	230	46	.	.	PUNCT
cord-326631-7gd3hjc3	231	1	if	if	SCONJ
cord-326631-7gd3hjc3	231	2	λ	λ	PROPN
cord-326631-7gd3hjc3	231	3	/	/	SYM
cord-326631-7gd3hjc3	231	4	γ	γ	X
cord-326631-7gd3hjc3	231	5	>	>	SYM
cord-326631-7gd3hjc3	231	6	1	1	NUM
cord-326631-7gd3hjc3	231	7	,	,	PUNCT
cord-326631-7gd3hjc3	231	8	then	then	ADV
cord-326631-7gd3hjc3	231	9	the	the	DET
cord-326631-7gd3hjc3	231	10	dfe	dfe	PROPN
cord-326631-7gd3hjc3	231	11	is	be	AUX
cord-326631-7gd3hjc3	231	12	unstable	unstable	ADJ
cord-326631-7gd3hjc3	231	13	,	,	PUNCT
cord-326631-7gd3hjc3	231	14	otherwise	otherwise	ADV
cord-326631-7gd3hjc3	231	15	it	it	PRON
cord-326631-7gd3hjc3	231	16	is	be	AUX
cord-326631-7gd3hjc3	231	17	stable	stable	ADJ
cord-326631-7gd3hjc3	231	18	.	.	PUNCT
cord-326631-7gd3hjc3	232	1	thus	thus	ADV
cord-326631-7gd3hjc3	232	2	,	,	PUNCT
cord-326631-7gd3hjc3	232	3	the	the	DET
cord-326631-7gd3hjc3	232	4	threshold	threshold	NOUN
cord-326631-7gd3hjc3	232	5	for	for	ADP
cord-326631-7gd3hjc3	232	6	exponential	exponential	ADJ
cord-326631-7gd3hjc3	232	7	growth	growth	NOUN
cord-326631-7gd3hjc3	232	8	of	of	ADP
cord-326631-7gd3hjc3	232	9	cases	case	NOUN
cord-326631-7gd3hjc3	232	10	(	(	PUNCT
cord-326631-7gd3hjc3	232	11	an	an	DET
cord-326631-7gd3hjc3	232	12	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	232	13	)	)	PUNCT
cord-326631-7gd3hjc3	232	14	is	be	AUX
cord-326631-7gd3hjc3	232	15	determined	determine	VERB
cord-326631-7gd3hjc3	232	16	by	by	ADP
cord-326631-7gd3hjc3	232	17	the	the	DET
cord-326631-7gd3hjc3	232	18	value	value	NOUN
cord-326631-7gd3hjc3	232	19	of	of	ADP
cord-326631-7gd3hjc3	232	20	r	r	NOUN
cord-326631-7gd3hjc3	232	21	0	0	NUM
cord-326631-7gd3hjc3	232	22	=	=	SYM
cord-326631-7gd3hjc3	232	23	λ	λ	PROPN
cord-326631-7gd3hjc3	232	24	/	/	SYM
cord-326631-7gd3hjc3	232	25	γ	γ	PROPN
cord-326631-7gd3hjc3	232	26	,	,	PUNCT
cord-326631-7gd3hjc3	232	27	which	which	PRON
cord-326631-7gd3hjc3	232	28	can	can	AUX
cord-326631-7gd3hjc3	232	29	be	be	AUX
cord-326631-7gd3hjc3	232	30	interpreted	interpret	VERB
cord-326631-7gd3hjc3	232	31	as	as	ADP
cord-326631-7gd3hjc3	232	32	the	the	DET
cord-326631-7gd3hjc3	232	33	basic	basic	ADJ
cord-326631-7gd3hjc3	232	34	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	232	35	number	number	NOUN
cord-326631-7gd3hjc3	232	36	(	(	PUNCT
cord-326631-7gd3hjc3	232	37	van	van	PROPN
cord-326631-7gd3hjc3	232	38	den	den	PROPN
cord-326631-7gd3hjc3	232	39	driessche	driessche	PROPN
cord-326631-7gd3hjc3	232	40	and	and	CCONJ
cord-326631-7gd3hjc3	232	41	watmough	watmough	PROPN
cord-326631-7gd3hjc3	232	42	,	,	PUNCT
cord-326631-7gd3hjc3	232	43	2002	2002	NUM
cord-326631-7gd3hjc3	232	44	)	)	PUNCT
cord-326631-7gd3hjc3	232	45	.	.	PUNCT
cord-326631-7gd3hjc3	233	1	the	the	DET
cord-326631-7gd3hjc3	233	2	final	final	ADJ
cord-326631-7gd3hjc3	233	3	size	size	NOUN
cord-326631-7gd3hjc3	233	4	in	in	ADP
cord-326631-7gd3hjc3	233	5	patch	patch	NOUN
cord-326631-7gd3hjc3	233	6	i	i	PRON
cord-326631-7gd3hjc3	233	7	is	be	AUX
cord-326631-7gd3hjc3	233	8	z	z	NOUN
cord-326631-7gd3hjc3	233	9	i	i	PRON
cord-326631-7gd3hjc3	233	10	=	=	NOUN
cord-326631-7gd3hjc3	233	11	s	s	PROPN
cord-326631-7gd3hjc3	233	12	i	i	NOUN
cord-326631-7gd3hjc3	233	13	(	(	PUNCT
cord-326631-7gd3hjc3	233	14	0	0	NUM
cord-326631-7gd3hjc3	233	15	)	)	PUNCT
cord-326631-7gd3hjc3	233	16	−	−	PUNCT
cord-326631-7gd3hjc3	233	17	s	s	PROPN
cord-326631-7gd3hjc3	233	18	i	i	NOUN
cord-326631-7gd3hjc3	233	19	(	(	PUNCT
cord-326631-7gd3hjc3	233	20	∞	∞	NUM
cord-326631-7gd3hjc3	233	21	)	)	PUNCT
cord-326631-7gd3hjc3	233	22	.	.	PUNCT
cord-326631-7gd3hjc3	234	1	we	we	PRON
cord-326631-7gd3hjc3	234	2	can	can	AUX
cord-326631-7gd3hjc3	234	3	obtain	obtain	VERB
cord-326631-7gd3hjc3	234	4	a	a	DET
cord-326631-7gd3hjc3	234	5	system	system	NOUN
cord-326631-7gd3hjc3	234	6	of	of	ADP
cord-326631-7gd3hjc3	234	7	n	n	ADV
cord-326631-7gd3hjc3	234	8	coupled	couple	VERB
cord-326631-7gd3hjc3	234	9	algebraic	algebraic	ADJ
cord-326631-7gd3hjc3	234	10	equations	equation	NOUN
cord-326631-7gd3hjc3	234	11	for	for	ADP
cord-326631-7gd3hjc3	234	12	the	the	DET
cord-326631-7gd3hjc3	234	13	z	z	NOUN
cord-326631-7gd3hjc3	234	14	i	i	PRON
cord-326631-7gd3hjc3	234	15	if	if	SCONJ
cord-326631-7gd3hjc3	234	16	we	we	PRON
cord-326631-7gd3hjc3	234	17	divide	divide	VERB
cord-326631-7gd3hjc3	234	18	by	by	ADP
cord-326631-7gd3hjc3	234	19	s	s	NOUN
cord-326631-7gd3hjc3	234	20	i	i	PRON
cord-326631-7gd3hjc3	234	21	on	on	ADP
cord-326631-7gd3hjc3	234	22	both	both	DET
cord-326631-7gd3hjc3	234	23	sides	side	NOUN
cord-326631-7gd3hjc3	234	24	of	of	ADP
cord-326631-7gd3hjc3	234	25	eq	eq	PROPN
cord-326631-7gd3hjc3	234	26	.	.	PUNCT
cord-326631-7gd3hjc3	235	1	(	(	PUNCT
cord-326631-7gd3hjc3	235	2	26a	26a	NUM
cord-326631-7gd3hjc3	235	3	)	)	PUNCT
cord-326631-7gd3hjc3	236	1	and	and	CCONJ
cord-326631-7gd3hjc3	236	2	integrate	integrate	VERB
cord-326631-7gd3hjc3	236	3	from	from	ADP
cord-326631-7gd3hjc3	236	4	0	0	NUM
cord-326631-7gd3hjc3	236	5	to	to	ADP
cord-326631-7gd3hjc3	236	6	∞.	∞.	PROPN
cord-326631-7gd3hjc3	236	7	these	these	DET
cord-326631-7gd3hjc3	236	8	algebraic	algebraic	ADJ
cord-326631-7gd3hjc3	236	9	equations	equation	NOUN
cord-326631-7gd3hjc3	236	10	contain	contain	VERB
cord-326631-7gd3hjc3	236	11	∞	∞	NUM
cord-326631-7gd3hjc3	236	12	0	0	NUM
cord-326631-7gd3hjc3	237	1	i	i	PRON
cord-326631-7gd3hjc3	237	2	i	i	PRON
cord-326631-7gd3hjc3	237	3	dt	dt	PROPN
cord-326631-7gd3hjc3	237	4	,	,	PUNCT
cord-326631-7gd3hjc3	237	5	which	which	PRON
cord-326631-7gd3hjc3	237	6	can	can	AUX
cord-326631-7gd3hjc3	237	7	be	be	AUX
cord-326631-7gd3hjc3	237	8	eliminated	eliminate	VERB
cord-326631-7gd3hjc3	237	9	by	by	ADP
cord-326631-7gd3hjc3	237	10	integrating	integrate	VERB
cord-326631-7gd3hjc3	237	11	eq	eq	PROPN
cord-326631-7gd3hjc3	237	12	.	.	PUNCT
cord-326631-7gd3hjc3	237	13	(	(	PUNCT
cord-326631-7gd3hjc3	237	14	26c	26c	NUM
cord-326631-7gd3hjc3	237	15	)	)	PUNCT
cord-326631-7gd3hjc3	237	16	and	and	CCONJ
cord-326631-7gd3hjc3	237	17	noting	note	VERB
cord-326631-7gd3hjc3	237	18	that	that	SCONJ
cord-326631-7gd3hjc3	237	19	z	z	X
cord-326631-7gd3hjc3	237	20	i	i	PRON
cord-326631-7gd3hjc3	237	21	=	=	NOUN
cord-326631-7gd3hjc3	237	22	r	r	NOUN
cord-326631-7gd3hjc3	237	23	i	i	NOUN
cord-326631-7gd3hjc3	237	24	(	(	PUNCT
cord-326631-7gd3hjc3	237	25	∞	∞	NUM
cord-326631-7gd3hjc3	237	26	)	)	PUNCT
cord-326631-7gd3hjc3	237	27	−	−	X
cord-326631-7gd3hjc3	237	28	r	r	NOUN
cord-326631-7gd3hjc3	237	29	i	i	NOUN
cord-326631-7gd3hjc3	237	30	(	(	PUNCT
cord-326631-7gd3hjc3	237	31	0	0	NUM
cord-326631-7gd3hjc3	237	32	)	)	PUNCT
cord-326631-7gd3hjc3	237	33	.	.	PUNCT
cord-326631-7gd3hjc3	238	1	in	in	ADP
cord-326631-7gd3hjc3	238	2	the	the	DET
cord-326631-7gd3hjc3	238	3	limit	limit	NOUN
cord-326631-7gd3hjc3	238	4	i	i	PRON
cord-326631-7gd3hjc3	238	5	i	i	NOUN
cord-326631-7gd3hjc3	238	6	(	(	PUNCT
cord-326631-7gd3hjc3	238	7	0	0	NUM
cord-326631-7gd3hjc3	238	8	)	)	PUNCT
cord-326631-7gd3hjc3	238	9	→	→	PUNCT
cord-326631-7gd3hjc3	238	10	0	0	NUM
cord-326631-7gd3hjc3	238	11	,	,	PUNCT
cord-326631-7gd3hjc3	238	12	s	s	NOUN
cord-326631-7gd3hjc3	238	13	i	i	NOUN
cord-326631-7gd3hjc3	238	14	(	(	PUNCT
cord-326631-7gd3hjc3	238	15	0	0	NUM
cord-326631-7gd3hjc3	238	16	)	)	PUNCT
cord-326631-7gd3hjc3	238	17	→	→	SYM
cord-326631-7gd3hjc3	238	18	1	1	X
cord-326631-7gd3hjc3	238	19	,	,	PUNCT
cord-326631-7gd3hjc3	238	20	we	we	PRON
cord-326631-7gd3hjc3	238	21	obtain	obtain	VERB
cord-326631-7gd3hjc3	238	22	these	these	DET
cord-326631-7gd3hjc3	238	23	equations	equation	NOUN
cord-326631-7gd3hjc3	238	24	form	form	VERB
cord-326631-7gd3hjc3	238	25	a	a	DET
cord-326631-7gd3hjc3	238	26	special	special	ADJ
cord-326631-7gd3hjc3	238	27	case	case	NOUN
cord-326631-7gd3hjc3	238	28	of	of	ADP
cord-326631-7gd3hjc3	238	29	a	a	DET
cord-326631-7gd3hjc3	238	30	more	more	ADV
cord-326631-7gd3hjc3	238	31	general	general	ADJ
cord-326631-7gd3hjc3	238	32	final	final	ADJ
cord-326631-7gd3hjc3	238	33	size	size	NOUN
cord-326631-7gd3hjc3	238	34	formula	formula	NOUN
cord-326631-7gd3hjc3	238	35	discussed	discuss	VERB
cord-326631-7gd3hjc3	238	36	by	by	ADP
cord-326631-7gd3hjc3	238	37	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	238	38	and	and	CCONJ
cord-326631-7gd3hjc3	238	39	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	238	40	(	(	PUNCT
cord-326631-7gd3hjc3	238	41	2000	2000	NUM
cord-326631-7gd3hjc3	238	42	)	)	PUNCT
cord-326631-7gd3hjc3	238	43	(	(	PUNCT
cord-326631-7gd3hjc3	238	44	exercises	exercise	VERB
cord-326631-7gd3hjc3	238	45	6.17	6.17	NUM
cord-326631-7gd3hjc3	238	46	and	and	CCONJ
cord-326631-7gd3hjc3	238	47	6.19	6.19	NUM
cord-326631-7gd3hjc3	238	48	)	)	PUNCT
cord-326631-7gd3hjc3	238	49	.	.	PUNCT
cord-326631-7gd3hjc3	239	1	in	in	ADP
cord-326631-7gd3hjc3	239	2	their	their	PRON
cord-326631-7gd3hjc3	239	3	solution	solution	NOUN
cord-326631-7gd3hjc3	239	4	to	to	PART
cord-326631-7gd3hjc3	239	5	exercise	exercise	VERB
cord-326631-7gd3hjc3	239	6	6.19	6.19	NUM
cord-326631-7gd3hjc3	239	7	,	,	PUNCT
cord-326631-7gd3hjc3	239	8	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	239	9	and	and	CCONJ
cord-326631-7gd3hjc3	239	10	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	239	11	(	(	PUNCT
cord-326631-7gd3hjc3	239	12	2000	2000	NUM
cord-326631-7gd3hjc3	239	13	)	)	PUNCT
cord-326631-7gd3hjc3	239	14	sketch	sketch	VERB
cord-326631-7gd3hjc3	239	15	an	an	DET
cord-326631-7gd3hjc3	239	16	argument	argument	NOUN
cord-326631-7gd3hjc3	239	17	that	that	PRON
cord-326631-7gd3hjc3	239	18	implies	imply	VERB
cord-326631-7gd3hjc3	239	19	that	that	SCONJ
cord-326631-7gd3hjc3	239	20	if	if	SCONJ
cord-326631-7gd3hjc3	239	21	r	r	NOUN
cord-326631-7gd3hjc3	239	22	0	0	PUNCT
cord-326631-7gd3hjc3	239	23	>	>	SYM
cord-326631-7gd3hjc3	239	24	1	1	NUM
cord-326631-7gd3hjc3	239	25	then	then	ADV
cord-326631-7gd3hjc3	239	26	there	there	PRON
cord-326631-7gd3hjc3	239	27	is	be	VERB
cord-326631-7gd3hjc3	239	28	a	a	DET
cord-326631-7gd3hjc3	239	29	unique	unique	ADJ
cord-326631-7gd3hjc3	239	30	non	non	ADJ
cord-326631-7gd3hjc3	239	31	-	-	ADJ
cord-326631-7gd3hjc3	239	32	trivial	trivial	ADJ
cord-326631-7gd3hjc3	239	33	(	(	PUNCT
cord-326631-7gd3hjc3	239	34	i.e.	i.e.	X
cord-326631-7gd3hjc3	239	35	,	,	PUNCT
cord-326631-7gd3hjc3	239	36	non	non	ADJ
cord-326631-7gd3hjc3	239	37	-	-	ADJ
cord-326631-7gd3hjc3	239	38	zero	zero	NUM
cord-326631-7gd3hjc3	239	39	)	)	PUNCT
cord-326631-7gd3hjc3	239	40	solution	solution	NOUN
cord-326631-7gd3hjc3	239	41	to	to	ADP
cord-326631-7gd3hjc3	239	42	eqs	eqs	PROPN
cord-326631-7gd3hjc3	239	43	.	.	PUNCT
cord-326631-7gd3hjc3	240	1	(	(	PUNCT
cord-326631-7gd3hjc3	240	2	27	27	NUM
cord-326631-7gd3hjc3	240	3	)	)	PUNCT
cord-326631-7gd3hjc3	240	4	.	.	PUNCT
cord-326631-7gd3hjc3	241	1	the	the	DET
cord-326631-7gd3hjc3	241	2	final	final	ADJ
cord-326631-7gd3hjc3	241	3	size	size	NOUN
cord-326631-7gd3hjc3	241	4	for	for	ADP
cord-326631-7gd3hjc3	241	5	the	the	DET
cord-326631-7gd3hjc3	241	6	whole	whole	ADJ
cord-326631-7gd3hjc3	241	7	metapopulation	metapopulation	NOUN
cord-326631-7gd3hjc3	241	8	,	,	PUNCT
cord-326631-7gd3hjc3	241	9	z	z	PROPN
cord-326631-7gd3hjc3	241	10	,	,	PUNCT
cord-326631-7gd3hjc3	241	11	is	be	AUX
cord-326631-7gd3hjc3	241	12	not	not	PART
cord-326631-7gd3hjc3	241	13	in	in	ADP
cord-326631-7gd3hjc3	241	14	general	general	ADJ
cord-326631-7gd3hjc3	241	15	the	the	DET
cord-326631-7gd3hjc3	241	16	simple	simple	ADJ
cord-326631-7gd3hjc3	241	17	average	average	NOUN
cord-326631-7gd3hjc3	241	18	of	of	ADP
cord-326631-7gd3hjc3	241	19	the	the	DET
cord-326631-7gd3hjc3	241	20	z	z	NOUN
cord-326631-7gd3hjc3	242	1	i	i	PRON
cord-326631-7gd3hjc3	242	2	's	be	AUX
cord-326631-7gd3hjc3	242	3	in	in	ADP
cord-326631-7gd3hjc3	242	4	eq	eq	PROPN
cord-326631-7gd3hjc3	242	5	.	.	PUNCT
cord-326631-7gd3hjc3	243	1	(	(	PUNCT
cord-326631-7gd3hjc3	243	2	27	27	NUM
cord-326631-7gd3hjc3	243	3	)	)	PUNCT
cord-326631-7gd3hjc3	243	4	.	.	PUNCT
cord-326631-7gd3hjc3	244	1	rather	rather	ADV
cord-326631-7gd3hjc3	244	2	,	,	PUNCT
cord-326631-7gd3hjc3	244	3	each	each	DET
cord-326631-7gd3hjc3	244	4	z	z	NOUN
cord-326631-7gd3hjc3	244	5	i	i	PRON
cord-326631-7gd3hjc3	244	6	must	must	AUX
cord-326631-7gd3hjc3	244	7	be	be	AUX
cord-326631-7gd3hjc3	244	8	weighted	weight	VERB
cord-326631-7gd3hjc3	244	9	by	by	ADP
cord-326631-7gd3hjc3	244	10	the	the	DET
cord-326631-7gd3hjc3	244	11	population	population	NOUN
cord-326631-7gd3hjc3	244	12	size	size	NOUN
cord-326631-7gd3hjc3	244	13	n	n	NOUN
cord-326631-7gd3hjc3	244	14	i	i	NOUN
cord-326631-7gd3hjc3	244	15	of	of	ADP
cord-326631-7gd3hjc3	244	16	patch	patch	PROPN
cord-326631-7gd3hjc3	244	17	i	i	PROPN
cord-326631-7gd3hjc3	244	18	,	,	PUNCT
cord-326631-7gd3hjc3	244	19	i.e.	i.e.	X
cord-326631-7gd3hjc3	244	20	,	,	PUNCT
cord-326631-7gd3hjc3	244	21	consequently	consequently	ADV
cord-326631-7gd3hjc3	244	22	,	,	PUNCT
cord-326631-7gd3hjc3	244	23	there	there	PRON
cord-326631-7gd3hjc3	244	24	will	will	AUX
cord-326631-7gd3hjc3	244	25	always	always	ADV
cord-326631-7gd3hjc3	244	26	be	be	AUX
cord-326631-7gd3hjc3	244	27	particular	particular	ADJ
cord-326631-7gd3hjc3	244	28	values	value	NOUN
cord-326631-7gd3hjc3	244	29	of	of	ADP
cord-326631-7gd3hjc3	244	30	the	the	DET
cord-326631-7gd3hjc3	244	31	n	n	NOUN
cord-326631-7gd3hjc3	244	32	i	i	NOUN
cord-326631-7gd3hjc3	244	33	that	that	PRON
cord-326631-7gd3hjc3	244	34	make	make	VERB
cord-326631-7gd3hjc3	244	35	z	z	NOUN
cord-326631-7gd3hjc3	244	36	in	in	ADP
cord-326631-7gd3hjc3	244	37	eq	eq	PROPN
cord-326631-7gd3hjc3	244	38	.	.	PUNCT
cord-326631-7gd3hjc3	245	1	(	(	PUNCT
cord-326631-7gd3hjc3	245	2	28	28	NUM
cord-326631-7gd3hjc3	245	3	)	)	PUNCT
cord-326631-7gd3hjc3	245	4	equal	equal	ADJ
cord-326631-7gd3hjc3	245	5	to	to	ADP
cord-326631-7gd3hjc3	245	6	the	the	DET
cord-326631-7gd3hjc3	245	7	solution	solution	NOUN
cord-326631-7gd3hjc3	245	8	of	of	ADP
cord-326631-7gd3hjc3	245	9	the	the	DET
cord-326631-7gd3hjc3	245	10	standard	standard	ADJ
cord-326631-7gd3hjc3	245	11	formula	formula	NOUN
cord-326631-7gd3hjc3	245	12	(	(	PUNCT
cord-326631-7gd3hjc3	245	13	5	5	NUM
cord-326631-7gd3hjc3	245	14	)	)	PUNCT
cord-326631-7gd3hjc3	245	15	.	.	PUNCT
cord-326631-7gd3hjc3	246	1	however	however	ADV
cord-326631-7gd3hjc3	246	2	,	,	PUNCT
cord-326631-7gd3hjc3	246	3	since	since	SCONJ
cord-326631-7gd3hjc3	246	4	population	population	NOUN
cord-326631-7gd3hjc3	246	5	sizes	size	NOUN
cord-326631-7gd3hjc3	246	6	are	be	AUX
cord-326631-7gd3hjc3	246	7	given	give	VERB
cord-326631-7gd3hjc3	246	8	a	a	DET
cord-326631-7gd3hjc3	246	9	priori	priori	X
cord-326631-7gd3hjc3	246	10	,	,	PUNCT
cord-326631-7gd3hjc3	246	11	the	the	DET
cord-326631-7gd3hjc3	246	12	problem	problem	NOUN
cord-326631-7gd3hjc3	246	13	of	of	ADP
cord-326631-7gd3hjc3	246	14	interest	interest	NOUN
cord-326631-7gd3hjc3	246	15	is	be	AUX
cord-326631-7gd3hjc3	246	16	to	to	PART
cord-326631-7gd3hjc3	246	17	find	find	VERB
cord-326631-7gd3hjc3	246	18	necessary	necessary	ADJ
cord-326631-7gd3hjc3	246	19	and	and	CCONJ
cord-326631-7gd3hjc3	246	20	sufficient	sufficient	ADJ
cord-326631-7gd3hjc3	246	21	conditions	condition	NOUN
cord-326631-7gd3hjc3	246	22	on	on	ADP
cord-326631-7gd3hjc3	246	23	the	the	DET
cord-326631-7gd3hjc3	246	24	transmission	transmission	NOUN
cord-326631-7gd3hjc3	246	25	matrix	matrix	NOUN
cord-326631-7gd3hjc3	246	26	(	(	PUNCT
cord-326631-7gd3hjc3	246	27	b	b	NOUN
cord-326631-7gd3hjc3	246	28	)	)	PUNCT
cord-326631-7gd3hjc3	246	29	that	that	PRON
cord-326631-7gd3hjc3	246	30	ensure	ensure	VERB
cord-326631-7gd3hjc3	246	31	that	that	SCONJ
cord-326631-7gd3hjc3	246	32	the	the	DET
cord-326631-7gd3hjc3	246	33	sum	sum	NOUN
cord-326631-7gd3hjc3	246	34	in	in	ADP
cord-326631-7gd3hjc3	246	35	eq	eq	PROPN
cord-326631-7gd3hjc3	246	36	.	.	PUNCT
cord-326631-7gd3hjc3	247	1	(	(	PUNCT
cord-326631-7gd3hjc3	247	2	28	28	NUM
cord-326631-7gd3hjc3	247	3	)	)	PUNCT
cord-326631-7gd3hjc3	247	4	is	be	AUX
cord-326631-7gd3hjc3	247	5	equal	equal	ADJ
cord-326631-7gd3hjc3	247	6	to	to	ADP
cord-326631-7gd3hjc3	247	7	the	the	DET
cord-326631-7gd3hjc3	247	8	final	final	ADJ
cord-326631-7gd3hjc3	247	9	size	size	NOUN
cord-326631-7gd3hjc3	247	10	obtained	obtain	VERB
cord-326631-7gd3hjc3	247	11	from	from	ADP
cord-326631-7gd3hjc3	247	12	the	the	DET
cord-326631-7gd3hjc3	247	13	standard	standard	ADJ
cord-326631-7gd3hjc3	247	14	formula	formula	NOUN
cord-326631-7gd3hjc3	247	15	(	(	PUNCT
cord-326631-7gd3hjc3	247	16	5	5	NUM
cord-326631-7gd3hjc3	247	17	)	)	PUNCT
cord-326631-7gd3hjc3	247	18	,	,	PUNCT
cord-326631-7gd3hjc3	247	19	regardless	regardless	ADV
cord-326631-7gd3hjc3	247	20	of	of	ADP
cord-326631-7gd3hjc3	247	21	the	the	DET
cord-326631-7gd3hjc3	247	22	values	value	NOUN
cord-326631-7gd3hjc3	247	23	of	of	ADP
cord-326631-7gd3hjc3	247	24	the	the	DET
cord-326631-7gd3hjc3	247	25	n	n	NOUN
cord-326631-7gd3hjc3	247	26	i	i	NOUN
cord-326631-7gd3hjc3	247	27	.	.	PUNCT
cord-326631-7gd3hjc3	248	1	in	in	ADP
cord-326631-7gd3hjc3	248	2	eq	eq	PROPN
cord-326631-7gd3hjc3	248	3	.	.	PUNCT
cord-326631-7gd3hjc3	249	1	(	(	PUNCT
cord-326631-7gd3hjc3	249	2	28	28	NUM
cord-326631-7gd3hjc3	249	3	)	)	PUNCT
cord-326631-7gd3hjc3	249	4	,	,	PUNCT
cord-326631-7gd3hjc3	249	5	z	z	PROPN
cord-326631-7gd3hjc3	249	6	will	will	AUX
cord-326631-7gd3hjc3	249	7	have	have	VERB
cord-326631-7gd3hjc3	249	8	no	no	DET
cord-326631-7gd3hjc3	249	9	dependence	dependence	NOUN
cord-326631-7gd3hjc3	249	10	on	on	ADP
cord-326631-7gd3hjc3	249	11	the	the	DET
cord-326631-7gd3hjc3	249	12	patch	patch	NOUN
cord-326631-7gd3hjc3	249	13	population	population	NOUN
cord-326631-7gd3hjc3	249	14	sizes	size	NOUN
cord-326631-7gd3hjc3	249	15	if	if	SCONJ
cord-326631-7gd3hjc3	249	16	and	and	CCONJ
cord-326631-7gd3hjc3	249	17	and	and	CCONJ
cord-326631-7gd3hjc3	249	18	only	only	ADV
cord-326631-7gd3hjc3	249	19	if	if	SCONJ
cord-326631-7gd3hjc3	249	20	given	give	VERB
cord-326631-7gd3hjc3	249	21	this	this	PRON
cord-326631-7gd3hjc3	249	22	,	,	PUNCT
cord-326631-7gd3hjc3	249	23	eq	eq	PROPN
cord-326631-7gd3hjc3	249	24	.	.	PUNCT
cord-326631-7gd3hjc3	249	25	(	(	PUNCT
cord-326631-7gd3hjc3	249	26	27	27	NUM
cord-326631-7gd3hjc3	249	27	)	)	PUNCT
cord-326631-7gd3hjc3	249	28	implies	imply	VERB
cord-326631-7gd3hjc3	249	29	i.e.	i.e.	ADV
cord-326631-7gd3hjc3	249	30	,	,	PUNCT
cord-326631-7gd3hjc3	249	31	the	the	DET
cord-326631-7gd3hjc3	249	32	transmission	transmission	NOUN
cord-326631-7gd3hjc3	249	33	rate	rate	NOUN
cord-326631-7gd3hjc3	249	34	is	be	AUX
cord-326631-7gd3hjc3	249	35	the	the	DET
cord-326631-7gd3hjc3	249	36	same	same	ADJ
cord-326631-7gd3hjc3	249	37	in	in	ADP
cord-326631-7gd3hjc3	249	38	all	all	DET
cord-326631-7gd3hjc3	249	39	patches	patch	NOUN
cord-326631-7gd3hjc3	249	40	.	.	PUNCT
cord-326631-7gd3hjc3	250	1	if	if	SCONJ
cord-326631-7gd3hjc3	250	2	,	,	PUNCT
cord-326631-7gd3hjc3	250	3	on	on	ADP
cord-326631-7gd3hjc3	250	4	the	the	DET
cord-326631-7gd3hjc3	250	5	other	other	ADJ
cord-326631-7gd3hjc3	250	6	hand	hand	NOUN
cord-326631-7gd3hjc3	250	7	,	,	PUNCT
cord-326631-7gd3hjc3	250	8	we	we	PRON
cord-326631-7gd3hjc3	250	9	start	start	VERB
cord-326631-7gd3hjc3	250	10	with	with	ADP
cord-326631-7gd3hjc3	250	11	eq	eq	PROPN
cord-326631-7gd3hjc3	250	12	.	.	PUNCT
cord-326631-7gd3hjc3	250	13	(	(	PUNCT
cord-326631-7gd3hjc3	250	14	30	30	NUM
cord-326631-7gd3hjc3	250	15	)	)	PUNCT
cord-326631-7gd3hjc3	250	16	as	as	ADP
cord-326631-7gd3hjc3	250	17	an	an	DET
cord-326631-7gd3hjc3	250	18	assumption	assumption	NOUN
cord-326631-7gd3hjc3	250	19	,	,	PUNCT
cord-326631-7gd3hjc3	250	20	then	then	ADV
cord-326631-7gd3hjc3	250	21	inserting	insert	VERB
cord-326631-7gd3hjc3	250	22	eq	eq	PROPN
cord-326631-7gd3hjc3	250	23	.	.	PUNCT
cord-326631-7gd3hjc3	251	1	(	(	PUNCT
cord-326631-7gd3hjc3	251	2	29	29	NUM
cord-326631-7gd3hjc3	251	3	)	)	PUNCT
cord-326631-7gd3hjc3	251	4	in	in	ADP
cord-326631-7gd3hjc3	251	5	eq	eq	PROPN
cord-326631-7gd3hjc3	251	6	.	.	PUNCT
cord-326631-7gd3hjc3	251	7	(	(	PUNCT
cord-326631-7gd3hjc3	251	8	27	27	NUM
cord-326631-7gd3hjc3	251	9	)	)	PUNCT
cord-326631-7gd3hjc3	251	10	restricting	restrict	VERB
cord-326631-7gd3hjc3	251	11	attention	attention	NOUN
cord-326631-7gd3hjc3	251	12	to	to	ADP
cord-326631-7gd3hjc3	251	13	situations	situation	NOUN
cord-326631-7gd3hjc3	251	14	in	in	ADP
cord-326631-7gd3hjc3	251	15	which	which	PRON
cord-326631-7gd3hjc3	251	16	the	the	DET
cord-326631-7gd3hjc3	251	17	transmission	transmission	NOUN
cord-326631-7gd3hjc3	251	18	rate	rate	NOUN
cord-326631-7gd3hjc3	251	19	is	be	AUX
cord-326631-7gd3hjc3	251	20	the	the	DET
cord-326631-7gd3hjc3	251	21	same	same	ADJ
cord-326631-7gd3hjc3	251	22	in	in	ADP
cord-326631-7gd3hjc3	251	23	every	every	DET
cord-326631-7gd3hjc3	251	24	patch	patch	NOUN
cord-326631-7gd3hjc3	251	25	may	may	AUX
cord-326631-7gd3hjc3	251	26	seem	seem	VERB
cord-326631-7gd3hjc3	251	27	to	to	PART
cord-326631-7gd3hjc3	251	28	be	be	AUX
cord-326631-7gd3hjc3	251	29	an	an	DET
cord-326631-7gd3hjc3	251	30	extremely	extremely	ADV
cord-326631-7gd3hjc3	251	31	stringent	stringent	ADJ
cord-326631-7gd3hjc3	251	32	constraint	constraint	NOUN
cord-326631-7gd3hjc3	251	33	.	.	PUNCT
cord-326631-7gd3hjc3	252	1	in	in	ADP
cord-326631-7gd3hjc3	252	2	fact	fact	NOUN
cord-326631-7gd3hjc3	252	3	,	,	PUNCT
cord-326631-7gd3hjc3	252	4	this	this	PRON
cord-326631-7gd3hjc3	252	5	is	be	AUX
cord-326631-7gd3hjc3	252	6	often	often	ADV
cord-326631-7gd3hjc3	252	7	the	the	DET
cord-326631-7gd3hjc3	252	8	situation	situation	NOUN
cord-326631-7gd3hjc3	252	9	of	of	ADP
cord-326631-7gd3hjc3	252	10	interest	interest	NOUN
cord-326631-7gd3hjc3	252	11	.	.	PUNCT
cord-326631-7gd3hjc3	253	1	for	for	ADP
cord-326631-7gd3hjc3	253	2	example	example	NOUN
cord-326631-7gd3hjc3	253	3	,	,	PUNCT
cord-326631-7gd3hjc3	253	4	individuals	individual	NOUN
cord-326631-7gd3hjc3	253	5	who	who	PRON
cord-326631-7gd3hjc3	253	6	normally	normally	ADV
cord-326631-7gd3hjc3	253	7	reside	reside	VERB
cord-326631-7gd3hjc3	253	8	in	in	ADP
cord-326631-7gd3hjc3	253	9	boston	boston	PROPN
cord-326631-7gd3hjc3	253	10	,	,	PUNCT
cord-326631-7gd3hjc3	253	11	philadelphia	philadelphia	PROPN
cord-326631-7gd3hjc3	253	12	or	or	CCONJ
cord-326631-7gd3hjc3	253	13	new	new	PROPN
cord-326631-7gd3hjc3	253	14	york	york	PROPN
cord-326631-7gd3hjc3	253	15	can	can	AUX
cord-326631-7gd3hjc3	253	16	expect	expect	VERB
cord-326631-7gd3hjc3	253	17	to	to	PART
cord-326631-7gd3hjc3	253	18	contact	contact	VERB
cord-326631-7gd3hjc3	253	19	similar	similar	ADJ
cord-326631-7gd3hjc3	253	20	numbers	number	NOUN
cord-326631-7gd3hjc3	253	21	of	of	ADP
cord-326631-7gd3hjc3	253	22	people	people	NOUN
cord-326631-7gd3hjc3	253	23	each	each	DET
cord-326631-7gd3hjc3	253	24	day	day	NOUN
cord-326631-7gd3hjc3	253	25	,	,	PUNCT
cord-326631-7gd3hjc3	253	26	even	even	ADV
cord-326631-7gd3hjc3	253	27	though	though	SCONJ
cord-326631-7gd3hjc3	253	28	the	the	DET
cord-326631-7gd3hjc3	253	29	new	new	PROPN
cord-326631-7gd3hjc3	253	30	york	york	PROPN
cord-326631-7gd3hjc3	253	31	metropolitan	metropolitan	PROPN
cord-326631-7gd3hjc3	253	32	area	area	NOUN
cord-326631-7gd3hjc3	253	33	has	have	VERB
cord-326631-7gd3hjc3	253	34	a	a	DET
cord-326631-7gd3hjc3	253	35	population	population	NOUN
cord-326631-7gd3hjc3	253	36	that	that	PRON
cord-326631-7gd3hjc3	253	37	is	be	AUX
cord-326631-7gd3hjc3	253	38	several	several	ADJ
cord-326631-7gd3hjc3	253	39	times	time	NOUN
cord-326631-7gd3hjc3	253	40	larger	large	ADJ
cord-326631-7gd3hjc3	253	41	than	than	ADP
cord-326631-7gd3hjc3	253	42	the	the	DET
cord-326631-7gd3hjc3	253	43	other	other	ADJ
cord-326631-7gd3hjc3	253	44	two	two	NUM
cord-326631-7gd3hjc3	253	45	.	.	PUNCT
cord-326631-7gd3hjc3	254	1	more	more	ADV
cord-326631-7gd3hjc3	254	2	generally	generally	ADV
cord-326631-7gd3hjc3	254	3	,	,	PUNCT
cord-326631-7gd3hjc3	254	4	if	if	SCONJ
cord-326631-7gd3hjc3	254	5	patches	patch	NOUN
cord-326631-7gd3hjc3	254	6	represent	represent	VERB
cord-326631-7gd3hjc3	254	7	large	large	ADJ
cord-326631-7gd3hjc3	254	8	cities	city	NOUN
cord-326631-7gd3hjc3	254	9	in	in	ADP
cord-326631-7gd3hjc3	254	10	a	a	DET
cord-326631-7gd3hjc3	254	11	given	give	VERB
cord-326631-7gd3hjc3	254	12	country	country	NOUN
cord-326631-7gd3hjc3	254	13	,	,	PUNCT
cord-326631-7gd3hjc3	254	14	then	then	ADV
cord-326631-7gd3hjc3	254	15	it	it	PRON
cord-326631-7gd3hjc3	254	16	is	be	AUX
cord-326631-7gd3hjc3	254	17	reasonable	reasonable	ADJ
cord-326631-7gd3hjc3	254	18	to	to	PART
cord-326631-7gd3hjc3	254	19	expect	expect	VERB
cord-326631-7gd3hjc3	254	20	that	that	SCONJ
cord-326631-7gd3hjc3	254	21	the	the	DET
cord-326631-7gd3hjc3	254	22	number	number	NOUN
cord-326631-7gd3hjc3	254	23	of	of	ADP
cord-326631-7gd3hjc3	254	24	contacts	contact	NOUN
cord-326631-7gd3hjc3	254	25	an	an	DET
cord-326631-7gd3hjc3	254	26	individual	individual	NOUN
cord-326631-7gd3hjc3	254	27	has	have	AUX
cord-326631-7gd3hjc3	254	28	will	will	AUX
cord-326631-7gd3hjc3	254	29	not	not	PART
cord-326631-7gd3hjc3	254	30	depend	depend	VERB
cord-326631-7gd3hjc3	254	31	strongly	strongly	ADV
cord-326631-7gd3hjc3	254	32	on	on	ADP
cord-326631-7gd3hjc3	254	33	the	the	DET
cord-326631-7gd3hjc3	254	34	size	size	NOUN
cord-326631-7gd3hjc3	254	35	of	of	ADP
cord-326631-7gd3hjc3	254	36	the	the	DET
cord-326631-7gd3hjc3	254	37	city	city	NOUN
cord-326631-7gd3hjc3	254	38	.	.	PUNCT
cord-326631-7gd3hjc3	255	1	given	give	VERB
cord-326631-7gd3hjc3	255	2	eq	eq	PROPN
cord-326631-7gd3hjc3	255	3	.	.	PUNCT
cord-326631-7gd3hjc3	255	4	(	(	PUNCT
cord-326631-7gd3hjc3	255	5	30	30	NUM
cord-326631-7gd3hjc3	255	6	)	)	PUNCT
cord-326631-7gd3hjc3	255	7	,	,	PUNCT
cord-326631-7gd3hjc3	255	8	we	we	PRON
cord-326631-7gd3hjc3	255	9	can	can	AUX
cord-326631-7gd3hjc3	255	10	write	write	VERB
cord-326631-7gd3hjc3	255	11	where	where	SCONJ
cord-326631-7gd3hjc3	256	1	p	p	PROPN
cord-326631-7gd3hjc3	256	2	i	i	PRON
cord-326631-7gd3hjc3	256	3	j	j	PROPN
cord-326631-7gd3hjc3	256	4	is	be	AUX
cord-326631-7gd3hjc3	256	5	the	the	DET
cord-326631-7gd3hjc3	256	6	probability	probability	NOUN
cord-326631-7gd3hjc3	256	7	,	,	PUNCT
cord-326631-7gd3hjc3	256	8	for	for	ADP
cord-326631-7gd3hjc3	256	9	an	an	DET
cord-326631-7gd3hjc3	256	10	individual	individual	NOUN
cord-326631-7gd3hjc3	256	11	in	in	ADP
cord-326631-7gd3hjc3	256	12	patch	patch	NOUN
cord-326631-7gd3hjc3	256	13	i	i	PROPN
cord-326631-7gd3hjc3	256	14	,	,	PUNCT
cord-326631-7gd3hjc3	256	15	that	that	SCONJ
cord-326631-7gd3hjc3	256	16	a	a	DET
cord-326631-7gd3hjc3	256	17	given	give	VERB
cord-326631-7gd3hjc3	256	18	contact	contact	NOUN
cord-326631-7gd3hjc3	256	19	is	be	AUX
cord-326631-7gd3hjc3	256	20	with	with	ADP
cord-326631-7gd3hjc3	256	21	an	an	DET
cord-326631-7gd3hjc3	256	22	individual	individual	NOUN
cord-326631-7gd3hjc3	256	23	in	in	ADP
cord-326631-7gd3hjc3	256	24	patch	patch	PROPN
cord-326631-7gd3hjc3	256	25	j	j	PROPN
cord-326631-7gd3hjc3	256	26	,	,	PUNCT
cord-326631-7gd3hjc3	256	27	and	and	CCONJ
cord-326631-7gd3hjc3	256	28	β	β	NOUN
cord-326631-7gd3hjc3	256	29	is	be	AUX
cord-326631-7gd3hjc3	256	30	the	the	DET
cord-326631-7gd3hjc3	256	31	transmission	transmission	NOUN
cord-326631-7gd3hjc3	256	32	rate	rate	NOUN
cord-326631-7gd3hjc3	256	33	(	(	PUNCT
cord-326631-7gd3hjc3	256	34	the	the	DET
cord-326631-7gd3hjc3	256	35	product	product	NOUN
cord-326631-7gd3hjc3	256	36	of	of	ADP
cord-326631-7gd3hjc3	256	37	the	the	DET
cord-326631-7gd3hjc3	256	38	number	number	NOUN
cord-326631-7gd3hjc3	256	39	of	of	ADP
cord-326631-7gd3hjc3	256	40	contacts	contact	NOUN
cord-326631-7gd3hjc3	256	41	per	per	ADP
cord-326631-7gd3hjc3	256	42	unit	unit	NOUN
cord-326631-7gd3hjc3	256	43	time	time	NOUN
cord-326631-7gd3hjc3	256	44	and	and	CCONJ
cord-326631-7gd3hjc3	256	45	the	the	DET
cord-326631-7gd3hjc3	256	46	probability	probability	NOUN
cord-326631-7gd3hjc3	256	47	that	that	SCONJ
cord-326631-7gd3hjc3	256	48	a	a	DET
cord-326631-7gd3hjc3	256	49	contact	contact	NOUN
cord-326631-7gd3hjc3	256	50	between	between	ADP
cord-326631-7gd3hjc3	256	51	a	a	DET
cord-326631-7gd3hjc3	256	52	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	256	53	and	and	CCONJ
cord-326631-7gd3hjc3	256	54	an	an	DET
cord-326631-7gd3hjc3	256	55	infectious	infectious	ADJ
cord-326631-7gd3hjc3	256	56	individual	individual	NOUN
cord-326631-7gd3hjc3	256	57	leads	lead	VERB
cord-326631-7gd3hjc3	256	58	to	to	ADP
cord-326631-7gd3hjc3	256	59	transmission	transmission	NOUN
cord-326631-7gd3hjc3	256	60	)	)	PUNCT
cord-326631-7gd3hjc3	256	61	.	.	PUNCT
cord-326631-7gd3hjc3	257	1	note	note	VERB
cord-326631-7gd3hjc3	257	2	that	that	SCONJ
cord-326631-7gd3hjc3	257	3	since	since	SCONJ
cord-326631-7gd3hjc3	257	4	the	the	DET
cord-326631-7gd3hjc3	257	5	rows	row	NOUN
cord-326631-7gd3hjc3	257	6	of	of	ADP
cord-326631-7gd3hjc3	257	7	the	the	DET
cord-326631-7gd3hjc3	257	8	matrix	matrix	NOUN
cord-326631-7gd3hjc3	257	9	p	p	PROPN
cord-326631-7gd3hjc3	257	10	are	be	AUX
cord-326631-7gd3hjc3	257	11	probability	probability	NOUN
cord-326631-7gd3hjc3	257	12	distributions	distribution	NOUN
cord-326631-7gd3hjc3	257	13	,	,	PUNCT
cord-326631-7gd3hjc3	257	14	it	it	PRON
cord-326631-7gd3hjc3	257	15	follows	follow	VERB
cord-326631-7gd3hjc3	257	16	that	that	PRON
cord-326631-7gd3hjc3	257	17	n	n	PROPN
cord-326631-7gd3hjc3	258	1	j=1	j=1	PROPN
cord-326631-7gd3hjc3	258	2	p	p	PROPN
cord-326631-7gd3hjc3	259	1	i	i	NOUN
cord-326631-7gd3hjc3	259	2	j	j	PROPN
cord-326631-7gd3hjc3	259	3	=	=	SYM
cord-326631-7gd3hjc3	259	4	1	1	NUM
cord-326631-7gd3hjc3	259	5	,	,	PUNCT
cord-326631-7gd3hjc3	259	6	i	i	NOUN
cord-326631-7gd3hjc3	259	7	=	=	NOUN
cord-326631-7gd3hjc3	259	8	1	1	NUM
cord-326631-7gd3hjc3	259	9	,	,	PUNCT
cord-326631-7gd3hjc3	259	10	.	.	PUNCT
cord-326631-7gd3hjc3	259	11	.	.	PUNCT
cord-326631-7gd3hjc3	259	12	.	.	PUNCT
cord-326631-7gd3hjc3	260	1	,	,	PUNCT
cord-326631-7gd3hjc3	260	2	n	n	CCONJ
cord-326631-7gd3hjc3	260	3	,	,	PUNCT
cord-326631-7gd3hjc3	260	4	i.e.	i.e.	X
cord-326631-7gd3hjc3	260	5	,	,	PUNCT
cord-326631-7gd3hjc3	260	6	p	p	PROPN
cord-326631-7gd3hjc3	260	7	is	be	AUX
cord-326631-7gd3hjc3	260	8	a	a	DET
cord-326631-7gd3hjc3	260	9	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	260	10	matrix	matrix	NOUN
cord-326631-7gd3hjc3	260	11	(	(	PUNCT
cord-326631-7gd3hjc3	260	12	horn	horn	NOUN
cord-326631-7gd3hjc3	260	13	and	and	CCONJ
cord-326631-7gd3hjc3	260	14	johnson	johnson	PROPN
cord-326631-7gd3hjc3	260	15	,	,	PUNCT
cord-326631-7gd3hjc3	260	16	1985	1985	NUM
cord-326631-7gd3hjc3	260	17	)	)	PUNCT
cord-326631-7gd3hjc3	260	18	.	.	PUNCT
cord-326631-7gd3hjc3	261	1	for	for	ADP
cord-326631-7gd3hjc3	261	2	convenience	convenience	NOUN
cord-326631-7gd3hjc3	261	3	,	,	PUNCT
cord-326631-7gd3hjc3	261	4	we	we	PRON
cord-326631-7gd3hjc3	261	5	make	make	VERB
cord-326631-7gd3hjc3	261	6	the	the	DET
cord-326631-7gd3hjc3	261	7	mild	mild	ADJ
cord-326631-7gd3hjc3	261	8	assumption	assumption	NOUN
cord-326631-7gd3hjc3	261	9	that	that	SCONJ
cord-326631-7gd3hjc3	261	10	p	p	PROPN
cord-326631-7gd3hjc3	261	11	i	i	X
cord-326631-7gd3hjc3	261	12	j	j	X
cord-326631-7gd3hjc3	261	13	>	>	PUNCT
cord-326631-7gd3hjc3	261	14	0	0	NUM
cord-326631-7gd3hjc3	261	15	for	for	ADP
cord-326631-7gd3hjc3	261	16	all	all	PRON
cord-326631-7gd3hjc3	261	17	i	i	PRON
cord-326631-7gd3hjc3	261	18	and	and	CCONJ
cord-326631-7gd3hjc3	261	19	j	j	NUM
cord-326631-7gd3hjc3	261	20	,	,	PUNCT
cord-326631-7gd3hjc3	261	21	i.e.	i.e.	X
cord-326631-7gd3hjc3	261	22	,	,	PUNCT
cord-326631-7gd3hjc3	261	23	for	for	ADP
cord-326631-7gd3hjc3	261	24	any	any	DET
cord-326631-7gd3hjc3	261	25	pair	pair	NOUN
cord-326631-7gd3hjc3	261	26	of	of	ADP
cord-326631-7gd3hjc3	261	27	patches	patch	NOUN
cord-326631-7gd3hjc3	261	28	,	,	PUNCT
cord-326631-7gd3hjc3	261	29	there	there	PRON
cord-326631-7gd3hjc3	261	30	is	be	VERB
cord-326631-7gd3hjc3	261	31	a	a	DET
cord-326631-7gd3hjc3	261	32	non	non	ADJ
cord-326631-7gd3hjc3	261	33	-	-	ADJ
cord-326631-7gd3hjc3	261	34	zero	zero	NUM
cord-326631-7gd3hjc3	261	35	probability	probability	NOUN
cord-326631-7gd3hjc3	261	36	that	that	SCONJ
cord-326631-7gd3hjc3	261	37	residents	resident	NOUN
cord-326631-7gd3hjc3	261	38	of	of	ADP
cord-326631-7gd3hjc3	261	39	the	the	DET
cord-326631-7gd3hjc3	261	40	two	two	NUM
cord-326631-7gd3hjc3	261	41	patches	patch	NOUN
cord-326631-7gd3hjc3	261	42	will	will	AUX
cord-326631-7gd3hjc3	261	43	come	come	VERB
cord-326631-7gd3hjc3	261	44	into	into	ADP
cord-326631-7gd3hjc3	261	45	contact	contact	NOUN
cord-326631-7gd3hjc3	261	46	.	.	PUNCT
cord-326631-7gd3hjc3	262	1	it	it	PRON
cord-326631-7gd3hjc3	262	2	then	then	ADV
cord-326631-7gd3hjc3	262	3	follows	follow	VERB
cord-326631-7gd3hjc3	262	4	that	that	SCONJ
cord-326631-7gd3hjc3	262	5	if	if	SCONJ
cord-326631-7gd3hjc3	262	6	the	the	DET
cord-326631-7gd3hjc3	262	7	final	final	ADJ
cord-326631-7gd3hjc3	262	8	size	size	NOUN
cord-326631-7gd3hjc3	262	9	z	z	PROPN
cord-326631-7gd3hjc3	262	10	is	be	AUX
cord-326631-7gd3hjc3	262	11	positive	positive	ADJ
cord-326631-7gd3hjc3	262	12	then	then	ADV
cord-326631-7gd3hjc3	262	13	the	the	DET
cord-326631-7gd3hjc3	262	14	final	final	ADJ
cord-326631-7gd3hjc3	262	15	size	size	NOUN
cord-326631-7gd3hjc3	262	16	z	z	NOUN
cord-326631-7gd3hjc3	263	1	i	i	PRON
cord-326631-7gd3hjc3	263	2	is	be	AUX
cord-326631-7gd3hjc3	263	3	strictly	strictly	ADV
cord-326631-7gd3hjc3	263	4	positive	positive	ADJ
cord-326631-7gd3hjc3	263	5	in	in	ADP
cord-326631-7gd3hjc3	263	6	every	every	DET
cord-326631-7gd3hjc3	263	7	patch	patch	NOUN
cord-326631-7gd3hjc3	263	8	.	.	PUNCT
cord-326631-7gd3hjc3	264	1	to	to	PART
cord-326631-7gd3hjc3	264	2	see	see	VERB
cord-326631-7gd3hjc3	264	3	this	this	PRON
cord-326631-7gd3hjc3	264	4	,	,	PUNCT
cord-326631-7gd3hjc3	264	5	note	note	VERB
cord-326631-7gd3hjc3	264	6	that	that	SCONJ
cord-326631-7gd3hjc3	264	7	if	if	SCONJ
cord-326631-7gd3hjc3	264	8	z	z	X
cord-326631-7gd3hjc3	264	9	i	i	PRON
cord-326631-7gd3hjc3	264	10	=	=	NOUN
cord-326631-7gd3hjc3	264	11	0	0	NUM
cord-326631-7gd3hjc3	264	12	for	for	ADP
cord-326631-7gd3hjc3	264	13	some	some	DET
cord-326631-7gd3hjc3	264	14	i	i	PRON
cord-326631-7gd3hjc3	264	15	then	then	ADV
cord-326631-7gd3hjc3	264	16	eq	eq	X
cord-326631-7gd3hjc3	264	17	.	.	PUNCT
cord-326631-7gd3hjc3	265	1	(	(	PUNCT
cord-326631-7gd3hjc3	265	2	27	27	NUM
cord-326631-7gd3hjc3	265	3	)	)	PUNCT
cord-326631-7gd3hjc3	265	4	since	since	SCONJ
cord-326631-7gd3hjc3	265	5	p	p	PROPN
cord-326631-7gd3hjc3	265	6	i	i	PROPN
cord-326631-7gd3hjc3	265	7	j	j	X
cord-326631-7gd3hjc3	265	8	>	>	X
cord-326631-7gd3hjc3	265	9	0	0	PUNCT
cord-326631-7gd3hjc3	265	10	implies	imply	VERB
cord-326631-7gd3hjc3	265	11	β	β	PROPN
cord-326631-7gd3hjc3	266	1	i	i	PRON
cord-326631-7gd3hjc3	266	2	j	j	X
cord-326631-7gd3hjc3	266	3	>	>	PUNCT
cord-326631-7gd3hjc3	266	4	0	0	NUM
cord-326631-7gd3hjc3	266	5	,	,	PUNCT
cord-326631-7gd3hjc3	266	6	eq	eq	PROPN
cord-326631-7gd3hjc3	266	7	.	.	PUNCT
cord-326631-7gd3hjc3	266	8	(	(	PUNCT
cord-326631-7gd3hjc3	266	9	33	33	NUM
cord-326631-7gd3hjc3	266	10	)	)	PUNCT
cord-326631-7gd3hjc3	266	11	implies	imply	VERB
cord-326631-7gd3hjc3	266	12	z	z	PROPN
cord-326631-7gd3hjc3	266	13	j	j	PROPN
cord-326631-7gd3hjc3	266	14	=	=	SYM
cord-326631-7gd3hjc3	266	15	0	0	NUM
cord-326631-7gd3hjc3	266	16	for	for	ADP
cord-326631-7gd3hjc3	266	17	all	all	DET
cord-326631-7gd3hjc3	266	18	j.	j.	PROPN
cord-326631-7gd3hjc3	266	19	since	since	SCONJ
cord-326631-7gd3hjc3	266	20	p	p	PROPN
cord-326631-7gd3hjc3	266	21	is	be	AUX
cord-326631-7gd3hjc3	266	22	a	a	DET
cord-326631-7gd3hjc3	266	23	positive	positive	ADJ
cord-326631-7gd3hjc3	266	24	,	,	PUNCT
cord-326631-7gd3hjc3	266	25	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	266	26	matrix	matrix	NOUN
cord-326631-7gd3hjc3	266	27	,	,	PUNCT
cord-326631-7gd3hjc3	266	28	its	its	PRON
cord-326631-7gd3hjc3	266	29	largest	large	ADJ
cord-326631-7gd3hjc3	266	30	eigenvalue	eigenvalue	NOUN
cord-326631-7gd3hjc3	266	31	is	be	AUX
cord-326631-7gd3hjc3	266	32	1	1	NUM
cord-326631-7gd3hjc3	266	33	(	(	PUNCT
cord-326631-7gd3hjc3	266	34	horn	horn	NOUN
cord-326631-7gd3hjc3	266	35	and	and	CCONJ
cord-326631-7gd3hjc3	266	36	johnson	johnson	PROPN
cord-326631-7gd3hjc3	266	37	,	,	PUNCT
cord-326631-7gd3hjc3	266	38	1985	1985	NUM
cord-326631-7gd3hjc3	266	39	)	)	PUNCT
cord-326631-7gd3hjc3	266	40	.	.	PUNCT
cord-326631-7gd3hjc3	267	1	consequently	consequently	ADV
cord-326631-7gd3hjc3	267	2	,	,	PUNCT
cord-326631-7gd3hjc3	267	3	the	the	DET
cord-326631-7gd3hjc3	267	4	largest	large	ADJ
cord-326631-7gd3hjc3	267	5	eigenvalue	eigenvalue	NOUN
cord-326631-7gd3hjc3	267	6	of	of	ADP
cord-326631-7gd3hjc3	267	7	b	b	PROPN
cord-326631-7gd3hjc3	267	8	=	=	NOUN
cord-326631-7gd3hjc3	267	9	β	β	NOUN
cord-326631-7gd3hjc3	267	10	p	p	PROPN
cord-326631-7gd3hjc3	267	11	is	be	AUX
cord-326631-7gd3hjc3	267	12	β	β	NOUN
cord-326631-7gd3hjc3	267	13	and	and	CCONJ
cord-326631-7gd3hjc3	267	14	the	the	DET
cord-326631-7gd3hjc3	267	15	basic	basic	ADJ
cord-326631-7gd3hjc3	267	16	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	267	17	number	number	NOUN
cord-326631-7gd3hjc3	267	18	is	be	AUX
cord-326631-7gd3hjc3	267	19	r	r	NOUN
cord-326631-7gd3hjc3	267	20	0	0	NUM
cord-326631-7gd3hjc3	267	21	=	=	NOUN
cord-326631-7gd3hjc3	267	22	β	β	NOUN
cord-326631-7gd3hjc3	267	23	γ	γ	PROPN
cord-326631-7gd3hjc3	267	24	.	.	PUNCT
cord-326631-7gd3hjc3	268	1	therefore	therefore	ADV
cord-326631-7gd3hjc3	268	2	,	,	PUNCT
cord-326631-7gd3hjc3	268	3	we	we	PRON
cord-326631-7gd3hjc3	268	4	have	have	VERB
cord-326631-7gd3hjc3	268	5	theorem	theorem	NOUN
cord-326631-7gd3hjc3	268	6	9.1	9.1	NUM
cord-326631-7gd3hjc3	268	7	.	.	PUNCT
cord-326631-7gd3hjc3	269	1	consider	consider	VERB
cord-326631-7gd3hjc3	269	2	the	the	DET
cord-326631-7gd3hjc3	269	3	multi	multi	ADJ
cord-326631-7gd3hjc3	269	4	-	-	ADJ
cord-326631-7gd3hjc3	269	5	patch	patch	ADJ
cord-326631-7gd3hjc3	269	6	sir	sir	PROPN
cord-326631-7gd3hjc3	269	7	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	269	8	model	model	NOUN
cord-326631-7gd3hjc3	269	9	specified	specify	VERB
cord-326631-7gd3hjc3	269	10	by	by	ADP
cord-326631-7gd3hjc3	269	11	eqs	eqs	PROPN
cord-326631-7gd3hjc3	269	12	.	.	PUNCT
cord-326631-7gd3hjc3	270	1	(	(	PUNCT
cord-326631-7gd3hjc3	270	2	26	26	NUM
cord-326631-7gd3hjc3	270	3	)	)	PUNCT
cord-326631-7gd3hjc3	270	4	.	.	PUNCT
cord-326631-7gd3hjc3	271	1	suppose	suppose	VERB
cord-326631-7gd3hjc3	271	2	the	the	DET
cord-326631-7gd3hjc3	271	3	transmission	transmission	NOUN
cord-326631-7gd3hjc3	271	4	rate	rate	NOUN
cord-326631-7gd3hjc3	271	5	in	in	ADP
cord-326631-7gd3hjc3	271	6	each	each	DET
cord-326631-7gd3hjc3	271	7	patch	patch	NOUN
cord-326631-7gd3hjc3	271	8	is	be	AUX
cord-326631-7gd3hjc3	271	9	the	the	DET
cord-326631-7gd3hjc3	271	10	same	same	ADJ
cord-326631-7gd3hjc3	271	11	,	,	PUNCT
cord-326631-7gd3hjc3	271	12	i.e.	i.e.	X
cord-326631-7gd3hjc3	271	13	,	,	PUNCT
cord-326631-7gd3hjc3	271	14	n	n	PROPN
cord-326631-7gd3hjc3	271	15	j=1	j=1	PROPN
cord-326631-7gd3hjc3	271	16	β	β	PROPN
cord-326631-7gd3hjc3	272	1	i	i	PRON
cord-326631-7gd3hjc3	272	2	j	j	PROPN
cord-326631-7gd3hjc3	272	3	=	=	SYM
cord-326631-7gd3hjc3	272	4	β	β	PROPN
cord-326631-7gd3hjc3	272	5	,	,	PUNCT
cord-326631-7gd3hjc3	272	6	for	for	ADP
cord-326631-7gd3hjc3	272	7	each	each	DET
cord-326631-7gd3hjc3	272	8	i.	i.	PROPN
cord-326631-7gd3hjc3	272	9	then	then	ADV
cord-326631-7gd3hjc3	272	10	,	,	PUNCT
cord-326631-7gd3hjc3	272	11	in	in	ADP
cord-326631-7gd3hjc3	272	12	the	the	DET
cord-326631-7gd3hjc3	272	13	limit	limit	NOUN
cord-326631-7gd3hjc3	272	14	that	that	SCONJ
cord-326631-7gd3hjc3	272	15	the	the	DET
cord-326631-7gd3hjc3	272	16	initial	initial	ADJ
cord-326631-7gd3hjc3	272	17	proportion	proportion	NOUN
cord-326631-7gd3hjc3	272	18	of	of	ADP
cord-326631-7gd3hjc3	272	19	individuals	individual	NOUN
cord-326631-7gd3hjc3	272	20	that	that	PRON
cord-326631-7gd3hjc3	272	21	are	be	AUX
cord-326631-7gd3hjc3	272	22	infectious	infectious	ADJ
cord-326631-7gd3hjc3	272	23	is	be	AUX
cord-326631-7gd3hjc3	272	24	small	small	ADJ
cord-326631-7gd3hjc3	272	25	,	,	PUNCT
cord-326631-7gd3hjc3	272	26	i.e.	i.e.	X
cord-326631-7gd3hjc3	272	27	,	,	PUNCT
cord-326631-7gd3hjc3	272	28	i	i	PRON
cord-326631-7gd3hjc3	272	29	i	i	NOUN
cord-326631-7gd3hjc3	272	30	(	(	PUNCT
cord-326631-7gd3hjc3	272	31	0	0	NUM
cord-326631-7gd3hjc3	272	32	)	)	PUNCT
cord-326631-7gd3hjc3	272	33	→	→	PUNCT
cord-326631-7gd3hjc3	272	34	0	0	NUM
cord-326631-7gd3hjc3	272	35	for	for	ADP
cord-326631-7gd3hjc3	272	36	each	each	DET
cord-326631-7gd3hjc3	272	37	i	i	PROPN
cord-326631-7gd3hjc3	272	38	,	,	PUNCT
cord-326631-7gd3hjc3	272	39	the	the	DET
cord-326631-7gd3hjc3	272	40	final	final	ADJ
cord-326631-7gd3hjc3	272	41	size	size	NOUN
cord-326631-7gd3hjc3	272	42	z	z	NOUN
cord-326631-7gd3hjc3	272	43	of	of	ADP
cord-326631-7gd3hjc3	272	44	an	an	DET
cord-326631-7gd3hjc3	272	45	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	272	46	is	be	AUX
cord-326631-7gd3hjc3	272	47	given	give	VERB
cord-326631-7gd3hjc3	272	48	implicitly	implicitly	ADV
cord-326631-7gd3hjc3	272	49	by	by	ADP
cord-326631-7gd3hjc3	272	50	eq	eq	PROPN
cord-326631-7gd3hjc3	272	51	.	.	PUNCT
cord-326631-7gd3hjc3	273	1	(	(	PUNCT
cord-326631-7gd3hjc3	273	2	5	5	NUM
cord-326631-7gd3hjc3	273	3	)	)	PUNCT
cord-326631-7gd3hjc3	273	4	,	,	PUNCT
cord-326631-7gd3hjc3	273	5	or	or	CCONJ
cord-326631-7gd3hjc3	273	6	explicitly	explicitly	ADV
cord-326631-7gd3hjc3	273	7	by	by	ADP
cord-326631-7gd3hjc3	273	8	eq	eq	PROPN
cord-326631-7gd3hjc3	273	9	.	.	PUNCT
cord-326631-7gd3hjc3	273	10	(	(	PUNCT
cord-326631-7gd3hjc3	273	11	a.2	a.2	NOUN
cord-326631-7gd3hjc3	273	12	)	)	PUNCT
cord-326631-7gd3hjc3	273	13	,	,	PUNCT
cord-326631-7gd3hjc3	273	14	where	where	SCONJ
cord-326631-7gd3hjc3	273	15	r	r	NOUN
cord-326631-7gd3hjc3	273	16	0	0	PUNCT
cord-326631-7gd3hjc3	273	17	=	=	NOUN
cord-326631-7gd3hjc3	273	18	β	β	NOUN
cord-326631-7gd3hjc3	273	19	γ	γ	PROPN
cord-326631-7gd3hjc3	273	20	.	.	PUNCT
cord-326631-7gd3hjc3	274	1	at	at	ADP
cord-326631-7gd3hjc3	274	2	this	this	DET
cord-326631-7gd3hjc3	274	3	point	point	NOUN
cord-326631-7gd3hjc3	274	4	,	,	PUNCT
cord-326631-7gd3hjc3	274	5	it	it	PRON
cord-326631-7gd3hjc3	274	6	will	will	AUX
cord-326631-7gd3hjc3	274	7	come	come	VERB
cord-326631-7gd3hjc3	274	8	as	as	ADP
cord-326631-7gd3hjc3	274	9	no	no	DET
cord-326631-7gd3hjc3	274	10	surprise	surprise	NOUN
cord-326631-7gd3hjc3	274	11	that	that	SCONJ
cord-326631-7gd3hjc3	274	12	with	with	ADP
cord-326631-7gd3hjc3	274	13	some	some	DET
cord-326631-7gd3hjc3	274	14	effort	effort	NOUN
cord-326631-7gd3hjc3	274	15	in	in	ADP
cord-326631-7gd3hjc3	274	16	keeping	keep	VERB
cord-326631-7gd3hjc3	274	17	track	track	NOUN
cord-326631-7gd3hjc3	274	18	of	of	ADP
cord-326631-7gd3hjc3	274	19	notation	notation	NOUN
cord-326631-7gd3hjc3	274	20	,	,	PUNCT
cord-326631-7gd3hjc3	274	21	theorem	theorem	VERB
cord-326631-7gd3hjc3	274	22	9.1	9.1	NUM
cord-326631-7gd3hjc3	274	23	can	can	AUX
cord-326631-7gd3hjc3	274	24	be	be	AUX
cord-326631-7gd3hjc3	274	25	generalized	generalize	VERB
cord-326631-7gd3hjc3	274	26	to	to	ADP
cord-326631-7gd3hjc3	274	27	a	a	DET
cord-326631-7gd3hjc3	274	28	multi	multi	ADJ
cord-326631-7gd3hjc3	274	29	-	-	ADJ
cord-326631-7gd3hjc3	274	30	patch	patch	ADJ
cord-326631-7gd3hjc3	274	31	si	si	PROPN
cord-326631-7gd3hjc3	274	32	n	n	NOUN
cord-326631-7gd3hjc3	274	33	r	r	NOUN
cord-326631-7gd3hjc3	274	34	model	model	NOUN
cord-326631-7gd3hjc3	274	35	with	with	ADP
cord-326631-7gd3hjc3	274	36	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	274	37	distributed	distribute	VERB
cord-326631-7gd3hjc3	274	38	stage	stage	NOUN
cord-326631-7gd3hjc3	274	39	durations	duration	NOUN
cord-326631-7gd3hjc3	274	40	and	and	CCONJ
cord-326631-7gd3hjc3	274	41	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	274	42	distributed	distribute	VERB
cord-326631-7gd3hjc3	274	43	transmission	transmission	NOUN
cord-326631-7gd3hjc3	274	44	rates	rate	NOUN
cord-326631-7gd3hjc3	274	45	.	.	PUNCT
cord-326631-7gd3hjc3	275	1	equations	equation	NOUN
cord-326631-7gd3hjc3	275	2	(	(	PUNCT
cord-326631-7gd3hjc3	275	3	26	26	NUM
cord-326631-7gd3hjc3	275	4	)	)	PUNCT
cord-326631-7gd3hjc3	275	5	,	,	PUNCT
cord-326631-7gd3hjc3	275	6	which	which	PRON
cord-326631-7gd3hjc3	275	7	specify	specify	VERB
cord-326631-7gd3hjc3	275	8	the	the	DET
cord-326631-7gd3hjc3	275	9	spatially	spatially	ADV
cord-326631-7gd3hjc3	275	10	heterogeneous	heterogeneous	ADJ
cord-326631-7gd3hjc3	275	11	model	model	NOUN
cord-326631-7gd3hjc3	275	12	we	we	PRON
cord-326631-7gd3hjc3	275	13	analyzed	analyze	VERB
cord-326631-7gd3hjc3	275	14	in	in	ADP
cord-326631-7gd3hjc3	275	15	the	the	DET
cord-326631-7gd3hjc3	275	16	previous	previous	ADJ
cord-326631-7gd3hjc3	275	17	section	section	NOUN
cord-326631-7gd3hjc3	275	18	,	,	PUNCT
cord-326631-7gd3hjc3	275	19	can	can	AUX
cord-326631-7gd3hjc3	275	20	be	be	AUX
cord-326631-7gd3hjc3	275	21	interpretted	interprette	VERB
cord-326631-7gd3hjc3	275	22	as	as	ADP
cord-326631-7gd3hjc3	275	23	representing	represent	VERB
cord-326631-7gd3hjc3	275	24	other	other	ADJ
cord-326631-7gd3hjc3	275	25	types	type	NOUN
cord-326631-7gd3hjc3	275	26	of	of	ADP
cord-326631-7gd3hjc3	275	27	social	social	ADJ
cord-326631-7gd3hjc3	275	28	heterogeneities	heterogeneity	NOUN
cord-326631-7gd3hjc3	275	29	,	,	PUNCT
cord-326631-7gd3hjc3	275	30	which	which	PRON
cord-326631-7gd3hjc3	275	31	are	be	AUX
cord-326631-7gd3hjc3	275	32	known	know	VERB
cord-326631-7gd3hjc3	275	33	to	to	PART
cord-326631-7gd3hjc3	275	34	yield	yield	VERB
cord-326631-7gd3hjc3	275	35	different	different	ADJ
cord-326631-7gd3hjc3	275	36	final	final	ADJ
cord-326631-7gd3hjc3	275	37	size	size	NOUN
cord-326631-7gd3hjc3	275	38	formulae	formulae	ADJ
cord-326631-7gd3hjc3	275	39	(	(	PUNCT
cord-326631-7gd3hjc3	275	40	gart	gart	PROPN
cord-326631-7gd3hjc3	275	41	,	,	PUNCT
cord-326631-7gd3hjc3	275	42	1968	1968	NUM
cord-326631-7gd3hjc3	275	43	;	;	PUNCT
cord-326631-7gd3hjc3	275	44	dwyer	dwyer	PROPN
cord-326631-7gd3hjc3	275	45	et	et	PROPN
cord-326631-7gd3hjc3	275	46	al	al	PROPN
cord-326631-7gd3hjc3	275	47	.	.	PROPN
cord-326631-7gd3hjc3	275	48	,	,	PUNCT
cord-326631-7gd3hjc3	275	49	2000	2000	NUM
cord-326631-7gd3hjc3	275	50	;	;	PUNCT
cord-326631-7gd3hjc3	275	51	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	275	52	and	and	CCONJ
cord-326631-7gd3hjc3	275	53	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	275	54	,	,	PUNCT
cord-326631-7gd3hjc3	275	55	2000	2000	NUM
cord-326631-7gd3hjc3	275	56	;	;	PUNCT
cord-326631-7gd3hjc3	275	57	andreasen	andreasen	PROPN
cord-326631-7gd3hjc3	275	58	,	,	PUNCT
cord-326631-7gd3hjc3	275	59	2003	2003	NUM
cord-326631-7gd3hjc3	275	60	)	)	PUNCT
cord-326631-7gd3hjc3	275	61	.	.	PUNCT
cord-326631-7gd3hjc3	276	1	in	in	ADP
cord-326631-7gd3hjc3	276	2	this	this	DET
cord-326631-7gd3hjc3	276	3	section	section	NOUN
cord-326631-7gd3hjc3	276	4	,	,	PUNCT
cord-326631-7gd3hjc3	276	5	we	we	PRON
cord-326631-7gd3hjc3	276	6	briefly	briefly	ADV
cord-326631-7gd3hjc3	276	7	discuss	discuss	VERB
cord-326631-7gd3hjc3	276	8	two	two	NUM
cord-326631-7gd3hjc3	276	9	other	other	ADJ
cord-326631-7gd3hjc3	276	10	interpretations	interpretation	NOUN
cord-326631-7gd3hjc3	276	11	,	,	PUNCT
cord-326631-7gd3hjc3	276	12	which	which	PRON
cord-326631-7gd3hjc3	276	13	lead	lead	VERB
cord-326631-7gd3hjc3	276	14	to	to	ADP
cord-326631-7gd3hjc3	276	15	a	a	DET
cord-326631-7gd3hjc3	276	16	transmision	transmision	NOUN
cord-326631-7gd3hjc3	276	17	matrix	matrix	NOUN
cord-326631-7gd3hjc3	276	18	that	that	PRON
cord-326631-7gd3hjc3	276	19	is	be	AUX
cord-326631-7gd3hjc3	276	20	not	not	PART
cord-326631-7gd3hjc3	276	21	proportional	proportional	ADJ
cord-326631-7gd3hjc3	276	22	to	to	ADP
cord-326631-7gd3hjc3	276	23	a	a	DET
cord-326631-7gd3hjc3	276	24	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	276	25	matrix	matrix	NOUN
cord-326631-7gd3hjc3	276	26	and	and	CCONJ
cord-326631-7gd3hjc3	276	27	will	will	AUX
cord-326631-7gd3hjc3	276	28	not	not	PART
cord-326631-7gd3hjc3	276	29	yield	yield	VERB
cord-326631-7gd3hjc3	276	30	the	the	DET
cord-326631-7gd3hjc3	276	31	usual	usual	ADJ
cord-326631-7gd3hjc3	276	32	final	final	ADJ
cord-326631-7gd3hjc3	276	33	size	size	NOUN
cord-326631-7gd3hjc3	276	34	formula	formula	NOUN
cord-326631-7gd3hjc3	276	35	(	(	PUNCT
cord-326631-7gd3hjc3	276	36	5	5	NUM
cord-326631-7gd3hjc3	276	37	)	)	PUNCT
cord-326631-7gd3hjc3	276	38	.	.	PUNCT
cord-326631-7gd3hjc3	277	1	rather	rather	ADV
cord-326631-7gd3hjc3	277	2	than	than	ADP
cord-326631-7gd3hjc3	277	3	specifying	specify	VERB
cord-326631-7gd3hjc3	277	4	heterogeneities	heterogeneity	NOUN
cord-326631-7gd3hjc3	277	5	of	of	ADP
cord-326631-7gd3hjc3	277	6	transmission	transmission	NOUN
cord-326631-7gd3hjc3	277	7	resulting	result	VERB
cord-326631-7gd3hjc3	277	8	from	from	ADP
cord-326631-7gd3hjc3	277	9	spatial	spatial	ADJ
cord-326631-7gd3hjc3	277	10	structure	structure	NOUN
cord-326631-7gd3hjc3	277	11	,	,	PUNCT
cord-326631-7gd3hjc3	277	12	as	as	ADP
cord-326631-7gd3hjc3	277	13	in	in	ADP
cord-326631-7gd3hjc3	277	14	the	the	DET
cord-326631-7gd3hjc3	277	15	previous	previous	ADJ
cord-326631-7gd3hjc3	277	16	section	section	NOUN
cord-326631-7gd3hjc3	277	17	,	,	PUNCT
cord-326631-7gd3hjc3	277	18	suppose	suppose	VERB
cord-326631-7gd3hjc3	277	19	that	that	SCONJ
cord-326631-7gd3hjc3	277	20	heterogeneities	heterogeneity	NOUN
cord-326631-7gd3hjc3	277	21	arise	arise	VERB
cord-326631-7gd3hjc3	277	22	from	from	ADP
cord-326631-7gd3hjc3	277	23	age	age	NOUN
cord-326631-7gd3hjc3	277	24	-	-	PUNCT
cord-326631-7gd3hjc3	277	25	structured	structure	VERB
cord-326631-7gd3hjc3	277	26	mixing	mixing	NOUN
cord-326631-7gd3hjc3	277	27	patterns	pattern	NOUN
cord-326631-7gd3hjc3	277	28	.	.	PUNCT
cord-326631-7gd3hjc3	278	1	one	one	NUM
cord-326631-7gd3hjc3	278	2	possible	possible	ADJ
cord-326631-7gd3hjc3	278	3	formulation	formulation	NOUN
cord-326631-7gd3hjc3	278	4	is	be	AUX
cord-326631-7gd3hjc3	278	5	to	to	PART
cord-326631-7gd3hjc3	278	6	categorize	categorize	VERB
cord-326631-7gd3hjc3	278	7	the	the	DET
cord-326631-7gd3hjc3	278	8	population	population	NOUN
cord-326631-7gd3hjc3	278	9	by	by	ADP
cord-326631-7gd3hjc3	278	10	discrete	discrete	ADJ
cord-326631-7gd3hjc3	278	11	age	age	NOUN
cord-326631-7gd3hjc3	278	12	cohorts	cohort	NOUN
cord-326631-7gd3hjc3	278	13	,	,	PUNCT
cord-326631-7gd3hjc3	278	14	which	which	PRON
cord-326631-7gd3hjc3	278	15	is	be	AUX
cord-326631-7gd3hjc3	278	16	typically	typically	ADV
cord-326631-7gd3hjc3	278	17	motivated	motivate	VERB
cord-326631-7gd3hjc3	278	18	by	by	ADP
cord-326631-7gd3hjc3	278	19	mixing	mix	VERB
cord-326631-7gd3hjc3	278	20	patterns	pattern	NOUN
cord-326631-7gd3hjc3	278	21	of	of	ADP
cord-326631-7gd3hjc3	278	22	children	child	NOUN
cord-326631-7gd3hjc3	278	23	in	in	ADP
cord-326631-7gd3hjc3	278	24	schools	school	NOUN
cord-326631-7gd3hjc3	278	25	.	.	PUNCT
cord-326631-7gd3hjc3	279	1	if	if	SCONJ
cord-326631-7gd3hjc3	279	2	we	we	PRON
cord-326631-7gd3hjc3	279	3	consider	consider	VERB
cord-326631-7gd3hjc3	279	4	a	a	DET
cord-326631-7gd3hjc3	279	5	time	time	NOUN
cord-326631-7gd3hjc3	279	6	-	-	PUNCT
cord-326631-7gd3hjc3	279	7	scale	scale	NOUN
cord-326631-7gd3hjc3	279	8	short	short	ADJ
cord-326631-7gd3hjc3	279	9	enough	enough	ADV
cord-326631-7gd3hjc3	279	10	that	that	SCONJ
cord-326631-7gd3hjc3	279	11	transfer	transfer	NOUN
cord-326631-7gd3hjc3	279	12	from	from	ADP
cord-326631-7gd3hjc3	279	13	one	one	NUM
cord-326631-7gd3hjc3	279	14	cohort	cohort	NOUN
cord-326631-7gd3hjc3	279	15	to	to	ADP
cord-326631-7gd3hjc3	279	16	the	the	DET
cord-326631-7gd3hjc3	279	17	next	next	ADJ
cord-326631-7gd3hjc3	279	18	can	can	AUX
cord-326631-7gd3hjc3	279	19	be	be	AUX
cord-326631-7gd3hjc3	279	20	ignored	ignore	VERB
cord-326631-7gd3hjc3	279	21	,	,	PUNCT
cord-326631-7gd3hjc3	279	22	then	then	ADV
cord-326631-7gd3hjc3	279	23	the	the	DET
cord-326631-7gd3hjc3	279	24	standard	standard	ADJ
cord-326631-7gd3hjc3	279	25	"	"	PUNCT
cord-326631-7gd3hjc3	279	26	realistic	realistic	ADJ
cord-326631-7gd3hjc3	279	27	agestructured	agestructured	ADJ
cord-326631-7gd3hjc3	279	28	model	model	NOUN
cord-326631-7gd3hjc3	279	29	"	"	PUNCT
cord-326631-7gd3hjc3	279	30	(	(	PUNCT
cord-326631-7gd3hjc3	279	31	schenzle	schenzle	NOUN
cord-326631-7gd3hjc3	279	32	,	,	PUNCT
cord-326631-7gd3hjc3	279	33	1984	1984	NUM
cord-326631-7gd3hjc3	279	34	)	)	PUNCT
cord-326631-7gd3hjc3	279	35	reduces	reduce	VERB
cord-326631-7gd3hjc3	279	36	to	to	ADP
cord-326631-7gd3hjc3	279	37	eqs	eqs	PROPN
cord-326631-7gd3hjc3	279	38	.	.	PUNCT
cord-326631-7gd3hjc3	280	1	(	(	PUNCT
cord-326631-7gd3hjc3	280	2	26	26	NUM
cord-326631-7gd3hjc3	280	3	)	)	PUNCT
cord-326631-7gd3hjc3	280	4	,	,	PUNCT
cord-326631-7gd3hjc3	280	5	where	where	SCONJ
cord-326631-7gd3hjc3	280	6	the	the	DET
cord-326631-7gd3hjc3	280	7	transmission	transmission	NOUN
cord-326631-7gd3hjc3	280	8	matrix	matrix	NOUN
cord-326631-7gd3hjc3	280	9	b	b	PROPN
cord-326631-7gd3hjc3	280	10	now	now	ADV
cord-326631-7gd3hjc3	280	11	refers	refer	VERB
cord-326631-7gd3hjc3	280	12	to	to	ADP
cord-326631-7gd3hjc3	280	13	contact	contact	NOUN
cord-326631-7gd3hjc3	280	14	patterns	pattern	NOUN
cord-326631-7gd3hjc3	280	15	among	among	ADP
cord-326631-7gd3hjc3	280	16	different	different	ADJ
cord-326631-7gd3hjc3	280	17	age	age	NOUN
cord-326631-7gd3hjc3	280	18	cohorts	cohort	NOUN
cord-326631-7gd3hjc3	280	19	.	.	PUNCT
cord-326631-7gd3hjc3	281	1	as	as	ADP
cord-326631-7gd3hjc3	281	2	in	in	ADP
cord-326631-7gd3hjc3	281	3	the	the	DET
cord-326631-7gd3hjc3	281	4	case	case	NOUN
cord-326631-7gd3hjc3	281	5	of	of	ADP
cord-326631-7gd3hjc3	281	6	the	the	DET
cord-326631-7gd3hjc3	281	7	spatial	spatial	ADJ
cord-326631-7gd3hjc3	281	8	patch	patch	NOUN
cord-326631-7gd3hjc3	281	9	interpretation	interpretation	NOUN
cord-326631-7gd3hjc3	281	10	,	,	PUNCT
cord-326631-7gd3hjc3	281	11	it	it	PRON
cord-326631-7gd3hjc3	281	12	might	might	AUX
cord-326631-7gd3hjc3	281	13	be	be	AUX
cord-326631-7gd3hjc3	281	14	reasonable	reasonable	ADJ
cord-326631-7gd3hjc3	281	15	to	to	PART
cord-326631-7gd3hjc3	281	16	assume	assume	VERB
cord-326631-7gd3hjc3	281	17	that	that	SCONJ
cord-326631-7gd3hjc3	281	18	there	there	PRON
cord-326631-7gd3hjc3	281	19	is	be	VERB
cord-326631-7gd3hjc3	281	20	a	a	DET
cord-326631-7gd3hjc3	281	21	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	281	22	matrix	matrix	NOUN
cord-326631-7gd3hjc3	281	23	p	p	NOUN
cord-326631-7gd3hjc3	281	24	such	such	ADJ
cord-326631-7gd3hjc3	281	25	that	that	SCONJ
cord-326631-7gd3hjc3	281	26	where	where	SCONJ
cord-326631-7gd3hjc3	281	27	the	the	DET
cord-326631-7gd3hjc3	281	28	interpretation	interpretation	NOUN
cord-326631-7gd3hjc3	281	29	is	be	AUX
cord-326631-7gd3hjc3	281	30	that	that	SCONJ
cord-326631-7gd3hjc3	281	31	individuals	individual	NOUN
cord-326631-7gd3hjc3	281	32	in	in	ADP
cord-326631-7gd3hjc3	281	33	cohort	cohort	NOUN
cord-326631-7gd3hjc3	281	34	i	i	PRON
cord-326631-7gd3hjc3	281	35	have	have	VERB
cord-326631-7gd3hjc3	281	36	a	a	DET
cord-326631-7gd3hjc3	281	37	proportion	proportion	NOUN
cord-326631-7gd3hjc3	281	38	p	p	NOUN
cord-326631-7gd3hjc3	281	39	i	i	NOUN
cord-326631-7gd3hjc3	281	40	j	j	NOUN
cord-326631-7gd3hjc3	281	41	of	of	ADP
cord-326631-7gd3hjc3	281	42	their	their	PRON
cord-326631-7gd3hjc3	281	43	contacts	contact	NOUN
cord-326631-7gd3hjc3	281	44	with	with	ADP
cord-326631-7gd3hjc3	281	45	individuals	individual	NOUN
cord-326631-7gd3hjc3	281	46	in	in	ADP
cord-326631-7gd3hjc3	281	47	cohort	cohort	PROPN
cord-326631-7gd3hjc3	281	48	j	j	PROPN
cord-326631-7gd3hjc3	281	49	,	,	PUNCT
cord-326631-7gd3hjc3	281	50	and	and	CCONJ
cord-326631-7gd3hjc3	281	51	β	β	NOUN
cord-326631-7gd3hjc3	281	52	i	i	PRON
cord-326631-7gd3hjc3	281	53	is	be	AUX
cord-326631-7gd3hjc3	281	54	the	the	DET
cord-326631-7gd3hjc3	281	55	transmission	transmission	NOUN
cord-326631-7gd3hjc3	281	56	rate	rate	NOUN
cord-326631-7gd3hjc3	281	57	for	for	ADP
cord-326631-7gd3hjc3	281	58	individuals	individual	NOUN
cord-326631-7gd3hjc3	281	59	in	in	ADP
cord-326631-7gd3hjc3	281	60	cohort	cohort	PROPN
cord-326631-7gd3hjc3	281	61	i.	i.	PROPN
cord-326631-7gd3hjc3	281	62	unlike	unlike	ADP
cord-326631-7gd3hjc3	281	63	the	the	DET
cord-326631-7gd3hjc3	281	64	spatial	spatial	ADJ
cord-326631-7gd3hjc3	281	65	interpretation	interpretation	NOUN
cord-326631-7gd3hjc3	281	66	,	,	PUNCT
cord-326631-7gd3hjc3	281	67	however	however	ADV
cord-326631-7gd3hjc3	281	68	,	,	PUNCT
cord-326631-7gd3hjc3	281	69	it	it	PRON
cord-326631-7gd3hjc3	281	70	would	would	AUX
cord-326631-7gd3hjc3	281	71	be	be	AUX
cord-326631-7gd3hjc3	281	72	hard	hard	ADJ
cord-326631-7gd3hjc3	281	73	to	to	PART
cord-326631-7gd3hjc3	281	74	justify	justify	VERB
cord-326631-7gd3hjc3	281	75	taking	take	VERB
cord-326631-7gd3hjc3	281	76	β	β	NOUN
cord-326631-7gd3hjc3	281	77	i	i	PRON
cord-326631-7gd3hjc3	281	78	to	to	PART
cord-326631-7gd3hjc3	281	79	be	be	AUX
cord-326631-7gd3hjc3	281	80	the	the	DET
cord-326631-7gd3hjc3	281	81	same	same	ADJ
cord-326631-7gd3hjc3	281	82	for	for	ADP
cord-326631-7gd3hjc3	281	83	each	each	DET
cord-326631-7gd3hjc3	281	84	i.	i.	PROPN
cord-326631-7gd3hjc3	281	85	in	in	ADP
cord-326631-7gd3hjc3	281	86	particular	particular	ADJ
cord-326631-7gd3hjc3	281	87	,	,	PUNCT
cord-326631-7gd3hjc3	281	88	young	young	ADJ
cord-326631-7gd3hjc3	281	89	children	child	NOUN
cord-326631-7gd3hjc3	281	90	tend	tend	VERB
cord-326631-7gd3hjc3	281	91	to	to	PART
cord-326631-7gd3hjc3	281	92	come	come	VERB
cord-326631-7gd3hjc3	281	93	into	into	ADP
cord-326631-7gd3hjc3	281	94	much	much	ADV
cord-326631-7gd3hjc3	281	95	closer	close	ADJ
cord-326631-7gd3hjc3	281	96	contact	contact	NOUN
cord-326631-7gd3hjc3	281	97	with	with	ADP
cord-326631-7gd3hjc3	281	98	their	their	PRON
cord-326631-7gd3hjc3	281	99	classmates	classmate	NOUN
cord-326631-7gd3hjc3	281	100	than	than	SCONJ
cord-326631-7gd3hjc3	281	101	teenagers	teenager	NOUN
cord-326631-7gd3hjc3	281	102	or	or	CCONJ
cord-326631-7gd3hjc3	281	103	adults	adult	NOUN
cord-326631-7gd3hjc3	281	104	do	do	VERB
cord-326631-7gd3hjc3	281	105	with	with	ADP
cord-326631-7gd3hjc3	281	106	members	member	NOUN
cord-326631-7gd3hjc3	281	107	of	of	ADP
cord-326631-7gd3hjc3	281	108	their	their	PRON
cord-326631-7gd3hjc3	281	109	cohorts	cohort	NOUN
cord-326631-7gd3hjc3	281	110	.	.	PUNCT
cord-326631-7gd3hjc3	282	1	as	as	ADP
cord-326631-7gd3hjc3	282	2	a	a	DET
cord-326631-7gd3hjc3	282	3	result	result	NOUN
cord-326631-7gd3hjc3	282	4	,	,	PUNCT
cord-326631-7gd3hjc3	282	5	theorem	theorem	VERB
cord-326631-7gd3hjc3	282	6	9.1	9.1	NUM
cord-326631-7gd3hjc3	282	7	will	will	AUX
cord-326631-7gd3hjc3	282	8	not	not	PART
cord-326631-7gd3hjc3	282	9	apply	apply	VERB
cord-326631-7gd3hjc3	282	10	and	and	CCONJ
cord-326631-7gd3hjc3	282	11	the	the	DET
cord-326631-7gd3hjc3	282	12	final	final	ADJ
cord-326631-7gd3hjc3	282	13	size	size	NOUN
cord-326631-7gd3hjc3	282	14	will	will	AUX
cord-326631-7gd3hjc3	282	15	not	not	PART
cord-326631-7gd3hjc3	282	16	be	be	AUX
cord-326631-7gd3hjc3	282	17	given	give	VERB
cord-326631-7gd3hjc3	282	18	by	by	ADP
cord-326631-7gd3hjc3	282	19	the	the	DET
cord-326631-7gd3hjc3	282	20	usual	usual	ADJ
cord-326631-7gd3hjc3	282	21	formula	formula	NOUN
cord-326631-7gd3hjc3	282	22	(	(	PUNCT
cord-326631-7gd3hjc3	282	23	5	5	NUM
cord-326631-7gd3hjc3	282	24	)	)	PUNCT
cord-326631-7gd3hjc3	282	25	.	.	PUNCT
cord-326631-7gd3hjc3	283	1	in	in	ADP
cord-326631-7gd3hjc3	283	2	section	section	NOUN
cord-326631-7gd3hjc3	283	3	8	8	NUM
cord-326631-7gd3hjc3	283	4	where	where	SCONJ
cord-326631-7gd3hjc3	283	5	we	we	PRON
cord-326631-7gd3hjc3	283	6	discussed	discuss	VERB
cord-326631-7gd3hjc3	283	7	super	super	NOUN
cord-326631-7gd3hjc3	283	8	-	-	NOUN
cord-326631-7gd3hjc3	283	9	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	283	10	,	,	PUNCT
cord-326631-7gd3hjc3	283	11	we	we	PRON
cord-326631-7gd3hjc3	283	12	specifically	specifically	ADV
cord-326631-7gd3hjc3	283	13	excluded	exclude	VERB
cord-326631-7gd3hjc3	283	14	the	the	DET
cord-326631-7gd3hjc3	283	15	types	type	NOUN
cord-326631-7gd3hjc3	283	16	of	of	ADP
cord-326631-7gd3hjc3	283	17	super	super	NOUN
cord-326631-7gd3hjc3	283	18	-	-	NOUN
cord-326631-7gd3hjc3	283	19	spreaders	spreader	NOUN
cord-326631-7gd3hjc3	283	20	that	that	PRON
cord-326631-7gd3hjc3	283	21	occur	occur	VERB
cord-326631-7gd3hjc3	283	22	for	for	ADP
cord-326631-7gd3hjc3	283	23	sexually	sexually	ADV
cord-326631-7gd3hjc3	283	24	transmitted	transmit	VERB
cord-326631-7gd3hjc3	283	25	diseases	disease	NOUN
cord-326631-7gd3hjc3	283	26	,	,	PUNCT
cord-326631-7gd3hjc3	283	27	namely	namely	ADV
cord-326631-7gd3hjc3	283	28	individuals	individual	NOUN
cord-326631-7gd3hjc3	283	29	who	who	PRON
cord-326631-7gd3hjc3	283	30	always	always	ADV
cord-326631-7gd3hjc3	283	31	have	have	VERB
cord-326631-7gd3hjc3	283	32	a	a	DET
cord-326631-7gd3hjc3	283	33	higher	high	ADJ
cord-326631-7gd3hjc3	283	34	rate	rate	NOUN
cord-326631-7gd3hjc3	283	35	of	of	ADP
cord-326631-7gd3hjc3	283	36	contact	contact	NOUN
cord-326631-7gd3hjc3	283	37	with	with	ADP
cord-326631-7gd3hjc3	283	38	others	other	NOUN
cord-326631-7gd3hjc3	283	39	,	,	PUNCT
cord-326631-7gd3hjc3	283	40	regardless	regardless	ADV
cord-326631-7gd3hjc3	283	41	of	of	ADP
cord-326631-7gd3hjc3	283	42	whether	whether	SCONJ
cord-326631-7gd3hjc3	283	43	they	they	PRON
cord-326631-7gd3hjc3	283	44	happen	happen	VERB
cord-326631-7gd3hjc3	283	45	to	to	PART
cord-326631-7gd3hjc3	283	46	be	be	AUX
cord-326631-7gd3hjc3	283	47	infected	infect	VERB
cord-326631-7gd3hjc3	283	48	.	.	PUNCT
cord-326631-7gd3hjc3	284	1	when	when	SCONJ
cord-326631-7gd3hjc3	284	2	such	such	ADJ
cord-326631-7gd3hjc3	284	3	"	"	PUNCT
cord-326631-7gd3hjc3	284	4	core	core	NOUN
cord-326631-7gd3hjc3	284	5	groups	group	NOUN
cord-326631-7gd3hjc3	284	6	"	"	PUNCT
cord-326631-7gd3hjc3	284	7	(	(	PUNCT
cord-326631-7gd3hjc3	284	8	yorke	yorke	NOUN
cord-326631-7gd3hjc3	284	9	and	and	CCONJ
cord-326631-7gd3hjc3	284	10	hethcote	hethcote	NOUN
cord-326631-7gd3hjc3	284	11	,	,	PUNCT
cord-326631-7gd3hjc3	284	12	1984	1984	NUM
cord-326631-7gd3hjc3	284	13	;	;	PUNCT
cord-326631-7gd3hjc3	284	14	anderson	anderson	PROPN
cord-326631-7gd3hjc3	284	15	et	et	PROPN
cord-326631-7gd3hjc3	284	16	al	al	PROPN
cord-326631-7gd3hjc3	284	17	.	.	PROPN
cord-326631-7gd3hjc3	284	18	,	,	PUNCT
cord-326631-7gd3hjc3	284	19	1986	1986	NUM
cord-326631-7gd3hjc3	284	20	)	)	PUNCT
cord-326631-7gd3hjc3	284	21	exist	exist	VERB
cord-326631-7gd3hjc3	284	22	,	,	PUNCT
cord-326631-7gd3hjc3	284	23	eqs	eqs	PROPN
cord-326631-7gd3hjc3	284	24	.	.	PUNCT
cord-326631-7gd3hjc3	285	1	(	(	PUNCT
cord-326631-7gd3hjc3	285	2	26	26	NUM
cord-326631-7gd3hjc3	285	3	)	)	PUNCT
cord-326631-7gd3hjc3	285	4	can	can	AUX
cord-326631-7gd3hjc3	285	5	still	still	ADV
cord-326631-7gd3hjc3	285	6	be	be	AUX
cord-326631-7gd3hjc3	285	7	used	use	VERB
cord-326631-7gd3hjc3	285	8	,	,	PUNCT
cord-326631-7gd3hjc3	285	9	with	with	ADP
cord-326631-7gd3hjc3	285	10	the	the	DET
cord-326631-7gd3hjc3	285	11	interpretation	interpretation	NOUN
cord-326631-7gd3hjc3	285	12	that	that	SCONJ
cord-326631-7gd3hjc3	285	13	the	the	DET
cord-326631-7gd3hjc3	285	14	stratification	stratification	NOUN
cord-326631-7gd3hjc3	285	15	of	of	ADP
cord-326631-7gd3hjc3	285	16	the	the	DET
cord-326631-7gd3hjc3	285	17	population	population	NOUN
cord-326631-7gd3hjc3	285	18	is	be	AUX
cord-326631-7gd3hjc3	285	19	by	by	ADP
cord-326631-7gd3hjc3	285	20	social	social	ADJ
cord-326631-7gd3hjc3	285	21	group	group	NOUN
cord-326631-7gd3hjc3	285	22	rather	rather	ADV
cord-326631-7gd3hjc3	285	23	than	than	ADP
cord-326631-7gd3hjc3	285	24	spatial	spatial	ADJ
cord-326631-7gd3hjc3	285	25	region	region	NOUN
cord-326631-7gd3hjc3	285	26	or	or	CCONJ
cord-326631-7gd3hjc3	285	27	age	age	NOUN
cord-326631-7gd3hjc3	285	28	cohort	cohort	NOUN
cord-326631-7gd3hjc3	285	29	.	.	PUNCT
cord-326631-7gd3hjc3	286	1	like	like	ADP
cord-326631-7gd3hjc3	286	2	the	the	DET
cord-326631-7gd3hjc3	286	3	age	age	NOUN
cord-326631-7gd3hjc3	286	4	-	-	PUNCT
cord-326631-7gd3hjc3	286	5	structured	structure	VERB
cord-326631-7gd3hjc3	286	6	situation	situation	NOUN
cord-326631-7gd3hjc3	286	7	,	,	PUNCT
cord-326631-7gd3hjc3	286	8	we	we	PRON
cord-326631-7gd3hjc3	286	9	can	can	AUX
cord-326631-7gd3hjc3	286	10	safely	safely	ADV
cord-326631-7gd3hjc3	286	11	assume	assume	VERB
cord-326631-7gd3hjc3	286	12	that	that	SCONJ
cord-326631-7gd3hjc3	286	13	eq	eq	X
cord-326631-7gd3hjc3	286	14	.	.	PUNCT
cord-326631-7gd3hjc3	286	15	(	(	PUNCT
cord-326631-7gd3hjc3	286	16	34	34	NUM
cord-326631-7gd3hjc3	286	17	)	)	PUNCT
cord-326631-7gd3hjc3	286	18	holds	hold	VERB
cord-326631-7gd3hjc3	286	19	but	but	CCONJ
cord-326631-7gd3hjc3	286	20	not	not	PART
cord-326631-7gd3hjc3	286	21	that	that	PRON
cord-326631-7gd3hjc3	287	1	β	β	PROPN
cord-326631-7gd3hjc3	288	1	i	i	PRON
cord-326631-7gd3hjc3	288	2	is	be	AUX
cord-326631-7gd3hjc3	288	3	the	the	DET
cord-326631-7gd3hjc3	288	4	same	same	ADJ
cord-326631-7gd3hjc3	288	5	for	for	ADP
cord-326631-7gd3hjc3	288	6	every	every	DET
cord-326631-7gd3hjc3	288	7	i	i	PRON
cord-326631-7gd3hjc3	288	8	as	as	ADP
cord-326631-7gd3hjc3	288	9	in	in	ADP
cord-326631-7gd3hjc3	288	10	eq	eq	PROPN
cord-326631-7gd3hjc3	288	11	.	.	PUNCT
cord-326631-7gd3hjc3	289	1	(	(	PUNCT
cord-326631-7gd3hjc3	289	2	30	30	NUM
cord-326631-7gd3hjc3	289	3	)	)	PUNCT
cord-326631-7gd3hjc3	289	4	.	.	PUNCT
cord-326631-7gd3hjc3	290	1	indeed	indeed	ADV
cord-326631-7gd3hjc3	290	2	,	,	PUNCT
cord-326631-7gd3hjc3	290	3	a	a	DET
cord-326631-7gd3hjc3	290	4	large	large	ADJ
cord-326631-7gd3hjc3	290	5	difference	difference	NOUN
cord-326631-7gd3hjc3	290	6	in	in	ADP
cord-326631-7gd3hjc3	290	7	β	β	NOUN
cord-326631-7gd3hjc3	291	1	i	i	PRON
cord-326631-7gd3hjc3	291	2	is	be	AUX
cord-326631-7gd3hjc3	291	3	precisely	precisely	ADV
cord-326631-7gd3hjc3	291	4	what	what	PRON
cord-326631-7gd3hjc3	291	5	defines	define	VERB
cord-326631-7gd3hjc3	291	6	the	the	DET
cord-326631-7gd3hjc3	291	7	core	core	NOUN
cord-326631-7gd3hjc3	291	8	groups	group	NOUN
cord-326631-7gd3hjc3	291	9	.	.	PUNCT
cord-326631-7gd3hjc3	292	1	again	again	ADV
cord-326631-7gd3hjc3	292	2	,	,	PUNCT
cord-326631-7gd3hjc3	292	3	we	we	PRON
cord-326631-7gd3hjc3	292	4	have	have	VERB
cord-326631-7gd3hjc3	292	5	a	a	DET
cord-326631-7gd3hjc3	292	6	situation	situation	NOUN
cord-326631-7gd3hjc3	292	7	where	where	SCONJ
cord-326631-7gd3hjc3	292	8	the	the	DET
cord-326631-7gd3hjc3	292	9	usual	usual	ADJ
cord-326631-7gd3hjc3	292	10	final	final	ADJ
cord-326631-7gd3hjc3	292	11	size	size	NOUN
cord-326631-7gd3hjc3	292	12	formula	formula	NOUN
cord-326631-7gd3hjc3	292	13	will	will	AUX
cord-326631-7gd3hjc3	292	14	not	not	PART
cord-326631-7gd3hjc3	292	15	apply	apply	VERB
cord-326631-7gd3hjc3	292	16	.	.	PUNCT
cord-326631-7gd3hjc3	293	1	core	core	NOUN
cord-326631-7gd3hjc3	293	2	groups	group	NOUN
cord-326631-7gd3hjc3	293	3	are	be	AUX
cord-326631-7gd3hjc3	293	4	well	well	ADV
cord-326631-7gd3hjc3	293	5	known	know	VERB
cord-326631-7gd3hjc3	293	6	to	to	PART
cord-326631-7gd3hjc3	293	7	have	have	VERB
cord-326631-7gd3hjc3	293	8	a	a	DET
cord-326631-7gd3hjc3	293	9	critical	critical	ADJ
cord-326631-7gd3hjc3	293	10	role	role	NOUN
cord-326631-7gd3hjc3	293	11	in	in	ADP
cord-326631-7gd3hjc3	293	12	the	the	DET
cord-326631-7gd3hjc3	293	13	transmission	transmission	NOUN
cord-326631-7gd3hjc3	293	14	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	293	15	of	of	ADP
cord-326631-7gd3hjc3	293	16	sexually	sexually	ADV
cord-326631-7gd3hjc3	293	17	transmitted	transmit	VERB
cord-326631-7gd3hjc3	293	18	diseases	disease	NOUN
cord-326631-7gd3hjc3	293	19	,	,	PUNCT
cord-326631-7gd3hjc3	293	20	so	so	CCONJ
cord-326631-7gd3hjc3	293	21	it	it	PRON
cord-326631-7gd3hjc3	293	22	is	be	AUX
cord-326631-7gd3hjc3	293	23	not	not	PART
cord-326631-7gd3hjc3	293	24	surprising	surprising	ADJ
cord-326631-7gd3hjc3	293	25	that	that	SCONJ
cord-326631-7gd3hjc3	293	26	they	they	PRON
cord-326631-7gd3hjc3	293	27	will	will	AUX
cord-326631-7gd3hjc3	293	28	affect	affect	VERB
cord-326631-7gd3hjc3	293	29	the	the	DET
cord-326631-7gd3hjc3	293	30	final	final	ADJ
cord-326631-7gd3hjc3	293	31	size	size	NOUN
cord-326631-7gd3hjc3	293	32	of	of	ADP
cord-326631-7gd3hjc3	293	33	epidemics	epidemic	NOUN
cord-326631-7gd3hjc3	293	34	.	.	PUNCT
cord-326631-7gd3hjc3	294	1	the	the	DET
cord-326631-7gd3hjc3	294	2	well	well	ADV
cord-326631-7gd3hjc3	294	3	-	-	PUNCT
cord-326631-7gd3hjc3	294	4	known	know	VERB
cord-326631-7gd3hjc3	294	5	formula	formula	NOUN
cord-326631-7gd3hjc3	294	6	(	(	PUNCT
cord-326631-7gd3hjc3	294	7	5	5	NUM
cord-326631-7gd3hjc3	294	8	)	)	PUNCT
cord-326631-7gd3hjc3	294	9	for	for	ADP
cord-326631-7gd3hjc3	294	10	the	the	DET
cord-326631-7gd3hjc3	294	11	expected	expect	VERB
cord-326631-7gd3hjc3	294	12	final	final	ADJ
cord-326631-7gd3hjc3	294	13	size	size	NOUN
cord-326631-7gd3hjc3	294	14	of	of	ADP
cord-326631-7gd3hjc3	294	15	an	an	DET
cord-326631-7gd3hjc3	294	16	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	294	17	is	be	AUX
cord-326631-7gd3hjc3	294	18	valid	valid	ADJ
cord-326631-7gd3hjc3	294	19	in	in	ADP
cord-326631-7gd3hjc3	294	20	remarkably	remarkably	ADV
cord-326631-7gd3hjc3	294	21	general	general	ADJ
cord-326631-7gd3hjc3	294	22	circumstances	circumstance	NOUN
cord-326631-7gd3hjc3	294	23	.	.	PUNCT
cord-326631-7gd3hjc3	295	1	previous	previous	ADJ
cord-326631-7gd3hjc3	295	2	work	work	NOUN
cord-326631-7gd3hjc3	295	3	(	(	PUNCT
cord-326631-7gd3hjc3	295	4	e.g.	e.g.	ADV
cord-326631-7gd3hjc3	295	5	,	,	PUNCT
cord-326631-7gd3hjc3	295	6	kermack	kermack	PROPN
cord-326631-7gd3hjc3	295	7	and	and	CCONJ
cord-326631-7gd3hjc3	295	8	mckendrick	mckendrick	PROPN
cord-326631-7gd3hjc3	295	9	(	(	PUNCT
cord-326631-7gd3hjc3	295	10	1927	1927	NUM
cord-326631-7gd3hjc3	295	11	)	)	PUNCT
cord-326631-7gd3hjc3	295	12	;	;	PUNCT
cord-326631-7gd3hjc3	295	13	anderson	anderson	PROPN
cord-326631-7gd3hjc3	295	14	and	and	CCONJ
cord-326631-7gd3hjc3	295	15	watsons	watson	NOUN
cord-326631-7gd3hjc3	295	16	(	(	PUNCT
cord-326631-7gd3hjc3	295	17	1980	1980	NUM
cord-326631-7gd3hjc3	295	18	)	)	PUNCT
cord-326631-7gd3hjc3	295	19	;	;	PUNCT
cord-326631-7gd3hjc3	295	20	diekmann	diekmann	PROPN
cord-326631-7gd3hjc3	295	21	and	and	CCONJ
cord-326631-7gd3hjc3	295	22	heesterbeek	heesterbeek	NOUN
cord-326631-7gd3hjc3	295	23	(	(	PUNCT
cord-326631-7gd3hjc3	295	24	2000	2000	NUM
cord-326631-7gd3hjc3	295	25	)	)	PUNCT
cord-326631-7gd3hjc3	295	26	)	)	PUNCT
cord-326631-7gd3hjc3	295	27	established	establish	VERB
cord-326631-7gd3hjc3	295	28	that	that	SCONJ
cord-326631-7gd3hjc3	295	29	the	the	DET
cord-326631-7gd3hjc3	295	30	formula	formula	NOUN
cord-326631-7gd3hjc3	295	31	is	be	AUX
cord-326631-7gd3hjc3	295	32	valid	valid	ADJ
cord-326631-7gd3hjc3	295	33	in	in	ADP
cord-326631-7gd3hjc3	295	34	an	an	DET
cord-326631-7gd3hjc3	295	35	sir	sir	NOUN
cord-326631-7gd3hjc3	295	36	model	model	NOUN
cord-326631-7gd3hjc3	295	37	with	with	ADP
cord-326631-7gd3hjc3	295	38	an	an	DET
cord-326631-7gd3hjc3	295	39	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	295	40	distributed	distribute	VERB
cord-326631-7gd3hjc3	295	41	infectious	infectious	ADJ
cord-326631-7gd3hjc3	295	42	period	period	NOUN
cord-326631-7gd3hjc3	295	43	(	(	PUNCT
cord-326631-7gd3hjc3	295	44	theorem	theorem	VERB
cord-326631-7gd3hjc3	295	45	6.1	6.1	NUM
cord-326631-7gd3hjc3	295	46	)	)	PUNCT
cord-326631-7gd3hjc3	295	47	.	.	PUNCT
cord-326631-7gd3hjc3	296	1	here	here	ADV
cord-326631-7gd3hjc3	296	2	we	we	PRON
cord-326631-7gd3hjc3	296	3	have	have	AUX
cord-326631-7gd3hjc3	296	4	shown	show	VERB
cord-326631-7gd3hjc3	296	5	,	,	PUNCT
cord-326631-7gd3hjc3	296	6	in	in	ADP
cord-326631-7gd3hjc3	296	7	addition	addition	NOUN
cord-326631-7gd3hjc3	296	8	,	,	PUNCT
cord-326631-7gd3hjc3	296	9	that	that	SCONJ
cord-326631-7gd3hjc3	296	10	the	the	DET
cord-326631-7gd3hjc3	296	11	standard	standard	ADJ
cord-326631-7gd3hjc3	296	12	formula	formula	NOUN
cord-326631-7gd3hjc3	296	13	(	(	PUNCT
cord-326631-7gd3hjc3	296	14	5	5	NUM
cord-326631-7gd3hjc3	296	15	)	)	PUNCT
cord-326631-7gd3hjc3	296	16	is	be	AUX
cord-326631-7gd3hjc3	296	17	invariant	invariant	ADJ
cord-326631-7gd3hjc3	296	18	to	to	ADP
cord-326631-7gd3hjc3	296	19	the	the	DET
cord-326631-7gd3hjc3	296	20	number	number	NOUN
cord-326631-7gd3hjc3	296	21	of	of	ADP
cord-326631-7gd3hjc3	296	22	latent	latent	ADJ
cord-326631-7gd3hjc3	296	23	and	and	CCONJ
cord-326631-7gd3hjc3	296	24	infectious	infectious	ADJ
cord-326631-7gd3hjc3	296	25	stages	stage	NOUN
cord-326631-7gd3hjc3	296	26	of	of	ADP
cord-326631-7gd3hjc3	296	27	disease	disease	NOUN
cord-326631-7gd3hjc3	296	28	(	(	PUNCT
cord-326631-7gd3hjc3	296	29	theorem	theorem	VERB
cord-326631-7gd3hjc3	296	30	7.1	7.1	NUM
cord-326631-7gd3hjc3	296	31	)	)	PUNCT
cord-326631-7gd3hjc3	296	32	,	,	PUNCT
cord-326631-7gd3hjc3	296	33	the	the	DET
cord-326631-7gd3hjc3	296	34	distributions	distribution	NOUN
cord-326631-7gd3hjc3	296	35	of	of	ADP
cord-326631-7gd3hjc3	296	36	transmission	transmission	NOUN
cord-326631-7gd3hjc3	296	37	rates	rate	NOUN
cord-326631-7gd3hjc3	296	38	within	within	ADP
cord-326631-7gd3hjc3	296	39	stages	stage	NOUN
cord-326631-7gd3hjc3	296	40	(	(	PUNCT
cord-326631-7gd3hjc3	296	41	theorem	theorem	X
cord-326631-7gd3hjc3	296	42	8.1	8.1	NUM
cord-326631-7gd3hjc3	296	43	)	)	PUNCT
cord-326631-7gd3hjc3	296	44	,	,	PUNCT
cord-326631-7gd3hjc3	296	45	and	and	CCONJ
cord-326631-7gd3hjc3	296	46	even	even	ADV
cord-326631-7gd3hjc3	296	47	to	to	ADP
cord-326631-7gd3hjc3	296	48	common	common	ADJ
cord-326631-7gd3hjc3	296	49	spatial	spatial	ADJ
cord-326631-7gd3hjc3	296	50	contact	contact	NOUN
cord-326631-7gd3hjc3	296	51	heterogeneities	heterogeneity	NOUN
cord-326631-7gd3hjc3	296	52	(	(	PUNCT
cord-326631-7gd3hjc3	296	53	theorem	theorem	X
cord-326631-7gd3hjc3	296	54	9.1	9.1	NUM
cord-326631-7gd3hjc3	296	55	)	)	PUNCT
cord-326631-7gd3hjc3	296	56	.	.	PUNCT
cord-326631-7gd3hjc3	297	1	the	the	DET
cord-326631-7gd3hjc3	297	2	invariance	invariance	NOUN
cord-326631-7gd3hjc3	297	3	of	of	ADP
cord-326631-7gd3hjc3	297	4	the	the	DET
cord-326631-7gd3hjc3	297	5	final	final	ADJ
cord-326631-7gd3hjc3	297	6	size	size	NOUN
cord-326631-7gd3hjc3	297	7	formula	formula	NOUN
cord-326631-7gd3hjc3	297	8	has	have	VERB
cord-326631-7gd3hjc3	297	9	important	important	ADJ
cord-326631-7gd3hjc3	297	10	practical	practical	ADJ
cord-326631-7gd3hjc3	297	11	implications	implication	NOUN
cord-326631-7gd3hjc3	297	12	.	.	PUNCT
cord-326631-7gd3hjc3	298	1	typically	typically	ADV
cord-326631-7gd3hjc3	298	2	,	,	PUNCT
cord-326631-7gd3hjc3	298	3	the	the	DET
cord-326631-7gd3hjc3	298	4	time	time	NOUN
cord-326631-7gd3hjc3	298	5	at	at	ADP
cord-326631-7gd3hjc3	298	6	which	which	PRON
cord-326631-7gd3hjc3	298	7	one	one	NOUN
cord-326631-7gd3hjc3	298	8	wishes	wish	VERB
cord-326631-7gd3hjc3	298	9	to	to	PART
cord-326631-7gd3hjc3	298	10	estimate	estimate	VERB
cord-326631-7gd3hjc3	298	11	the	the	DET
cord-326631-7gd3hjc3	298	12	expected	expect	VERB
cord-326631-7gd3hjc3	298	13	final	final	ADJ
cord-326631-7gd3hjc3	298	14	size	size	NOUN
cord-326631-7gd3hjc3	298	15	of	of	ADP
cord-326631-7gd3hjc3	298	16	an	an	DET
cord-326631-7gd3hjc3	298	17	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	298	18	is	be	AUX
cord-326631-7gd3hjc3	298	19	long	long	ADV
cord-326631-7gd3hjc3	298	20	before	before	SCONJ
cord-326631-7gd3hjc3	298	21	enough	enough	ADJ
cord-326631-7gd3hjc3	298	22	information	information	NOUN
cord-326631-7gd3hjc3	298	23	has	have	AUX
cord-326631-7gd3hjc3	298	24	been	be	AUX
cord-326631-7gd3hjc3	298	25	gathered	gather	VERB
cord-326631-7gd3hjc3	298	26	to	to	PART
cord-326631-7gd3hjc3	298	27	estimate	estimate	VERB
cord-326631-7gd3hjc3	298	28	the	the	DET
cord-326631-7gd3hjc3	298	29	distributions	distribution	NOUN
cord-326631-7gd3hjc3	298	30	of	of	ADP
cord-326631-7gd3hjc3	298	31	latent	latent	ADJ
cord-326631-7gd3hjc3	298	32	and	and	CCONJ
cord-326631-7gd3hjc3	298	33	infectious	infectious	ADJ
cord-326631-7gd3hjc3	298	34	periods	period	NOUN
cord-326631-7gd3hjc3	298	35	or	or	CCONJ
cord-326631-7gd3hjc3	298	36	other	other	ADJ
cord-326631-7gd3hjc3	298	37	epidemiological	epidemiological	ADJ
cord-326631-7gd3hjc3	298	38	details	detail	NOUN
cord-326631-7gd3hjc3	298	39	.	.	PUNCT
cord-326631-7gd3hjc3	299	1	our	our	PRON
cord-326631-7gd3hjc3	299	2	theorems	theorem	NOUN
cord-326631-7gd3hjc3	299	3	provide	provide	VERB
cord-326631-7gd3hjc3	299	4	rigorous	rigorous	ADJ
cord-326631-7gd3hjc3	299	5	support	support	NOUN
cord-326631-7gd3hjc3	299	6	for	for	ADP
cord-326631-7gd3hjc3	299	7	estimates	estimate	NOUN
cord-326631-7gd3hjc3	299	8	of	of	ADP
cord-326631-7gd3hjc3	299	9	the	the	DET
cord-326631-7gd3hjc3	299	10	expected	expect	VERB
cord-326631-7gd3hjc3	299	11	magnitude	magnitude	NOUN
cord-326631-7gd3hjc3	299	12	of	of	ADP
cord-326631-7gd3hjc3	299	13	epidemics	epidemic	NOUN
cord-326631-7gd3hjc3	299	14	based	base	VERB
cord-326631-7gd3hjc3	299	15	solely	solely	ADV
cord-326631-7gd3hjc3	299	16	on	on	ADP
cord-326631-7gd3hjc3	299	17	estimates	estimate	NOUN
cord-326631-7gd3hjc3	299	18	of	of	ADP
cord-326631-7gd3hjc3	299	19	the	the	DET
cord-326631-7gd3hjc3	299	20	basic	basic	ADJ
cord-326631-7gd3hjc3	299	21	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	299	22	number	number	NOUN
cord-326631-7gd3hjc3	299	23	r	r	NOUN
cord-326631-7gd3hjc3	299	24	0	0	NUM
cord-326631-7gd3hjc3	299	25	,	,	PUNCT
cord-326631-7gd3hjc3	299	26	which	which	PRON
cord-326631-7gd3hjc3	299	27	is	be	AUX
cord-326631-7gd3hjc3	299	28	the	the	DET
cord-326631-7gd3hjc3	299	29	only	only	ADJ
cord-326631-7gd3hjc3	299	30	parameter	parameter	NOUN
cord-326631-7gd3hjc3	299	31	that	that	PRON
cord-326631-7gd3hjc3	299	32	appears	appear	VERB
cord-326631-7gd3hjc3	299	33	in	in	ADP
cord-326631-7gd3hjc3	299	34	the	the	DET
cord-326631-7gd3hjc3	299	35	final	final	ADJ
cord-326631-7gd3hjc3	299	36	size	size	NOUN
cord-326631-7gd3hjc3	299	37	formula	formula	NOUN
cord-326631-7gd3hjc3	299	38	(	(	PUNCT
cord-326631-7gd3hjc3	299	39	5	5	NUM
cord-326631-7gd3hjc3	299	40	)	)	PUNCT
cord-326631-7gd3hjc3	299	41	.	.	PUNCT
cord-326631-7gd3hjc3	300	1	it	it	PRON
cord-326631-7gd3hjc3	300	2	should	should	AUX
cord-326631-7gd3hjc3	300	3	be	be	AUX
cord-326631-7gd3hjc3	300	4	noted	note	VERB
cord-326631-7gd3hjc3	300	5	that	that	SCONJ
cord-326631-7gd3hjc3	300	6	the	the	DET
cord-326631-7gd3hjc3	300	7	final	final	ADJ
cord-326631-7gd3hjc3	300	8	size	size	NOUN
cord-326631-7gd3hjc3	300	9	formula	formula	NOUN
cord-326631-7gd3hjc3	300	10	refers	refer	VERB
cord-326631-7gd3hjc3	300	11	only	only	ADV
cord-326631-7gd3hjc3	300	12	to	to	ADP
cord-326631-7gd3hjc3	300	13	the	the	DET
cord-326631-7gd3hjc3	300	14	ensemble	ensemble	ADJ
cord-326631-7gd3hjc3	300	15	average	average	ADJ
cord-326631-7gd3hjc3	300	16	size	size	NOUN
cord-326631-7gd3hjc3	300	17	of	of	ADP
cord-326631-7gd3hjc3	300	18	an	an	DET
cord-326631-7gd3hjc3	300	19	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	300	20	for	for	ADP
cord-326631-7gd3hjc3	300	21	a	a	DET
cord-326631-7gd3hjc3	300	22	disease	disease	NOUN
cord-326631-7gd3hjc3	300	23	with	with	ADP
cord-326631-7gd3hjc3	300	24	a	a	DET
cord-326631-7gd3hjc3	300	25	given	give	VERB
cord-326631-7gd3hjc3	300	26	r	r	NOUN
cord-326631-7gd3hjc3	300	27	0	0	NUM
cord-326631-7gd3hjc3	300	28	.	.	PUNCT
cord-326631-7gd3hjc3	301	1	different	different	ADJ
cord-326631-7gd3hjc3	301	2	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	301	3	realizations	realization	NOUN
cord-326631-7gd3hjc3	301	4	of	of	ADP
cord-326631-7gd3hjc3	301	5	the	the	DET
cord-326631-7gd3hjc3	301	6	same	same	ADJ
cord-326631-7gd3hjc3	301	7	process	process	NOUN
cord-326631-7gd3hjc3	301	8	will	will	AUX
cord-326631-7gd3hjc3	301	9	lead	lead	VERB
cord-326631-7gd3hjc3	301	10	to	to	ADP
cord-326631-7gd3hjc3	301	11	different	different	ADJ
cord-326631-7gd3hjc3	301	12	final	final	ADJ
cord-326631-7gd3hjc3	301	13	sizes	size	NOUN
cord-326631-7gd3hjc3	301	14	and	and	CCONJ
cord-326631-7gd3hjc3	301	15	our	our	PRON
cord-326631-7gd3hjc3	301	16	analysis	analysis	NOUN
cord-326631-7gd3hjc3	301	17	says	say	VERB
cord-326631-7gd3hjc3	301	18	nothing	nothing	PRON
cord-326631-7gd3hjc3	301	19	about	about	ADP
cord-326631-7gd3hjc3	301	20	the	the	DET
cord-326631-7gd3hjc3	301	21	variance	variance	NOUN
cord-326631-7gd3hjc3	301	22	or	or	CCONJ
cord-326631-7gd3hjc3	301	23	higher	high	ADJ
cord-326631-7gd3hjc3	301	24	moments	moment	NOUN
cord-326631-7gd3hjc3	301	25	of	of	ADP
cord-326631-7gd3hjc3	301	26	the	the	DET
cord-326631-7gd3hjc3	301	27	final	final	ADJ
cord-326631-7gd3hjc3	301	28	size	size	NOUN
cord-326631-7gd3hjc3	301	29	distribution	distribution	NOUN
cord-326631-7gd3hjc3	301	30	.	.	PUNCT
cord-326631-7gd3hjc3	302	1	kurtz	kurtz	PROPN
cord-326631-7gd3hjc3	302	2	(	(	PUNCT
cord-326631-7gd3hjc3	302	3	1980	1980	NUM
cord-326631-7gd3hjc3	302	4	)	)	PUNCT
cord-326631-7gd3hjc3	302	5	proved	prove	VERB
cord-326631-7gd3hjc3	302	6	that	that	SCONJ
cord-326631-7gd3hjc3	302	7	in	in	ADP
cord-326631-7gd3hjc3	302	8	the	the	DET
cord-326631-7gd3hjc3	302	9	limit	limit	NOUN
cord-326631-7gd3hjc3	302	10	that	that	SCONJ
cord-326631-7gd3hjc3	302	11	the	the	DET
cord-326631-7gd3hjc3	302	12	population	population	NOUN
cord-326631-7gd3hjc3	302	13	size	size	NOUN
cord-326631-7gd3hjc3	302	14	goes	go	VERB
cord-326631-7gd3hjc3	302	15	to	to	ADP
cord-326631-7gd3hjc3	302	16	infinity	infinity	NOUN
cord-326631-7gd3hjc3	302	17	,	,	PUNCT
cord-326631-7gd3hjc3	302	18	the	the	DET
cord-326631-7gd3hjc3	302	19	ensemble	ensemble	ADJ
cord-326631-7gd3hjc3	302	20	mean	mean	NOUN
cord-326631-7gd3hjc3	302	21	of	of	ADP
cord-326631-7gd3hjc3	302	22	the	the	DET
cord-326631-7gd3hjc3	302	23	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	302	24	sir	sir	NOUN
cord-326631-7gd3hjc3	302	25	model	model	NOUN
cord-326631-7gd3hjc3	302	26	with	with	ADP
cord-326631-7gd3hjc3	302	27	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	302	28	distributed	distribute	VERB
cord-326631-7gd3hjc3	302	29	infectious	infectious	ADJ
cord-326631-7gd3hjc3	302	30	period	period	NOUN
cord-326631-7gd3hjc3	302	31	converges	converge	NOUN
cord-326631-7gd3hjc3	302	32	to	to	ADP
cord-326631-7gd3hjc3	302	33	the	the	DET
cord-326631-7gd3hjc3	302	34	solutions	solution	NOUN
cord-326631-7gd3hjc3	302	35	of	of	ADP
cord-326631-7gd3hjc3	302	36	the	the	DET
cord-326631-7gd3hjc3	302	37	integro	integro	NOUN
cord-326631-7gd3hjc3	302	38	-	-	PUNCT
cord-326631-7gd3hjc3	302	39	differential	differential	ADJ
cord-326631-7gd3hjc3	302	40	equation	equation	NOUN
cord-326631-7gd3hjc3	302	41	model	model	NOUN
cord-326631-7gd3hjc3	302	42	specified	specify	VERB
cord-326631-7gd3hjc3	302	43	in	in	ADP
cord-326631-7gd3hjc3	302	44	our	our	PRON
cord-326631-7gd3hjc3	302	45	eqs	eqs	PROPN
cord-326631-7gd3hjc3	302	46	.	.	PUNCT
cord-326631-7gd3hjc3	303	1	(	(	PUNCT
cord-326631-7gd3hjc3	303	2	11	11	NUM
cord-326631-7gd3hjc3	303	3	)	)	PUNCT
cord-326631-7gd3hjc3	303	4	.	.	PUNCT
cord-326631-7gd3hjc3	304	1	hence	hence	ADV
cord-326631-7gd3hjc3	304	2	,	,	PUNCT
cord-326631-7gd3hjc3	304	3	the	the	DET
cord-326631-7gd3hjc3	304	4	standard	standard	ADJ
cord-326631-7gd3hjc3	304	5	final	final	ADJ
cord-326631-7gd3hjc3	304	6	size	size	NOUN
cord-326631-7gd3hjc3	304	7	formula	formula	NOUN
cord-326631-7gd3hjc3	304	8	gives	give	VERB
cord-326631-7gd3hjc3	304	9	the	the	DET
cord-326631-7gd3hjc3	304	10	mean	mean	ADJ
cord-326631-7gd3hjc3	304	11	final	final	ADJ
cord-326631-7gd3hjc3	304	12	size	size	NOUN
cord-326631-7gd3hjc3	304	13	of	of	ADP
cord-326631-7gd3hjc3	304	14	the	the	DET
cord-326631-7gd3hjc3	304	15	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	304	16	sir	sir	NOUN
cord-326631-7gd3hjc3	304	17	model	model	NOUN
cord-326631-7gd3hjc3	304	18	.	.	PUNCT
cord-326631-7gd3hjc3	305	1	however	however	ADV
cord-326631-7gd3hjc3	305	2	,	,	PUNCT
cord-326631-7gd3hjc3	305	3	it	it	PRON
cord-326631-7gd3hjc3	305	4	is	be	AUX
cord-326631-7gd3hjc3	305	5	difficult	difficult	ADJ
cord-326631-7gd3hjc3	305	6	to	to	PART
cord-326631-7gd3hjc3	305	7	deduce	deduce	VERB
cord-326631-7gd3hjc3	305	8	the	the	DET
cord-326631-7gd3hjc3	305	9	distribution	distribution	NOUN
cord-326631-7gd3hjc3	305	10	of	of	ADP
cord-326631-7gd3hjc3	305	11	the	the	DET
cord-326631-7gd3hjc3	305	12	final	final	ADJ
cord-326631-7gd3hjc3	305	13	size	size	NOUN
cord-326631-7gd3hjc3	305	14	,	,	PUNCT
cord-326631-7gd3hjc3	305	15	and	and	CCONJ
cord-326631-7gd3hjc3	305	16	this	this	PRON
cord-326631-7gd3hjc3	305	17	remains	remain	VERB
cord-326631-7gd3hjc3	305	18	an	an	DET
cord-326631-7gd3hjc3	305	19	open	open	ADJ
cord-326631-7gd3hjc3	305	20	problem	problem	NOUN
cord-326631-7gd3hjc3	305	21	for	for	ADP
cord-326631-7gd3hjc3	305	22	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	305	23	sir	sir	NOUN
cord-326631-7gd3hjc3	305	24	models	model	NOUN
cord-326631-7gd3hjc3	305	25	with	with	ADP
cord-326631-7gd3hjc3	305	26	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	305	27	distributed	distribute	VERB
cord-326631-7gd3hjc3	305	28	infectious	infectious	ADJ
cord-326631-7gd3hjc3	305	29	periods	period	NOUN
cord-326631-7gd3hjc3	305	30	.	.	PUNCT
cord-326631-7gd3hjc3	306	1	for	for	ADP
cord-326631-7gd3hjc3	306	2	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	306	3	seir	seir	NOUN
cord-326631-7gd3hjc3	306	4	models	model	NOUN
cord-326631-7gd3hjc3	306	5	with	with	ADP
cord-326631-7gd3hjc3	306	6	gamma	gamma	NOUN
cord-326631-7gd3hjc3	306	7	distributed	distribute	VERB
cord-326631-7gd3hjc3	306	8	latent	latent	ADJ
cord-326631-7gd3hjc3	306	9	and	and	CCONJ
cord-326631-7gd3hjc3	306	10	infectious	infectious	ADJ
cord-326631-7gd3hjc3	306	11	periods	period	NOUN
cord-326631-7gd3hjc3	306	12	,	,	PUNCT
cord-326631-7gd3hjc3	306	13	anderson	anderson	PROPN
cord-326631-7gd3hjc3	306	14	and	and	CCONJ
cord-326631-7gd3hjc3	306	15	watsons	watson	NOUN
cord-326631-7gd3hjc3	306	16	(	(	PUNCT
cord-326631-7gd3hjc3	306	17	1980	1980	NUM
cord-326631-7gd3hjc3	306	18	)	)	PUNCT
cord-326631-7gd3hjc3	306	19	derived	derive	VERB
cord-326631-7gd3hjc3	306	20	a	a	DET
cord-326631-7gd3hjc3	306	21	normal	normal	ADJ
cord-326631-7gd3hjc3	306	22	approximation	approximation	NOUN
cord-326631-7gd3hjc3	306	23	to	to	ADP
cord-326631-7gd3hjc3	306	24	the	the	DET
cord-326631-7gd3hjc3	306	25	final	final	ADJ
cord-326631-7gd3hjc3	306	26	size	size	NOUN
cord-326631-7gd3hjc3	306	27	distribution	distribution	NOUN
cord-326631-7gd3hjc3	306	28	that	that	PRON
cord-326631-7gd3hjc3	306	29	is	be	AUX
cord-326631-7gd3hjc3	306	30	valid	valid	ADJ
cord-326631-7gd3hjc3	306	31	in	in	ADP
cord-326631-7gd3hjc3	306	32	the	the	DET
cord-326631-7gd3hjc3	306	33	limit	limit	NOUN
cord-326631-7gd3hjc3	306	34	of	of	ADP
cord-326631-7gd3hjc3	306	35	large	large	ADJ
cord-326631-7gd3hjc3	306	36	population	population	NOUN
cord-326631-7gd3hjc3	306	37	size	size	NOUN
cord-326631-7gd3hjc3	306	38	.	.	PUNCT
cord-326631-7gd3hjc3	307	1	if	if	SCONJ
cord-326631-7gd3hjc3	307	2	there	there	PRON
cord-326631-7gd3hjc3	307	3	is	be	VERB
cord-326631-7gd3hjc3	307	4	little	little	ADJ
cord-326631-7gd3hjc3	307	5	variation	variation	NOUN
cord-326631-7gd3hjc3	307	6	in	in	ADP
cord-326631-7gd3hjc3	307	7	the	the	DET
cord-326631-7gd3hjc3	307	8	length	length	NOUN
cord-326631-7gd3hjc3	307	9	of	of	ADP
cord-326631-7gd3hjc3	307	10	the	the	DET
cord-326631-7gd3hjc3	307	11	latent	latent	ADJ
cord-326631-7gd3hjc3	307	12	period	period	NOUN
cord-326631-7gd3hjc3	307	13	,	,	PUNCT
cord-326631-7gd3hjc3	307	14	and	and	CCONJ
cord-326631-7gd3hjc3	307	15	the	the	DET
cord-326631-7gd3hjc3	307	16	infectious	infectious	ADJ
cord-326631-7gd3hjc3	307	17	period	period	NOUN
cord-326631-7gd3hjc3	307	18	is	be	AUX
cord-326631-7gd3hjc3	307	19	short	short	ADJ
cord-326631-7gd3hjc3	307	20	,	,	PUNCT
cord-326631-7gd3hjc3	307	21	the	the	DET
cord-326631-7gd3hjc3	307	22	stochastic	stochastic	ADJ
cord-326631-7gd3hjc3	307	23	seir	seir	NOUN
cord-326631-7gd3hjc3	307	24	model	model	NOUN
cord-326631-7gd3hjc3	307	25	can	can	AUX
cord-326631-7gd3hjc3	307	26	be	be	AUX
cord-326631-7gd3hjc3	307	27	approximated	approximate	VERB
cord-326631-7gd3hjc3	307	28	by	by	ADP
cord-326631-7gd3hjc3	307	29	a	a	DET
cord-326631-7gd3hjc3	307	30	chain	chain	NOUN
cord-326631-7gd3hjc3	307	31	binomial	binomial	NOUN
cord-326631-7gd3hjc3	307	32	model	model	NOUN
cord-326631-7gd3hjc3	307	33	(	(	PUNCT
cord-326631-7gd3hjc3	307	34	bailey	bailey	NOUN
cord-326631-7gd3hjc3	307	35	,	,	PUNCT
cord-326631-7gd3hjc3	307	36	1975	1975	NUM
cord-326631-7gd3hjc3	307	37	)	)	PUNCT
cord-326631-7gd3hjc3	307	38	,	,	PUNCT
cord-326631-7gd3hjc3	307	39	which	which	PRON
cord-326631-7gd3hjc3	307	40	is	be	AUX
cord-326631-7gd3hjc3	307	41	a	a	DET
cord-326631-7gd3hjc3	307	42	discrete	discrete	ADJ
cord-326631-7gd3hjc3	307	43	time	time	NOUN
cord-326631-7gd3hjc3	307	44	markov	markov	NOUN
cord-326631-7gd3hjc3	307	45	chain	chain	NOUN
cord-326631-7gd3hjc3	307	46	.	.	PUNCT
cord-326631-7gd3hjc3	308	1	the	the	DET
cord-326631-7gd3hjc3	308	2	time	time	NOUN
cord-326631-7gd3hjc3	308	3	step	step	NOUN
cord-326631-7gd3hjc3	308	4	for	for	ADP
cord-326631-7gd3hjc3	308	5	this	this	DET
cord-326631-7gd3hjc3	308	6	chain	chain	NOUN
cord-326631-7gd3hjc3	308	7	is	be	AUX
cord-326631-7gd3hjc3	308	8	equal	equal	ADJ
cord-326631-7gd3hjc3	308	9	to	to	ADP
cord-326631-7gd3hjc3	308	10	the	the	DET
cord-326631-7gd3hjc3	308	11	fixed	fix	VERB
cord-326631-7gd3hjc3	308	12	-	-	PUNCT
cord-326631-7gd3hjc3	308	13	length	length	NOUN
cord-326631-7gd3hjc3	308	14	latent	latent	ADJ
cord-326631-7gd3hjc3	308	15	period	period	NOUN
cord-326631-7gd3hjc3	308	16	,	,	PUNCT
cord-326631-7gd3hjc3	308	17	since	since	SCONJ
cord-326631-7gd3hjc3	308	18	the	the	DET
cord-326631-7gd3hjc3	308	19	infectious	infectious	ADJ
cord-326631-7gd3hjc3	308	20	period	period	NOUN
cord-326631-7gd3hjc3	308	21	is	be	AUX
cord-326631-7gd3hjc3	308	22	presumed	presume	VERB
cord-326631-7gd3hjc3	308	23	infinitesimal	infinitesimal	NOUN
cord-326631-7gd3hjc3	308	24	(	(	PUNCT
cord-326631-7gd3hjc3	308	25	all	all	DET
cord-326631-7gd3hjc3	308	26	contacts	contact	NOUN
cord-326631-7gd3hjc3	308	27	occur	occur	VERB
cord-326631-7gd3hjc3	308	28	instantaneously	instantaneously	ADV
cord-326631-7gd3hjc3	308	29	at	at	ADP
cord-326631-7gd3hjc3	308	30	the	the	DET
cord-326631-7gd3hjc3	308	31	end	end	NOUN
cord-326631-7gd3hjc3	308	32	of	of	ADP
cord-326631-7gd3hjc3	308	33	the	the	DET
cord-326631-7gd3hjc3	308	34	latent	latent	ADJ
cord-326631-7gd3hjc3	308	35	period	period	NOUN
cord-326631-7gd3hjc3	308	36	)	)	PUNCT
cord-326631-7gd3hjc3	308	37	.	.	PUNCT
cord-326631-7gd3hjc3	309	1	for	for	ADP
cord-326631-7gd3hjc3	309	2	such	such	ADJ
cord-326631-7gd3hjc3	309	3	models	model	NOUN
cord-326631-7gd3hjc3	309	4	,	,	PUNCT
cord-326631-7gd3hjc3	309	5	the	the	DET
cord-326631-7gd3hjc3	309	6	only	only	ADJ
cord-326631-7gd3hjc3	309	7	parameter	parameter	NOUN
cord-326631-7gd3hjc3	309	8	is	be	AUX
cord-326631-7gd3hjc3	309	9	the	the	DET
cord-326631-7gd3hjc3	309	10	probability	probability	NOUN
cord-326631-7gd3hjc3	309	11	q	q	NOUN
cord-326631-7gd3hjc3	309	12	that	that	SCONJ
cord-326631-7gd3hjc3	309	13	a	a	DET
cord-326631-7gd3hjc3	309	14	contact	contact	NOUN
cord-326631-7gd3hjc3	309	15	between	between	ADP
cord-326631-7gd3hjc3	309	16	an	an	DET
cord-326631-7gd3hjc3	309	17	infectious	infectious	ADJ
cord-326631-7gd3hjc3	309	18	individual	individual	NOUN
cord-326631-7gd3hjc3	309	19	and	and	CCONJ
cord-326631-7gd3hjc3	309	20	a	a	DET
cord-326631-7gd3hjc3	309	21	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	309	22	individual	individual	NOUN
cord-326631-7gd3hjc3	309	23	leads	lead	VERB
cord-326631-7gd3hjc3	309	24	to	to	ADP
cord-326631-7gd3hjc3	309	25	infection	infection	NOUN
cord-326631-7gd3hjc3	309	26	.	.	PUNCT
cord-326631-7gd3hjc3	310	1	with	with	ADP
cord-326631-7gd3hjc3	310	2	the	the	DET
cord-326631-7gd3hjc3	310	3	assumption	assumption	NOUN
cord-326631-7gd3hjc3	311	1	that	that	SCONJ
cord-326631-7gd3hjc3	311	2	q	q	X
cord-326631-7gd3hjc3	311	3	=	=	NOUN
cord-326631-7gd3hjc3	311	4	1	1	NUM
cord-326631-7gd3hjc3	311	5	−	−	NOUN
cord-326631-7gd3hjc3	311	6	e	e	NOUN
cord-326631-7gd3hjc3	312	1	−r0	−r0	INTJ
cord-326631-7gd3hjc3	312	2	,	,	PUNCT
cord-326631-7gd3hjc3	312	3	von	von	PROPN
cord-326631-7gd3hjc3	312	4	bahr	bahr	PROPN
cord-326631-7gd3hjc3	312	5	and	and	CCONJ
cord-326631-7gd3hjc3	312	6	martin	martin	PROPN
cord-326631-7gd3hjc3	312	7	-	-	PUNCT
cord-326631-7gd3hjc3	312	8	lof	lof	PROPN
cord-326631-7gd3hjc3	312	9	(	(	PUNCT
cord-326631-7gd3hjc3	312	10	1980	1980	NUM
cord-326631-7gd3hjc3	312	11	)	)	PUNCT
cord-326631-7gd3hjc3	312	12	and	and	CCONJ
cord-326631-7gd3hjc3	312	13	scalia	scalia	PROPN
cord-326631-7gd3hjc3	312	14	-	-	PUNCT
cord-326631-7gd3hjc3	312	15	tomba	tomba	NOUN
cord-326631-7gd3hjc3	312	16	(	(	PUNCT
cord-326631-7gd3hjc3	312	17	1985	1985	NUM
cord-326631-7gd3hjc3	312	18	)	)	PUNCT
cord-326631-7gd3hjc3	312	19	showed	show	VERB
cord-326631-7gd3hjc3	312	20	that	that	PRON
cord-326631-7gd3hjc3	312	21	final	final	ADJ
cord-326631-7gd3hjc3	312	22	size	size	NOUN
cord-326631-7gd3hjc3	312	23	distribution	distribution	NOUN
cord-326631-7gd3hjc3	312	24	for	for	ADP
cord-326631-7gd3hjc3	312	25	the	the	DET
cord-326631-7gd3hjc3	312	26	traditional	traditional	ADJ
cord-326631-7gd3hjc3	312	27	chain	chain	NOUN
cord-326631-7gd3hjc3	312	28	binomial	binomial	NOUN
cord-326631-7gd3hjc3	312	29	model	model	NOUN
cord-326631-7gd3hjc3	312	30	is	be	AUX
cord-326631-7gd3hjc3	312	31	asymptotically	asymptotically	ADV
cord-326631-7gd3hjc3	312	32	normal	normal	ADJ
cord-326631-7gd3hjc3	312	33	in	in	ADP
cord-326631-7gd3hjc3	312	34	the	the	DET
cord-326631-7gd3hjc3	312	35	limit	limit	NOUN
cord-326631-7gd3hjc3	312	36	of	of	ADP
cord-326631-7gd3hjc3	312	37	large	large	ADJ
cord-326631-7gd3hjc3	312	38	population	population	NOUN
cord-326631-7gd3hjc3	312	39	size	size	NOUN
cord-326631-7gd3hjc3	312	40	.	.	PUNCT
cord-326631-7gd3hjc3	313	1	scalia	scalia	PROPN
cord-326631-7gd3hjc3	313	2	-	-	PUNCT
cord-326631-7gd3hjc3	313	3	tomba	tomba	NOUN
cord-326631-7gd3hjc3	313	4	(	(	PUNCT
cord-326631-7gd3hjc3	313	5	1986	1986	NUM
cord-326631-7gd3hjc3	313	6	)	)	PUNCT
cord-326631-7gd3hjc3	313	7	and	and	CCONJ
cord-326631-7gd3hjc3	313	8	andersson	andersson	PROPN
cord-326631-7gd3hjc3	313	9	(	(	PUNCT
cord-326631-7gd3hjc3	313	10	1999	1999	NUM
cord-326631-7gd3hjc3	313	11	)	)	PUNCT
cord-326631-7gd3hjc3	313	12	studied	study	VERB
cord-326631-7gd3hjc3	313	13	more	more	ADJ
cord-326631-7gd3hjc3	313	14	general	general	ADJ
cord-326631-7gd3hjc3	313	15	chain	chain	NOUN
cord-326631-7gd3hjc3	313	16	binomial	binomial	NOUN
cord-326631-7gd3hjc3	313	17	models	model	NOUN
cord-326631-7gd3hjc3	313	18	(	(	PUNCT
cord-326631-7gd3hjc3	313	19	with	with	ADP
cord-326631-7gd3hjc3	313	20	heterogeneous	heterogeneous	ADJ
cord-326631-7gd3hjc3	313	21	contact	contact	NOUN
cord-326631-7gd3hjc3	313	22	structures	structure	NOUN
cord-326631-7gd3hjc3	313	23	equivalent	equivalent	ADJ
cord-326631-7gd3hjc3	313	24	to	to	ADP
cord-326631-7gd3hjc3	313	25	those	those	PRON
cord-326631-7gd3hjc3	313	26	we	we	PRON
cord-326631-7gd3hjc3	313	27	discussed	discuss	VERB
cord-326631-7gd3hjc3	313	28	in	in	ADP
cord-326631-7gd3hjc3	313	29	sections	section	NOUN
cord-326631-7gd3hjc3	313	30	9	9	NUM
cord-326631-7gd3hjc3	313	31	and	and	CCONJ
cord-326631-7gd3hjc3	313	32	10	10	NUM
cord-326631-7gd3hjc3	313	33	)	)	PUNCT
cord-326631-7gd3hjc3	313	34	and	and	CCONJ
cord-326631-7gd3hjc3	313	35	found	find	VERB
cord-326631-7gd3hjc3	313	36	asymptotic	asymptotic	ADJ
cord-326631-7gd3hjc3	313	37	final	final	ADJ
cord-326631-7gd3hjc3	313	38	size	size	NOUN
cord-326631-7gd3hjc3	313	39	distributions	distribution	NOUN
cord-326631-7gd3hjc3	313	40	.	.	PUNCT
cord-326631-7gd3hjc3	314	1	their	their	PRON
cord-326631-7gd3hjc3	314	2	results	result	NOUN
cord-326631-7gd3hjc3	314	3	imply	imply	VERB
cord-326631-7gd3hjc3	314	4	that	that	SCONJ
cord-326631-7gd3hjc3	314	5	if	if	SCONJ
cord-326631-7gd3hjc3	314	6	q	q	X
cord-326631-7gd3hjc3	314	7	=	=	NOUN
cord-326631-7gd3hjc3	314	8	1	1	NUM
cord-326631-7gd3hjc3	314	9	−	−	NOUN
cord-326631-7gd3hjc3	314	10	e	e	NOUN
cord-326631-7gd3hjc3	315	1	−r0	−r0	INTJ
cord-326631-7gd3hjc3	315	2	then	then	ADV
cord-326631-7gd3hjc3	315	3	the	the	DET
cord-326631-7gd3hjc3	315	4	ensemble	ensemble	ADJ
cord-326631-7gd3hjc3	315	5	mean	mean	ADJ
cord-326631-7gd3hjc3	315	6	final	final	ADJ
cord-326631-7gd3hjc3	315	7	size	size	NOUN
cord-326631-7gd3hjc3	315	8	in	in	ADP
cord-326631-7gd3hjc3	315	9	these	these	DET
cord-326631-7gd3hjc3	315	10	chain	chain	NOUN
cord-326631-7gd3hjc3	315	11	binomial	binomial	NOUN
cord-326631-7gd3hjc3	315	12	models	model	NOUN
cord-326631-7gd3hjc3	315	13	is	be	AUX
cord-326631-7gd3hjc3	315	14	the	the	DET
cord-326631-7gd3hjc3	315	15	solution	solution	NOUN
cord-326631-7gd3hjc3	315	16	of	of	ADP
cord-326631-7gd3hjc3	315	17	our	our	PRON
cord-326631-7gd3hjc3	315	18	eqs	eqs	PROPN
cord-326631-7gd3hjc3	315	19	.	.	PUNCT
cord-326631-7gd3hjc3	316	1	(	(	PUNCT
cord-326631-7gd3hjc3	316	2	27	27	NUM
cord-326631-7gd3hjc3	316	3	)	)	PUNCT
cord-326631-7gd3hjc3	316	4	.	.	PUNCT
cord-326631-7gd3hjc3	317	1	we	we	PRON
cord-326631-7gd3hjc3	317	2	emphasized	emphasize	VERB
cord-326631-7gd3hjc3	317	3	two	two	NUM
cord-326631-7gd3hjc3	317	4	circumstances	circumstance	NOUN
cord-326631-7gd3hjc3	317	5	under	under	ADP
cord-326631-7gd3hjc3	317	6	which	which	PRON
cord-326631-7gd3hjc3	317	7	the	the	DET
cord-326631-7gd3hjc3	317	8	usual	usual	ADJ
cord-326631-7gd3hjc3	317	9	final	final	ADJ
cord-326631-7gd3hjc3	317	10	size	size	NOUN
cord-326631-7gd3hjc3	317	11	formula	formula	NOUN
cord-326631-7gd3hjc3	317	12	will	will	AUX
cord-326631-7gd3hjc3	317	13	not	not	PART
cord-326631-7gd3hjc3	317	14	apply	apply	VERB
cord-326631-7gd3hjc3	317	15	.	.	PUNCT
cord-326631-7gd3hjc3	318	1	one	one	NUM
cord-326631-7gd3hjc3	318	2	was	be	AUX
cord-326631-7gd3hjc3	318	3	the	the	DET
cord-326631-7gd3hjc3	318	4	case	case	NOUN
cord-326631-7gd3hjc3	318	5	of	of	ADP
cord-326631-7gd3hjc3	318	6	age	age	NOUN
cord-326631-7gd3hjc3	318	7	-	-	PUNCT
cord-326631-7gd3hjc3	318	8	structured	structure	VERB
cord-326631-7gd3hjc3	318	9	heterogeneity	heterogeneity	NOUN
cord-326631-7gd3hjc3	318	10	of	of	ADP
cord-326631-7gd3hjc3	318	11	transmission	transmission	NOUN
cord-326631-7gd3hjc3	318	12	;	;	PUNCT
cord-326631-7gd3hjc3	318	13	while	while	SCONJ
cord-326631-7gd3hjc3	318	14	this	this	PRON
cord-326631-7gd3hjc3	318	15	would	would	AUX
cord-326631-7gd3hjc3	318	16	influence	influence	VERB
cord-326631-7gd3hjc3	318	17	the	the	DET
cord-326631-7gd3hjc3	318	18	final	final	ADJ
cord-326631-7gd3hjc3	318	19	size	size	NOUN
cord-326631-7gd3hjc3	318	20	,	,	PUNCT
cord-326631-7gd3hjc3	318	21	it	it	PRON
cord-326631-7gd3hjc3	318	22	is	be	AUX
cord-326631-7gd3hjc3	318	23	unlikely	unlikely	ADJ
cord-326631-7gd3hjc3	318	24	that	that	SCONJ
cord-326631-7gd3hjc3	318	25	we	we	PRON
cord-326631-7gd3hjc3	318	26	would	would	AUX
cord-326631-7gd3hjc3	318	27	be	be	AUX
cord-326631-7gd3hjc3	318	28	able	able	ADJ
cord-326631-7gd3hjc3	318	29	to	to	PART
cord-326631-7gd3hjc3	318	30	parameterize	parameterize	VERB
cord-326631-7gd3hjc3	318	31	the	the	DET
cord-326631-7gd3hjc3	318	32	age	age	NOUN
cord-326631-7gd3hjc3	318	33	-	-	PUNCT
cord-326631-7gd3hjc3	318	34	structured	structure	VERB
cord-326631-7gd3hjc3	318	35	contact	contact	NOUN
cord-326631-7gd3hjc3	318	36	patterns	pattern	NOUN
cord-326631-7gd3hjc3	318	37	sufficiently	sufficiently	ADV
cord-326631-7gd3hjc3	318	38	well	well	ADV
cord-326631-7gd3hjc3	318	39	to	to	PART
cord-326631-7gd3hjc3	318	40	improve	improve	VERB
cord-326631-7gd3hjc3	318	41	on	on	ADP
cord-326631-7gd3hjc3	318	42	the	the	DET
cord-326631-7gd3hjc3	318	43	final	final	ADJ
cord-326631-7gd3hjc3	318	44	size	size	NOUN
cord-326631-7gd3hjc3	318	45	estimate	estimate	NOUN
cord-326631-7gd3hjc3	318	46	generated	generate	VERB
cord-326631-7gd3hjc3	318	47	with	with	ADP
cord-326631-7gd3hjc3	318	48	the	the	DET
cord-326631-7gd3hjc3	318	49	assumption	assumption	NOUN
cord-326631-7gd3hjc3	318	50	of	of	ADP
cord-326631-7gd3hjc3	318	51	homogeneous	homogeneous	ADJ
cord-326631-7gd3hjc3	318	52	mixing	mixing	NOUN
cord-326631-7gd3hjc3	318	53	.	.	PUNCT
cord-326631-7gd3hjc3	319	1	the	the	DET
cord-326631-7gd3hjc3	319	2	other	other	ADJ
cord-326631-7gd3hjc3	319	3	case	case	NOUN
cord-326631-7gd3hjc3	319	4	we	we	PRON
cord-326631-7gd3hjc3	319	5	discussed	discuss	VERB
cord-326631-7gd3hjc3	319	6	was	be	AUX
cord-326631-7gd3hjc3	319	7	the	the	DET
cord-326631-7gd3hjc3	319	8	existence	existence	NOUN
cord-326631-7gd3hjc3	319	9	of	of	ADP
cord-326631-7gd3hjc3	319	10	social	social	ADJ
cord-326631-7gd3hjc3	319	11	core	core	NOUN
cord-326631-7gd3hjc3	319	12	groups	group	NOUN
cord-326631-7gd3hjc3	319	13	,	,	PUNCT
cord-326631-7gd3hjc3	319	14	which	which	PRON
cord-326631-7gd3hjc3	319	15	are	be	AUX
cord-326631-7gd3hjc3	319	16	extremely	extremely	ADV
cord-326631-7gd3hjc3	319	17	important	important	ADJ
cord-326631-7gd3hjc3	319	18	in	in	ADP
cord-326631-7gd3hjc3	319	19	the	the	DET
cord-326631-7gd3hjc3	319	20	epidemiological	epidemiological	ADJ
cord-326631-7gd3hjc3	319	21	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	319	22	of	of	ADP
cord-326631-7gd3hjc3	319	23	sexually	sexually	ADV
cord-326631-7gd3hjc3	319	24	transmitted	transmit	VERB
cord-326631-7gd3hjc3	319	25	diseases	disease	NOUN
cord-326631-7gd3hjc3	319	26	;	;	PUNCT
cord-326631-7gd3hjc3	319	27	in	in	ADP
cord-326631-7gd3hjc3	319	28	this	this	DET
cord-326631-7gd3hjc3	319	29	case	case	NOUN
cord-326631-7gd3hjc3	319	30	,	,	PUNCT
cord-326631-7gd3hjc3	319	31	some	some	DET
cord-326631-7gd3hjc3	319	32	estimate	estimate	NOUN
cord-326631-7gd3hjc3	319	33	of	of	ADP
cord-326631-7gd3hjc3	319	34	the	the	DET
cord-326631-7gd3hjc3	319	35	difference	difference	NOUN
cord-326631-7gd3hjc3	319	36	in	in	ADP
cord-326631-7gd3hjc3	319	37	transmission	transmission	NOUN
cord-326631-7gd3hjc3	319	38	rates	rate	NOUN
cord-326631-7gd3hjc3	319	39	in	in	ADP
cord-326631-7gd3hjc3	319	40	different	different	ADJ
cord-326631-7gd3hjc3	319	41	social	social	ADJ
cord-326631-7gd3hjc3	319	42	groups	group	NOUN
cord-326631-7gd3hjc3	319	43	would	would	AUX
cord-326631-7gd3hjc3	319	44	likely	likely	ADV
cord-326631-7gd3hjc3	319	45	be	be	AUX
cord-326631-7gd3hjc3	319	46	needed	need	VERB
cord-326631-7gd3hjc3	319	47	to	to	PART
cord-326631-7gd3hjc3	319	48	obtain	obtain	VERB
cord-326631-7gd3hjc3	319	49	a	a	DET
cord-326631-7gd3hjc3	319	50	useful	useful	ADJ
cord-326631-7gd3hjc3	319	51	estimate	estimate	NOUN
cord-326631-7gd3hjc3	319	52	of	of	ADP
cord-326631-7gd3hjc3	319	53	the	the	DET
cord-326631-7gd3hjc3	319	54	final	final	ADJ
cord-326631-7gd3hjc3	319	55	size	size	NOUN
cord-326631-7gd3hjc3	319	56	.	.	PUNCT
cord-326631-7gd3hjc3	320	1	in	in	ADP
cord-326631-7gd3hjc3	320	2	computing	compute	VERB
cord-326631-7gd3hjc3	320	3	the	the	DET
cord-326631-7gd3hjc3	320	4	final	final	ADJ
cord-326631-7gd3hjc3	320	5	size	size	NOUN
cord-326631-7gd3hjc3	320	6	,	,	PUNCT
cord-326631-7gd3hjc3	320	7	we	we	PRON
cord-326631-7gd3hjc3	320	8	have	have	AUX
cord-326631-7gd3hjc3	320	9	always	always	ADV
cord-326631-7gd3hjc3	320	10	assumed	assume	VERB
cord-326631-7gd3hjc3	320	11	that	that	SCONJ
cord-326631-7gd3hjc3	320	12	there	there	PRON
cord-326631-7gd3hjc3	320	13	are	be	VERB
cord-326631-7gd3hjc3	320	14	no	no	DET
cord-326631-7gd3hjc3	320	15	temporal	temporal	ADJ
cord-326631-7gd3hjc3	320	16	changes	change	NOUN
cord-326631-7gd3hjc3	320	17	in	in	ADP
cord-326631-7gd3hjc3	320	18	the	the	DET
cord-326631-7gd3hjc3	320	19	transmission	transmission	NOUN
cord-326631-7gd3hjc3	320	20	rate	rate	NOUN
cord-326631-7gd3hjc3	320	21	β	β	PROPN
cord-326631-7gd3hjc3	320	22	.	.	PUNCT
cord-326631-7gd3hjc3	321	1	temporal	temporal	ADJ
cord-326631-7gd3hjc3	321	2	variations	variation	NOUN
cord-326631-7gd3hjc3	321	3	in	in	ADP
cord-326631-7gd3hjc3	321	4	β	β	PROPN
cord-326631-7gd3hjc3	321	5	could	could	AUX
cord-326631-7gd3hjc3	321	6	result	result	VERB
cord-326631-7gd3hjc3	321	7	from	from	ADP
cord-326631-7gd3hjc3	321	8	intrinsic	intrinsic	ADJ
cord-326631-7gd3hjc3	321	9	seasonality	seasonality	NOUN
cord-326631-7gd3hjc3	321	10	of	of	ADP
cord-326631-7gd3hjc3	321	11	contact	contact	NOUN
cord-326631-7gd3hjc3	321	12	rates	rate	NOUN
cord-326631-7gd3hjc3	321	13	,	,	PUNCT
cord-326631-7gd3hjc3	321	14	imposition	imposition	NOUN
cord-326631-7gd3hjc3	321	15	of	of	ADP
cord-326631-7gd3hjc3	321	16	control	control	NOUN
cord-326631-7gd3hjc3	321	17	measures	measure	NOUN
cord-326631-7gd3hjc3	321	18	,	,	PUNCT
cord-326631-7gd3hjc3	321	19	or	or	CCONJ
cord-326631-7gd3hjc3	321	20	behavioral	behavioral	ADJ
cord-326631-7gd3hjc3	321	21	change	change	NOUN
cord-326631-7gd3hjc3	321	22	in	in	ADP
cord-326631-7gd3hjc3	321	23	response	response	NOUN
cord-326631-7gd3hjc3	321	24	to	to	ADP
cord-326631-7gd3hjc3	321	25	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	321	26	alerts	alert	NOUN
cord-326631-7gd3hjc3	321	27	.	.	PUNCT
cord-326631-7gd3hjc3	322	1	small	small	ADJ
cord-326631-7gd3hjc3	322	2	seasonal	seasonal	ADJ
cord-326631-7gd3hjc3	322	3	variations	variation	NOUN
cord-326631-7gd3hjc3	322	4	in	in	ADP
cord-326631-7gd3hjc3	322	5	β	β	NOUN
cord-326631-7gd3hjc3	322	6	cause	cause	VERB
cord-326631-7gd3hjc3	322	7	only	only	ADV
cord-326631-7gd3hjc3	322	8	small	small	ADJ
cord-326631-7gd3hjc3	322	9	perturbations	perturbation	NOUN
cord-326631-7gd3hjc3	322	10	to	to	ADP
cord-326631-7gd3hjc3	322	11	the	the	DET
cord-326631-7gd3hjc3	322	12	final	final	ADJ
cord-326631-7gd3hjc3	322	13	size	size	NOUN
cord-326631-7gd3hjc3	322	14	formula	formula	NOUN
cord-326631-7gd3hjc3	322	15	,	,	PUNCT
cord-326631-7gd3hjc3	322	16	and	and	CCONJ
cord-326631-7gd3hjc3	322	17	substantial	substantial	ADJ
cord-326631-7gd3hjc3	322	18	seasonality	seasonality	NOUN
cord-326631-7gd3hjc3	322	19	is	be	AUX
cord-326631-7gd3hjc3	322	20	generally	generally	ADV
cord-326631-7gd3hjc3	322	21	associated	associate	VERB
cord-326631-7gd3hjc3	322	22	with	with	ADP
cord-326631-7gd3hjc3	322	23	school	school	NOUN
cord-326631-7gd3hjc3	322	24	-	-	PUNCT
cord-326631-7gd3hjc3	322	25	age	age	NOUN
cord-326631-7gd3hjc3	322	26	children	child	NOUN
cord-326631-7gd3hjc3	322	27	(	(	PUNCT
cord-326631-7gd3hjc3	322	28	london	london	PROPN
cord-326631-7gd3hjc3	322	29	and	and	CCONJ
cord-326631-7gd3hjc3	322	30	yorke	yorke	PROPN
cord-326631-7gd3hjc3	322	31	,	,	PUNCT
cord-326631-7gd3hjc3	322	32	1973	1973	NUM
cord-326631-7gd3hjc3	322	33	)	)	PUNCT
cord-326631-7gd3hjc3	322	34	who	who	PRON
cord-326631-7gd3hjc3	322	35	form	form	VERB
cord-326631-7gd3hjc3	322	36	a	a	DET
cord-326631-7gd3hjc3	322	37	small	small	ADJ
cord-326631-7gd3hjc3	322	38	fraction	fraction	NOUN
cord-326631-7gd3hjc3	322	39	of	of	ADP
cord-326631-7gd3hjc3	322	40	the	the	DET
cord-326631-7gd3hjc3	322	41	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	322	42	pool	pool	NOUN
cord-326631-7gd3hjc3	322	43	when	when	SCONJ
cord-326631-7gd3hjc3	322	44	a	a	DET
cord-326631-7gd3hjc3	322	45	new	new	ADJ
cord-326631-7gd3hjc3	322	46	infection	infection	NOUN
cord-326631-7gd3hjc3	322	47	enters	enter	VERB
cord-326631-7gd3hjc3	322	48	a	a	DET
cord-326631-7gd3hjc3	322	49	population	population	NOUN
cord-326631-7gd3hjc3	322	50	.	.	PUNCT
cord-326631-7gd3hjc3	323	1	infection	infection	NOUN
cord-326631-7gd3hjc3	323	2	control	control	NOUN
cord-326631-7gd3hjc3	323	3	measures	measure	NOUN
cord-326631-7gd3hjc3	323	4	,	,	PUNCT
cord-326631-7gd3hjc3	323	5	such	such	ADJ
cord-326631-7gd3hjc3	323	6	as	as	ADP
cord-326631-7gd3hjc3	323	7	those	those	PRON
cord-326631-7gd3hjc3	323	8	adopted	adopt	VERB
cord-326631-7gd3hjc3	323	9	during	during	ADP
cord-326631-7gd3hjc3	323	10	the	the	DET
cord-326631-7gd3hjc3	323	11	2003	2003	NUM
cord-326631-7gd3hjc3	323	12	sars	sar	NOUN
cord-326631-7gd3hjc3	323	13	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	323	14	(	(	PUNCT
cord-326631-7gd3hjc3	323	15	lipsitch	lipsitch	PROPN
cord-326631-7gd3hjc3	323	16	et	et	PROPN
cord-326631-7gd3hjc3	323	17	al	al	PROPN
cord-326631-7gd3hjc3	323	18	.	.	PROPN
cord-326631-7gd3hjc3	323	19	,	,	PUNCT
cord-326631-7gd3hjc3	323	20	2003	2003	NUM
cord-326631-7gd3hjc3	323	21	;	;	PUNCT
cord-326631-7gd3hjc3	323	22	wallinga	wallinga	NOUN
cord-326631-7gd3hjc3	323	23	and	and	CCONJ
cord-326631-7gd3hjc3	323	24	teunis	teunis	PROPN
cord-326631-7gd3hjc3	323	25	,	,	PUNCT
cord-326631-7gd3hjc3	323	26	2004	2004	NUM
cord-326631-7gd3hjc3	323	27	)	)	PUNCT
cord-326631-7gd3hjc3	323	28	,	,	PUNCT
cord-326631-7gd3hjc3	323	29	could	could	AUX
cord-326631-7gd3hjc3	323	30	have	have	VERB
cord-326631-7gd3hjc3	323	31	a	a	DET
cord-326631-7gd3hjc3	323	32	dramatic	dramatic	ADJ
cord-326631-7gd3hjc3	323	33	effect	effect	NOUN
cord-326631-7gd3hjc3	323	34	on	on	ADP
cord-326631-7gd3hjc3	323	35	the	the	DET
cord-326631-7gd3hjc3	323	36	final	final	ADJ
cord-326631-7gd3hjc3	323	37	size	size	NOUN
cord-326631-7gd3hjc3	323	38	;	;	PUNCT
cord-326631-7gd3hjc3	323	39	in	in	ADP
cord-326631-7gd3hjc3	323	40	this	this	DET
cord-326631-7gd3hjc3	323	41	case	case	NOUN
cord-326631-7gd3hjc3	323	42	,	,	PUNCT
cord-326631-7gd3hjc3	323	43	rather	rather	ADV
cord-326631-7gd3hjc3	323	44	than	than	ADP
cord-326631-7gd3hjc3	323	45	r	r	NOUN
cord-326631-7gd3hjc3	323	46	0	0	NUM
cord-326631-7gd3hjc3	323	47	,	,	PUNCT
cord-326631-7gd3hjc3	323	48	the	the	DET
cord-326631-7gd3hjc3	323	49	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	323	50	number	number	NOUN
cord-326631-7gd3hjc3	323	51	that	that	PRON
cord-326631-7gd3hjc3	323	52	is	be	AUX
cord-326631-7gd3hjc3	323	53	relevant	relevant	ADJ
cord-326631-7gd3hjc3	323	54	for	for	SCONJ
cord-326631-7gd3hjc3	323	55	the	the	DET
cord-326631-7gd3hjc3	323	56	final	final	ADJ
cord-326631-7gd3hjc3	323	57	size	size	NOUN
cord-326631-7gd3hjc3	323	58	formula	formula	NOUN
cord-326631-7gd3hjc3	323	59	must	must	AUX
cord-326631-7gd3hjc3	323	60	be	be	AUX
cord-326631-7gd3hjc3	323	61	calculated	calculate	VERB
cord-326631-7gd3hjc3	323	62	after	after	SCONJ
cord-326631-7gd3hjc3	323	63	sustainable	sustainable	ADJ
cord-326631-7gd3hjc3	323	64	precautionary	precautionary	ADJ
cord-326631-7gd3hjc3	323	65	measures	measure	NOUN
cord-326631-7gd3hjc3	323	66	have	have	AUX
cord-326631-7gd3hjc3	323	67	been	be	AUX
cord-326631-7gd3hjc3	323	68	put	put	VERB
cord-326631-7gd3hjc3	323	69	into	into	ADP
cord-326631-7gd3hjc3	323	70	place	place	NOUN
cord-326631-7gd3hjc3	323	71	.	.	PUNCT
cord-326631-7gd3hjc3	324	1	individual	individual	ADJ
cord-326631-7gd3hjc3	324	2	behavioral	behavioral	ADJ
cord-326631-7gd3hjc3	324	3	change	change	NOUN
cord-326631-7gd3hjc3	324	4	could	could	AUX
cord-326631-7gd3hjc3	324	5	alter	alter	VERB
cord-326631-7gd3hjc3	324	6	the	the	DET
cord-326631-7gd3hjc3	324	7	transmission	transmission	NOUN
cord-326631-7gd3hjc3	324	8	rate	rate	NOUN
cord-326631-7gd3hjc3	324	9	through	through	ADP
cord-326631-7gd3hjc3	324	10	time	time	NOUN
cord-326631-7gd3hjc3	324	11	-	-	PUNCT
cord-326631-7gd3hjc3	324	12	dependence	dependence	NOUN
cord-326631-7gd3hjc3	324	13	(	(	PUNCT
cord-326631-7gd3hjc3	324	14	β	β	PROPN
cord-326631-7gd3hjc3	324	15	=	=	NOUN
cord-326631-7gd3hjc3	324	16	β(t	β(t	PUNCT
cord-326631-7gd3hjc3	324	17	)	)	PUNCT
cord-326631-7gd3hjc3	324	18	,	,	PUNCT
cord-326631-7gd3hjc3	324	19	as	as	ADP
cord-326631-7gd3hjc3	324	20	in	in	ADP
cord-326631-7gd3hjc3	324	21	the	the	DET
cord-326631-7gd3hjc3	324	22	case	case	NOUN
cord-326631-7gd3hjc3	324	23	of	of	ADP
cord-326631-7gd3hjc3	324	24	imposed	impose	VERB
cord-326631-7gd3hjc3	324	25	control	control	NOUN
cord-326631-7gd3hjc3	324	26	measures	measure	NOUN
cord-326631-7gd3hjc3	324	27	)	)	PUNCT
cord-326631-7gd3hjc3	324	28	or	or	CCONJ
cord-326631-7gd3hjc3	324	29	through	through	ADP
cord-326631-7gd3hjc3	324	30	density	density	NOUN
cord-326631-7gd3hjc3	324	31	-	-	PUNCT
cord-326631-7gd3hjc3	324	32	dependence	dependence	NOUN
cord-326631-7gd3hjc3	324	33	(	(	PUNCT
cord-326631-7gd3hjc3	324	34	β	β	PROPN
cord-326631-7gd3hjc3	324	35	=	=	NOUN
cord-326631-7gd3hjc3	324	36	β(i	β(i	X
cord-326631-7gd3hjc3	324	37	)	)	PUNCT
cord-326631-7gd3hjc3	324	38	,	,	PUNCT
cord-326631-7gd3hjc3	324	39	with	with	ADP
cord-326631-7gd3hjc3	324	40	β	β	NOUN
cord-326631-7gd3hjc3	324	41	decreasing	decrease	VERB
cord-326631-7gd3hjc3	324	42	as	as	SCONJ
cord-326631-7gd3hjc3	324	43	i	i	PRON
cord-326631-7gd3hjc3	324	44	increases	increase	VERB
cord-326631-7gd3hjc3	324	45	,	,	PUNCT
cord-326631-7gd3hjc3	324	46	which	which	PRON
cord-326631-7gd3hjc3	324	47	would	would	AUX
cord-326631-7gd3hjc3	324	48	arise	arise	VERB
cord-326631-7gd3hjc3	324	49	if	if	SCONJ
cord-326631-7gd3hjc3	324	50	people	people	NOUN
cord-326631-7gd3hjc3	324	51	tend	tend	VERB
cord-326631-7gd3hjc3	324	52	to	to	PART
cord-326631-7gd3hjc3	324	53	be	be	AUX
cord-326631-7gd3hjc3	324	54	more	more	ADV
cord-326631-7gd3hjc3	324	55	careful	careful	ADJ
cord-326631-7gd3hjc3	324	56	when	when	SCONJ
cord-326631-7gd3hjc3	324	57	they	they	PRON
cord-326631-7gd3hjc3	324	58	are	be	AUX
cord-326631-7gd3hjc3	324	59	aware	aware	ADJ
cord-326631-7gd3hjc3	324	60	of	of	ADP
cord-326631-7gd3hjc3	324	61	more	more	ADJ
cord-326631-7gd3hjc3	324	62	cases	case	NOUN
cord-326631-7gd3hjc3	324	63	)	)	PUNCT
cord-326631-7gd3hjc3	324	64	.	.	PUNCT
cord-326631-7gd3hjc3	325	1	in	in	ADP
cord-326631-7gd3hjc3	325	2	either	either	DET
cord-326631-7gd3hjc3	325	3	case	case	NOUN
cord-326631-7gd3hjc3	325	4	,	,	PUNCT
cord-326631-7gd3hjc3	325	5	the	the	DET
cord-326631-7gd3hjc3	325	6	standard	standard	ADJ
cord-326631-7gd3hjc3	325	7	final	final	ADJ
cord-326631-7gd3hjc3	325	8	size	size	NOUN
cord-326631-7gd3hjc3	325	9	formula	formula	NOUN
cord-326631-7gd3hjc3	325	10	might	might	AUX
cord-326631-7gd3hjc3	325	11	yield	yield	VERB
cord-326631-7gd3hjc3	325	12	a	a	DET
cord-326631-7gd3hjc3	325	13	poor	poor	ADJ
cord-326631-7gd3hjc3	325	14	approximation	approximation	NOUN
cord-326631-7gd3hjc3	325	15	of	of	ADP
cord-326631-7gd3hjc3	325	16	the	the	DET
cord-326631-7gd3hjc3	325	17	true	true	ADJ
cord-326631-7gd3hjc3	325	18	final	final	ADJ
cord-326631-7gd3hjc3	325	19	size	size	NOUN
cord-326631-7gd3hjc3	325	20	.	.	PUNCT
cord-326631-7gd3hjc3	326	1	all	all	PRON
cord-326631-7gd3hjc3	326	2	of	of	ADP
cord-326631-7gd3hjc3	326	3	our	our	PRON
cord-326631-7gd3hjc3	326	4	analysis	analysis	NOUN
cord-326631-7gd3hjc3	326	5	is	be	AUX
cord-326631-7gd3hjc3	326	6	predicated	predicate	VERB
cord-326631-7gd3hjc3	326	7	on	on	ADP
cord-326631-7gd3hjc3	326	8	the	the	DET
cord-326631-7gd3hjc3	326	9	assumption	assumption	NOUN
cord-326631-7gd3hjc3	326	10	that	that	SCONJ
cord-326631-7gd3hjc3	326	11	vital	vital	ADJ
cord-326631-7gd3hjc3	326	12	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	326	13	(	(	PUNCT
cord-326631-7gd3hjc3	326	14	births	birth	NOUN
cord-326631-7gd3hjc3	326	15	and	and	CCONJ
cord-326631-7gd3hjc3	326	16	deaths	death	NOUN
cord-326631-7gd3hjc3	326	17	)	)	PUNCT
cord-326631-7gd3hjc3	326	18	,	,	PUNCT
cord-326631-7gd3hjc3	326	19	and	and	CCONJ
cord-326631-7gd3hjc3	326	20	more	more	ADV
cord-326631-7gd3hjc3	326	21	generally	generally	ADV
cord-326631-7gd3hjc3	326	22	any	any	DET
cord-326631-7gd3hjc3	326	23	source	source	NOUN
cord-326631-7gd3hjc3	326	24	of	of	ADP
cord-326631-7gd3hjc3	326	25	new	new	ADJ
cord-326631-7gd3hjc3	326	26	susceptible	susceptible	ADJ
cord-326631-7gd3hjc3	326	27	individuals	individual	NOUN
cord-326631-7gd3hjc3	326	28	,	,	PUNCT
cord-326631-7gd3hjc3	326	29	can	can	AUX
cord-326631-7gd3hjc3	326	30	be	be	AUX
cord-326631-7gd3hjc3	326	31	ignored	ignore	VERB
cord-326631-7gd3hjc3	326	32	.	.	PUNCT
cord-326631-7gd3hjc3	327	1	this	this	DET
cord-326631-7gd3hjc3	327	2	approximation	approximation	NOUN
cord-326631-7gd3hjc3	327	3	is	be	AUX
cord-326631-7gd3hjc3	327	4	not	not	PART
cord-326631-7gd3hjc3	327	5	valid	valid	ADJ
cord-326631-7gd3hjc3	327	6	in	in	ADP
cord-326631-7gd3hjc3	327	7	circumstances	circumstance	NOUN
cord-326631-7gd3hjc3	327	8	where	where	SCONJ
cord-326631-7gd3hjc3	327	9	infectious	infectious	ADJ
cord-326631-7gd3hjc3	327	10	periods	period	NOUN
cord-326631-7gd3hjc3	327	11	are	be	AUX
cord-326631-7gd3hjc3	327	12	substantial	substantial	ADJ
cord-326631-7gd3hjc3	327	13	compared	compare	VERB
cord-326631-7gd3hjc3	327	14	with	with	ADP
cord-326631-7gd3hjc3	327	15	life	life	NOUN
cord-326631-7gd3hjc3	327	16	expectancy	expectancy	NOUN
cord-326631-7gd3hjc3	327	17	or	or	CCONJ
cord-326631-7gd3hjc3	327	18	where	where	SCONJ
cord-326631-7gd3hjc3	327	19	immunity	immunity	NOUN
cord-326631-7gd3hjc3	327	20	decays	decay	VERB
cord-326631-7gd3hjc3	327	21	rapidly	rapidly	ADV
cord-326631-7gd3hjc3	327	22	.	.	PUNCT
cord-326631-7gd3hjc3	328	1	it	it	PRON
cord-326631-7gd3hjc3	328	2	will	will	AUX
cord-326631-7gd3hjc3	328	3	,	,	PUNCT
cord-326631-7gd3hjc3	328	4	however	however	ADV
cord-326631-7gd3hjc3	328	5	,	,	PUNCT
cord-326631-7gd3hjc3	328	6	typically	typically	ADV
cord-326631-7gd3hjc3	328	7	be	be	AUX
cord-326631-7gd3hjc3	328	8	relevant	relevant	ADJ
cord-326631-7gd3hjc3	328	9	whenever	whenever	SCONJ
cord-326631-7gd3hjc3	328	10	a	a	DET
cord-326631-7gd3hjc3	328	11	new	new	ADJ
cord-326631-7gd3hjc3	328	12	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	328	13	pathogen	pathogen	PROPN
cord-326631-7gd3hjc3	328	14	emerges	emerge	VERB
cord-326631-7gd3hjc3	328	15	,	,	PUNCT
cord-326631-7gd3hjc3	328	16	as	as	ADP
cord-326631-7gd3hjc3	328	17	in	in	ADP
cord-326631-7gd3hjc3	328	18	the	the	DET
cord-326631-7gd3hjc3	328	19	case	case	NOUN
cord-326631-7gd3hjc3	328	20	of	of	ADP
cord-326631-7gd3hjc3	328	21	the	the	DET
cord-326631-7gd3hjc3	328	22	sars	sar	NOUN
cord-326631-7gd3hjc3	328	23	outbreak	outbreak	NOUN
cord-326631-7gd3hjc3	328	24	in	in	ADP
cord-326631-7gd3hjc3	328	25	2003	2003	NUM
cord-326631-7gd3hjc3	328	26	(	(	PUNCT
cord-326631-7gd3hjc3	328	27	donnelly	donnelly	ADV
cord-326631-7gd3hjc3	328	28	et	et	PROPN
cord-326631-7gd3hjc3	328	29	al	al	PROPN
cord-326631-7gd3hjc3	328	30	.	.	PROPN
cord-326631-7gd3hjc3	328	31	,	,	PUNCT
cord-326631-7gd3hjc3	328	32	2003	2003	NUM
cord-326631-7gd3hjc3	328	33	)	)	PUNCT
cord-326631-7gd3hjc3	328	34	or	or	CCONJ
cord-326631-7gd3hjc3	328	35	the	the	DET
cord-326631-7gd3hjc3	328	36	emergence	emergence	NOUN
cord-326631-7gd3hjc3	328	37	of	of	ADP
cord-326631-7gd3hjc3	328	38	a	a	DET
cord-326631-7gd3hjc3	328	39	new	new	ADJ
cord-326631-7gd3hjc3	328	40	subtype	subtype	NOUN
cord-326631-7gd3hjc3	328	41	of	of	ADP
cord-326631-7gd3hjc3	328	42	influenza	influenza	NOUN
cord-326631-7gd3hjc3	328	43	(	(	PUNCT
cord-326631-7gd3hjc3	328	44	earn	earn	VERB
cord-326631-7gd3hjc3	328	45	et	et	X
cord-326631-7gd3hjc3	328	46	al	al	PROPN
cord-326631-7gd3hjc3	328	47	.	.	PROPN
cord-326631-7gd3hjc3	328	48	,	,	PUNCT
cord-326631-7gd3hjc3	328	49	2002	2002	NUM
cord-326631-7gd3hjc3	328	50	)	)	PUNCT
cord-326631-7gd3hjc3	328	51	.	.	PUNCT
cord-326631-7gd3hjc3	329	1	we	we	PRON
cord-326631-7gd3hjc3	329	2	are	be	AUX
cord-326631-7gd3hjc3	329	3	interested	interested	ADJ
cord-326631-7gd3hjc3	329	4	in	in	ADP
cord-326631-7gd3hjc3	329	5	growth	growth	NOUN
cord-326631-7gd3hjc3	329	6	or	or	CCONJ
cord-326631-7gd3hjc3	329	7	decay	decay	NOUN
cord-326631-7gd3hjc3	329	8	of	of	ADP
cord-326631-7gd3hjc3	329	9	i(β	i(β	PROPN
cord-326631-7gd3hjc3	329	10	,	,	PUNCT
cord-326631-7gd3hjc3	329	11	)	)	PUNCT
cord-326631-7gd3hjc3	329	12	,	,	PUNCT
cord-326631-7gd3hjc3	329	13	which	which	PRON
cord-326631-7gd3hjc3	329	14	is	be	AUX
cord-326631-7gd3hjc3	329	15	determined	determine	VERB
cord-326631-7gd3hjc3	329	16	only	only	ADV
cord-326631-7gd3hjc3	329	17	by	by	ADP
cord-326631-7gd3hjc3	329	18	eq	eq	PROPN
cord-326631-7gd3hjc3	329	19	.	.	PUNCT
cord-326631-7gd3hjc3	330	1	(	(	PUNCT
cord-326631-7gd3hjc3	330	2	d.1b	d.1b	PROPN
cord-326631-7gd3hjc3	330	3	)	)	PUNCT
cord-326631-7gd3hjc3	330	4	.	.	PUNCT
cord-326631-7gd3hjc3	331	1	defining	define	VERB
cord-326631-7gd3hjc3	331	2	x(t	x(t	PROPN
cord-326631-7gd3hjc3	331	3	)	)	PUNCT
cord-326631-7gd3hjc3	331	4	=	=	NOUN
cord-326631-7gd3hjc3	331	5	∞	∞	X
cord-326631-7gd3hjc3	331	6	0	0	PUNCT
cord-326631-7gd3hjc3	331	7	β	β	NOUN
cord-326631-7gd3hjc3	331	8	i(β	i(β	PROPN
cord-326631-7gd3hjc3	331	9	,	,	PUNCT
cord-326631-7gd3hjc3	331	10	t	t	PROPN
cord-326631-7gd3hjc3	331	11	)	)	PUNCT
cord-326631-7gd3hjc3	331	12	dβ	dβ	ADJ
cord-326631-7gd3hjc3	331	13	,	,	PUNCT
cord-326631-7gd3hjc3	331	14	multiplying	multiply	VERB
cord-326631-7gd3hjc3	331	15	both	both	DET
cord-326631-7gd3hjc3	331	16	sides	side	NOUN
cord-326631-7gd3hjc3	331	17	of	of	ADP
cord-326631-7gd3hjc3	331	18	eq	eq	PROPN
cord-326631-7gd3hjc3	331	19	.	.	PUNCT
cord-326631-7gd3hjc3	332	1	(	(	PUNCT
cord-326631-7gd3hjc3	332	2	d.1b	d.1b	PROPN
cord-326631-7gd3hjc3	332	3	)	)	PUNCT
cord-326631-7gd3hjc3	332	4	by	by	ADP
cord-326631-7gd3hjc3	332	5	β	β	NUM
cord-326631-7gd3hjc3	332	6	,	,	PUNCT
cord-326631-7gd3hjc3	332	7	and	and	CCONJ
cord-326631-7gd3hjc3	332	8	integrating	integrate	VERB
cord-326631-7gd3hjc3	332	9	with	with	ADP
cord-326631-7gd3hjc3	332	10	respect	respect	NOUN
cord-326631-7gd3hjc3	332	11	to	to	ADP
cord-326631-7gd3hjc3	332	12	β	β	NOUN
cord-326631-7gd3hjc3	332	13	,	,	PUNCT
cord-326631-7gd3hjc3	332	14	we	we	PRON
cord-326631-7gd3hjc3	332	15	find	find	VERB
cord-326631-7gd3hjc3	332	16	on	on	ADP
cord-326631-7gd3hjc3	332	17	the	the	DET
cord-326631-7gd3hjc3	332	18	other	other	ADJ
cord-326631-7gd3hjc3	332	19	hand	hand	NOUN
cord-326631-7gd3hjc3	332	20	,	,	PUNCT
cord-326631-7gd3hjc3	332	21	recall	recall	VERB
cord-326631-7gd3hjc3	332	22	that	that	SCONJ
cord-326631-7gd3hjc3	332	23	i(t	i(t	PROPN
cord-326631-7gd3hjc3	332	24	)	)	PUNCT
cord-326631-7gd3hjc3	332	25	=	=	SYM
cord-326631-7gd3hjc3	332	26	∞	∞	X
cord-326631-7gd3hjc3	332	27	0	0	NUM
cord-326631-7gd3hjc3	332	28	i(β	i(β	PROPN
cord-326631-7gd3hjc3	332	29	,	,	PUNCT
cord-326631-7gd3hjc3	332	30	t	t	PROPN
cord-326631-7gd3hjc3	332	31	)	)	PUNCT
cord-326631-7gd3hjc3	332	32	dt	dt	PROPN
cord-326631-7gd3hjc3	332	33	(	(	PUNCT
cord-326631-7gd3hjc3	332	34	the	the	DET
cord-326631-7gd3hjc3	332	35	total	total	ADJ
cord-326631-7gd3hjc3	332	36	number	number	NOUN
cord-326631-7gd3hjc3	332	37	of	of	ADP
cord-326631-7gd3hjc3	332	38	infectious	infectious	ADJ
cord-326631-7gd3hjc3	332	39	individuals	individual	NOUN
cord-326631-7gd3hjc3	332	40	at	at	ADP
cord-326631-7gd3hjc3	332	41	time	time	NOUN
cord-326631-7gd3hjc3	332	42	t	t	NOUN
cord-326631-7gd3hjc3	332	43	)	)	PUNCT
cord-326631-7gd3hjc3	332	44	.	.	PUNCT
cord-326631-7gd3hjc3	333	1	therefore	therefore	ADV
cord-326631-7gd3hjc3	333	2	,	,	PUNCT
cord-326631-7gd3hjc3	333	3	integrating	integrate	VERB
cord-326631-7gd3hjc3	333	4	eq	eq	PROPN
cord-326631-7gd3hjc3	333	5	.	.	PUNCT
cord-326631-7gd3hjc3	334	1	(	(	PUNCT
cord-326631-7gd3hjc3	334	2	b.2b	b.2b	X
cord-326631-7gd3hjc3	334	3	)	)	PUNCT
cord-326631-7gd3hjc3	334	4	with	with	ADP
cord-326631-7gd3hjc3	334	5	respect	respect	NOUN
cord-326631-7gd3hjc3	334	6	to	to	ADP
cord-326631-7gd3hjc3	334	7	β	β	NOUN
cord-326631-7gd3hjc3	334	8	,	,	PUNCT
cord-326631-7gd3hjc3	334	9	noting	note	VERB
cord-326631-7gd3hjc3	334	10	that	that	SCONJ
cord-326631-7gd3hjc3	334	11	q(β	q(β	PROPN
cord-326631-7gd3hjc3	334	12	)	)	PUNCT
cord-326631-7gd3hjc3	334	13	is	be	AUX
cord-326631-7gd3hjc3	334	14	a	a	DET
cord-326631-7gd3hjc3	334	15	probability	probability	NOUN
cord-326631-7gd3hjc3	334	16	density	density	NOUN
cord-326631-7gd3hjc3	334	17	function	function	NOUN
cord-326631-7gd3hjc3	334	18	so	so	SCONJ
cord-326631-7gd3hjc3	334	19	the	the	DET
cord-326631-7gd3hjc3	334	20	origin	origin	NOUN
cord-326631-7gd3hjc3	334	21	of	of	ADP
cord-326631-7gd3hjc3	334	22	this	this	DET
cord-326631-7gd3hjc3	334	23	system	system	NOUN
cord-326631-7gd3hjc3	334	24	of	of	ADP
cord-326631-7gd3hjc3	334	25	two	two	NUM
cord-326631-7gd3hjc3	334	26	ordinary	ordinary	ADJ
cord-326631-7gd3hjc3	334	27	differential	differential	ADJ
cord-326631-7gd3hjc3	334	28	equations	equation	NOUN
cord-326631-7gd3hjc3	334	29	is	be	AUX
cord-326631-7gd3hjc3	334	30	locally	locally	ADV
cord-326631-7gd3hjc3	334	31	stable	stable	ADJ
cord-326631-7gd3hjc3	334	32	if	if	SCONJ
cord-326631-7gd3hjc3	334	33	and	and	CCONJ
cord-326631-7gd3hjc3	334	34	only	only	ADV
cord-326631-7gd3hjc3	334	35	if	if	SCONJ
cord-326631-7gd3hjc3	334	36	∞	∞	NUM
cord-326631-7gd3hjc3	334	37	0	0	PUNCT
cord-326631-7gd3hjc3	334	38	βq(β	βq(β	PUNCT
cord-326631-7gd3hjc3	334	39	)	)	PUNCT
cord-326631-7gd3hjc3	334	40	dβ	dβ	PROPN
cord-326631-7gd3hjc3	334	41	−	−	PROPN
cord-326631-7gd3hjc3	334	42	γ	γ	X
cord-326631-7gd3hjc3	334	43	<	<	X
cord-326631-7gd3hjc3	334	44	0	0	NUM
cord-326631-7gd3hjc3	334	45	or	or	CCONJ
cord-326631-7gd3hjc3	334	46	,	,	PUNCT
cord-326631-7gd3hjc3	334	47	equivalently	equivalently	ADV
cord-326631-7gd3hjc3	334	48	,	,	PUNCT
cord-326631-7gd3hjc3	334	49	r	r	NOUN
cord-326631-7gd3hjc3	334	50	0	0	PUNCT
cord-326631-7gd3hjc3	334	51	<	<	X
cord-326631-7gd3hjc3	334	52	1	1	NUM
cord-326631-7gd3hjc3	334	53	.	.	PUNCT
cord-326631-7gd3hjc3	335	1	thus	thus	ADV
cord-326631-7gd3hjc3	335	2	,	,	PUNCT
cord-326631-7gd3hjc3	335	3	the	the	DET
cord-326631-7gd3hjc3	335	4	dfe	dfe	PROPN
cord-326631-7gd3hjc3	335	5	is	be	AUX
cord-326631-7gd3hjc3	335	6	stable	stable	ADJ
cord-326631-7gd3hjc3	335	7	if	if	SCONJ
cord-326631-7gd3hjc3	335	8	r	r	NOUN
cord-326631-7gd3hjc3	335	9	0	0	NUM
cord-326631-7gd3hjc3	335	10	<	<	X
cord-326631-7gd3hjc3	335	11	1	1	NUM
cord-326631-7gd3hjc3	335	12	and	and	CCONJ
cord-326631-7gd3hjc3	335	13	unstable	unstable	ADJ
cord-326631-7gd3hjc3	335	14	if	if	SCONJ
cord-326631-7gd3hjc3	335	15	r	r	NOUN
cord-326631-7gd3hjc3	335	16	0	0	PUNCT
cord-326631-7gd3hjc3	335	17	>	>	SYM
cord-326631-7gd3hjc3	335	18	1	1	NUM
cord-326631-7gd3hjc3	335	19	.	.	PUNCT
cord-326631-7gd3hjc3	336	1	we	we	PRON
cord-326631-7gd3hjc3	336	2	can	can	AUX
cord-326631-7gd3hjc3	336	3	expand	expand	VERB
cord-326631-7gd3hjc3	336	4	model	model	NOUN
cord-326631-7gd3hjc3	336	5	(	(	PUNCT
cord-326631-7gd3hjc3	336	6	21	21	NUM
cord-326631-7gd3hjc3	336	7	)	)	PUNCT
cord-326631-7gd3hjc3	336	8	to	to	PART
cord-326631-7gd3hjc3	336	9	include	include	VERB
cord-326631-7gd3hjc3	336	10	multiple	multiple	ADJ
cord-326631-7gd3hjc3	336	11	stages	stage	NOUN
cord-326631-7gd3hjc3	336	12	.	.	PUNCT
cord-326631-7gd3hjc3	337	1	using	use	VERB
cord-326631-7gd3hjc3	337	2	the	the	DET
cord-326631-7gd3hjc3	337	3	same	same	ADJ
cord-326631-7gd3hjc3	337	4	techniques	technique	NOUN
cord-326631-7gd3hjc3	337	5	,	,	PUNCT
cord-326631-7gd3hjc3	337	6	we	we	PRON
cord-326631-7gd3hjc3	337	7	find	find	VERB
cord-326631-7gd3hjc3	337	8	that	that	SCONJ
cord-326631-7gd3hjc3	337	9	the	the	DET
cord-326631-7gd3hjc3	337	10	conclusion	conclusion	NOUN
cord-326631-7gd3hjc3	337	11	that	that	SCONJ
cord-326631-7gd3hjc3	337	12	the	the	DET
cord-326631-7gd3hjc3	337	13	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	337	14	threshold	threshold	NOUN
cord-326631-7gd3hjc3	337	15	is	be	AUX
cord-326631-7gd3hjc3	337	16	given	give	VERB
cord-326631-7gd3hjc3	337	17	by	by	ADP
cord-326631-7gd3hjc3	337	18	r	r	NOUN
cord-326631-7gd3hjc3	337	19	0	0	NUM
cord-326631-7gd3hjc3	337	20	=	=	SYM
cord-326631-7gd3hjc3	337	21	1	1	NUM
cord-326631-7gd3hjc3	337	22	remains	remain	VERB
cord-326631-7gd3hjc3	337	23	valid	valid	ADJ
cord-326631-7gd3hjc3	337	24	.	.	PUNCT
cord-326631-7gd3hjc3	338	1	on	on	ADP
cord-326631-7gd3hjc3	338	2	the	the	DET
cord-326631-7gd3hjc3	338	3	spread	spread	NOUN
cord-326631-7gd3hjc3	338	4	of	of	ADP
cord-326631-7gd3hjc3	338	5	a	a	DET
cord-326631-7gd3hjc3	338	6	disease	disease	NOUN
cord-326631-7gd3hjc3	338	7	with	with	ADP
cord-326631-7gd3hjc3	338	8	gamma	gamma	NOUN
cord-326631-7gd3hjc3	338	9	distributed	distribute	VERB
cord-326631-7gd3hjc3	338	10	latent	latent	ADJ
cord-326631-7gd3hjc3	338	11	and	and	CCONJ
cord-326631-7gd3hjc3	338	12	infectious	infectious	ADJ
cord-326631-7gd3hjc3	338	13	periods	period	NOUN
cord-326631-7gd3hjc3	338	14	infectious	infectious	ADJ
cord-326631-7gd3hjc3	338	15	diseases	disease	NOUN
cord-326631-7gd3hjc3	338	16	of	of	ADP
cord-326631-7gd3hjc3	338	17	humans	human	NOUN
cord-326631-7gd3hjc3	338	18	:	:	PUNCT
cord-326631-7gd3hjc3	338	19	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	338	20	and	and	CCONJ
cord-326631-7gd3hjc3	338	21	control	control	VERB
cord-326631-7gd3hjc3	338	22	a	a	DET
cord-326631-7gd3hjc3	338	23	preliminary	preliminary	ADJ
cord-326631-7gd3hjc3	338	24	study	study	NOUN
cord-326631-7gd3hjc3	338	25	of	of	ADP
cord-326631-7gd3hjc3	338	26	the	the	DET
cord-326631-7gd3hjc3	338	27	transmission	transmission	NOUN
cord-326631-7gd3hjc3	338	28	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	338	29	of	of	ADP
cord-326631-7gd3hjc3	338	30	the	the	DET
cord-326631-7gd3hjc3	338	31	human	human	ADJ
cord-326631-7gd3hjc3	338	32	immunodeficiency	immunodeficiency	NOUN
cord-326631-7gd3hjc3	338	33	virus	virus	NOUN
cord-326631-7gd3hjc3	338	34	(	(	PUNCT
cord-326631-7gd3hjc3	338	35	hiv	hiv	PROPN
cord-326631-7gd3hjc3	338	36	)	)	PUNCT
cord-326631-7gd3hjc3	338	37	,	,	PUNCT
cord-326631-7gd3hjc3	338	38	the	the	DET
cord-326631-7gd3hjc3	338	39	causative	causative	ADJ
cord-326631-7gd3hjc3	338	40	agent	agent	NOUN
cord-326631-7gd3hjc3	338	41	of	of	ADP
cord-326631-7gd3hjc3	338	42	aids	aids	PROPN
cord-326631-7gd3hjc3	338	43	stochastic	stochastic	NOUN
cord-326631-7gd3hjc3	338	44	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	338	45	models	model	NOUN
cord-326631-7gd3hjc3	338	46	and	and	CCONJ
cord-326631-7gd3hjc3	338	47	their	their	PRON
cord-326631-7gd3hjc3	338	48	statistical	statistical	ADJ
cord-326631-7gd3hjc3	338	49	analysis	analysis	NOUN
cord-326631-7gd3hjc3	338	50	the	the	DET
cord-326631-7gd3hjc3	338	51	asymptotic	asymptotic	ADJ
cord-326631-7gd3hjc3	338	52	final	final	ADJ
cord-326631-7gd3hjc3	338	53	size	size	NOUN
cord-326631-7gd3hjc3	338	54	distribution	distribution	NOUN
cord-326631-7gd3hjc3	338	55	of	of	ADP
cord-326631-7gd3hjc3	338	56	multitype	multitype	NOUN
cord-326631-7gd3hjc3	338	57	chain	chain	NOUN
cord-326631-7gd3hjc3	338	58	-	-	PUNCT
cord-326631-7gd3hjc3	338	59	binomial	binomial	NOUN
cord-326631-7gd3hjc3	338	60	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	338	61	processes	process	VERB
cord-326631-7gd3hjc3	338	62	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	338	63	of	of	ADP
cord-326631-7gd3hjc3	338	64	annual	annual	ADJ
cord-326631-7gd3hjc3	338	65	influenza	influenza	NOUN
cord-326631-7gd3hjc3	338	66	a	a	DET
cord-326631-7gd3hjc3	338	67	epidemics	epidemic	NOUN
cord-326631-7gd3hjc3	338	68	with	with	ADP
cord-326631-7gd3hjc3	338	69	immuno	immuno	NOUN
cord-326631-7gd3hjc3	338	70	-	-	PUNCT
cord-326631-7gd3hjc3	338	71	selection	selection	NOUN
cord-326631-7gd3hjc3	338	72	the	the	DET
cord-326631-7gd3hjc3	338	73	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	338	74	theory	theory	NOUN
cord-326631-7gd3hjc3	338	75	of	of	ADP
cord-326631-7gd3hjc3	338	76	infectious	infectious	ADJ
cord-326631-7gd3hjc3	338	77	diseases	disease	NOUN
cord-326631-7gd3hjc3	338	78	and	and	CCONJ
cord-326631-7gd3hjc3	338	79	its	its	PRON
cord-326631-7gd3hjc3	338	80	application	application	NOUN
cord-326631-7gd3hjc3	338	81	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	338	82	models	model	NOUN
cord-326631-7gd3hjc3	338	83	in	in	ADP
cord-326631-7gd3hjc3	338	84	population	population	NOUN
cord-326631-7gd3hjc3	338	85	biology	biology	NOUN
cord-326631-7gd3hjc3	338	86	and	and	CCONJ
cord-326631-7gd3hjc3	338	87	epidemiology	epidemiology	NOUN
cord-326631-7gd3hjc3	338	88	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	338	89	epidemiology	epidemiology	NOUN
cord-326631-7gd3hjc3	338	90	of	of	ADP
cord-326631-7gd3hjc3	338	91	infectious	infectious	ADJ
cord-326631-7gd3hjc3	338	92	diseases	disease	NOUN
cord-326631-7gd3hjc3	338	93	:	:	PUNCT
cord-326631-7gd3hjc3	338	94	model	model	NOUN
cord-326631-7gd3hjc3	338	95	building	building	NOUN
cord-326631-7gd3hjc3	338	96	,	,	PUNCT
cord-326631-7gd3hjc3	338	97	analysis	analysis	NOUN
cord-326631-7gd3hjc3	338	98	and	and	CCONJ
cord-326631-7gd3hjc3	338	99	interpretation	interpretation	NOUN
cord-326631-7gd3hjc3	338	100	epidemiological	epidemiological	ADJ
cord-326631-7gd3hjc3	338	101	determinants	determinant	NOUN
cord-326631-7gd3hjc3	338	102	of	of	ADP
cord-326631-7gd3hjc3	338	103	spread	spread	NOUN
cord-326631-7gd3hjc3	338	104	of	of	ADP
cord-326631-7gd3hjc3	338	105	causal	causal	ADJ
cord-326631-7gd3hjc3	338	106	agent	agent	NOUN
cord-326631-7gd3hjc3	338	107	of	of	ADP
cord-326631-7gd3hjc3	338	108	severe	severe	ADJ
cord-326631-7gd3hjc3	338	109	acute	acute	ADJ
cord-326631-7gd3hjc3	338	110	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	338	111	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	338	112	in	in	ADP
cord-326631-7gd3hjc3	338	113	hong	hong	PROPN
cord-326631-7gd3hjc3	338	114	kong	kong	PROPN
cord-326631-7gd3hjc3	338	115	pathogen	pathogen	PROPN
cord-326631-7gd3hjc3	338	116	-	-	PUNCT
cord-326631-7gd3hjc3	338	117	driven	drive	VERB
cord-326631-7gd3hjc3	338	118	outbreaks	outbreak	NOUN
cord-326631-7gd3hjc3	338	119	in	in	ADP
cord-326631-7gd3hjc3	338	120	forest	forest	NOUN
cord-326631-7gd3hjc3	338	121	defoliators	defoliator	NOUN
cord-326631-7gd3hjc3	338	122	revisited	revisit	VERB
cord-326631-7gd3hjc3	338	123	:	:	PUNCT
cord-326631-7gd3hjc3	338	124	building	building	NOUN
cord-326631-7gd3hjc3	338	125	models	model	NOUN
cord-326631-7gd3hjc3	338	126	from	from	ADP
cord-326631-7gd3hjc3	338	127	exprimental	exprimental	PROPN
cord-326631-7gd3hjc3	338	128	data	data	PROPN
cord-326631-7gd3hjc3	338	129	ecology	ecology	NOUN
cord-326631-7gd3hjc3	338	130	and	and	CCONJ
cord-326631-7gd3hjc3	338	131	evolution	evolution	NOUN
cord-326631-7gd3hjc3	338	132	of	of	ADP
cord-326631-7gd3hjc3	338	133	the	the	DET
cord-326631-7gd3hjc3	338	134	flu	flu	NOUN
cord-326631-7gd3hjc3	338	135	coherence	coherence	NOUN
cord-326631-7gd3hjc3	338	136	and	and	CCONJ
cord-326631-7gd3hjc3	338	137	conservation	conservation	VERB
cord-326631-7gd3hjc3	338	138	a	a	DET
cord-326631-7gd3hjc3	338	139	simple	simple	ADJ
cord-326631-7gd3hjc3	338	140	model	model	NOUN
cord-326631-7gd3hjc3	338	141	for	for	ADP
cord-326631-7gd3hjc3	338	142	complex	complex	ADJ
cord-326631-7gd3hjc3	338	143	dynamical	dynamical	ADJ
cord-326631-7gd3hjc3	338	144	transitions	transition	NOUN
cord-326631-7gd3hjc3	338	145	in	in	ADP
cord-326631-7gd3hjc3	338	146	epidemics	epidemic	NOUN
cord-326631-7gd3hjc3	338	147	endemic	endemic	ADJ
cord-326631-7gd3hjc3	338	148	models	model	NOUN
cord-326631-7gd3hjc3	338	149	with	with	ADP
cord-326631-7gd3hjc3	338	150	arbitrarily	arbitrarily	ADV
cord-326631-7gd3hjc3	338	151	distributed	distribute	VERB
cord-326631-7gd3hjc3	338	152	periods	period	NOUN
cord-326631-7gd3hjc3	338	153	of	of	ADP
cord-326631-7gd3hjc3	338	154	infection	infection	NOUN
cord-326631-7gd3hjc3	339	1	i	i	PRON
cord-326631-7gd3hjc3	339	2	:	:	PUNCT
cord-326631-7gd3hjc3	339	3	fundamental	fundamental	ADJ
cord-326631-7gd3hjc3	339	4	properties	property	NOUN
cord-326631-7gd3hjc3	339	5	of	of	ADP
cord-326631-7gd3hjc3	339	6	the	the	DET
cord-326631-7gd3hjc3	339	7	model	model	NOUN
cord-326631-7gd3hjc3	339	8	the	the	DET
cord-326631-7gd3hjc3	339	9	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	339	10	analysis	analysis	NOUN
cord-326631-7gd3hjc3	339	11	of	of	ADP
cord-326631-7gd3hjc3	339	12	an	an	DET
cord-326631-7gd3hjc3	339	13	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	339	14	with	with	ADP
cord-326631-7gd3hjc3	339	15	two	two	NUM
cord-326631-7gd3hjc3	339	16	kinds	kind	NOUN
cord-326631-7gd3hjc3	339	17	of	of	ADP
cord-326631-7gd3hjc3	339	18	susceptibles	susceptibles	ADJ
cord-326631-7gd3hjc3	339	19	metapopulation	metapopulation	NOUN
cord-326631-7gd3hjc3	339	20	biology	biology	NOUN
cord-326631-7gd3hjc3	339	21	:	:	PUNCT
cord-326631-7gd3hjc3	339	22	ecology	ecology	NOUN
cord-326631-7gd3hjc3	339	23	,	,	PUNCT
cord-326631-7gd3hjc3	339	24	genetics	genetic	NOUN
cord-326631-7gd3hjc3	339	25	,	,	PUNCT
cord-326631-7gd3hjc3	339	26	and	and	CCONJ
cord-326631-7gd3hjc3	339	27	evolution	evolution	NOUN
cord-326631-7gd3hjc3	339	28	matrix	matrix	NOUN
cord-326631-7gd3hjc3	339	29	analysis	analysis	NOUN
cord-326631-7gd3hjc3	339	30	the	the	DET
cord-326631-7gd3hjc3	339	31	differential	differential	ADJ
cord-326631-7gd3hjc3	339	32	infectivity	infectivity	NOUN
cord-326631-7gd3hjc3	339	33	and	and	CCONJ
cord-326631-7gd3hjc3	339	34	staged	stage	VERB
cord-326631-7gd3hjc3	339	35	progression	progression	NOUN
cord-326631-7gd3hjc3	339	36	models	model	NOUN
cord-326631-7gd3hjc3	339	37	for	for	ADP
cord-326631-7gd3hjc3	339	38	the	the	DET
cord-326631-7gd3hjc3	339	39	transmission	transmission	NOUN
cord-326631-7gd3hjc3	339	40	of	of	ADP
cord-326631-7gd3hjc3	339	41	hiv	hiv	PROPN
cord-326631-7gd3hjc3	339	42	a	a	DET
cord-326631-7gd3hjc3	339	43	contribution	contribution	NOUN
cord-326631-7gd3hjc3	339	44	to	to	ADP
cord-326631-7gd3hjc3	339	45	the	the	DET
cord-326631-7gd3hjc3	339	46	mathematical	mathematical	ADJ
cord-326631-7gd3hjc3	339	47	theory	theory	NOUN
cord-326631-7gd3hjc3	339	48	of	of	ADP
cord-326631-7gd3hjc3	339	49	epidemics	epidemic	NOUN
cord-326631-7gd3hjc3	339	50	relationships	relationship	NOUN
cord-326631-7gd3hjc3	339	51	between	between	ADP
cord-326631-7gd3hjc3	339	52	stochastic	stochastic	NOUN
cord-326631-7gd3hjc3	339	53	and	and	CCONJ
cord-326631-7gd3hjc3	339	54	deterministic	deterministic	ADJ
cord-326631-7gd3hjc3	339	55	population	population	NOUN
cord-326631-7gd3hjc3	339	56	models	model	NOUN
cord-326631-7gd3hjc3	339	57	transmission	transmission	NOUN
cord-326631-7gd3hjc3	339	58	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	339	59	and	and	CCONJ
cord-326631-7gd3hjc3	339	60	control	control	NOUN
cord-326631-7gd3hjc3	339	61	of	of	ADP
cord-326631-7gd3hjc3	339	62	severe	severe	ADJ
cord-326631-7gd3hjc3	339	63	acute	acute	ADJ
cord-326631-7gd3hjc3	339	64	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	339	65	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	339	66	destabilization	destabilization	NOUN
cord-326631-7gd3hjc3	339	67	of	of	ADP
cord-326631-7gd3hjc3	339	68	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	339	69	models	model	NOUN
cord-326631-7gd3hjc3	339	70	with	with	ADP
cord-326631-7gd3hjc3	339	71	the	the	DET
cord-326631-7gd3hjc3	339	72	inclusion	inclusion	NOUN
cord-326631-7gd3hjc3	339	73	of	of	ADP
cord-326631-7gd3hjc3	339	74	realistic	realistic	ADJ
cord-326631-7gd3hjc3	339	75	distributions	distribution	NOUN
cord-326631-7gd3hjc3	339	76	of	of	ADP
cord-326631-7gd3hjc3	339	77	infectious	infectious	ADJ
cord-326631-7gd3hjc3	339	78	periods	period	NOUN
cord-326631-7gd3hjc3	339	79	realistic	realistic	ADJ
cord-326631-7gd3hjc3	339	80	distributions	distribution	NOUN
cord-326631-7gd3hjc3	339	81	of	of	ADP
cord-326631-7gd3hjc3	339	82	infectious	infectious	ADJ
cord-326631-7gd3hjc3	339	83	periods	period	NOUN
cord-326631-7gd3hjc3	339	84	in	in	ADP
cord-326631-7gd3hjc3	339	85	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	339	86	models	model	NOUN
cord-326631-7gd3hjc3	339	87	:	:	PUNCT
cord-326631-7gd3hjc3	339	88	changing	change	VERB
cord-326631-7gd3hjc3	339	89	patterns	pattern	NOUN
cord-326631-7gd3hjc3	339	90	of	of	ADP
cord-326631-7gd3hjc3	339	91	persistence	persistence	NOUN
cord-326631-7gd3hjc3	339	92	and	and	CCONJ
cord-326631-7gd3hjc3	339	93	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	339	94	.	.	PUNCT
cord-326631-7gd3hjc3	340	1	theor	theor	PROPN
cord-326631-7gd3hjc3	340	2	recurrent	recurrent	PROPN
cord-326631-7gd3hjc3	340	3	outbreaks	outbreak	NOUN
cord-326631-7gd3hjc3	340	4	of	of	ADP
cord-326631-7gd3hjc3	340	5	measles	measle	NOUN
cord-326631-7gd3hjc3	340	6	,	,	PUNCT
cord-326631-7gd3hjc3	340	7	chickenpox	chickenpox	NOUN
cord-326631-7gd3hjc3	340	8	and	and	CCONJ
cord-326631-7gd3hjc3	340	9	mumps	mump	NOUN
cord-326631-7gd3hjc3	340	10	.	.	PUNCT
cord-326631-7gd3hjc3	341	1	i	i	PRON
cord-326631-7gd3hjc3	341	2	seasonal	seasonal	ADJ
cord-326631-7gd3hjc3	341	3	variation	variation	NOUN
cord-326631-7gd3hjc3	341	4	in	in	ADP
cord-326631-7gd3hjc3	341	5	contact	contact	NOUN
cord-326631-7gd3hjc3	341	6	rates	rate	NOUN
cord-326631-7gd3hjc3	341	7	sars	sar	NOUN
cord-326631-7gd3hjc3	341	8	-	-	PUNCT
cord-326631-7gd3hjc3	341	9	one	one	NUM
cord-326631-7gd3hjc3	341	10	year	year	NOUN
cord-326631-7gd3hjc3	341	11	later	later	ADV
cord-326631-7gd3hjc3	341	12	identification	identification	NOUN
cord-326631-7gd3hjc3	341	13	of	of	ADP
cord-326631-7gd3hjc3	341	14	severe	severe	ADJ
cord-326631-7gd3hjc3	341	15	acute	acute	ADJ
cord-326631-7gd3hjc3	341	16	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	341	17	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	341	18	in	in	ADP
cord-326631-7gd3hjc3	341	19	canada	canada	PROPN
cord-326631-7gd3hjc3	341	20	the	the	DET
cord-326631-7gd3hjc3	341	21	walter	walter	PROPN
cord-326631-7gd3hjc3	341	22	reed	reed	NOUN
cord-326631-7gd3hjc3	341	23	staging	stage	VERB
cord-326631-7gd3hjc3	341	24	classification	classification	NOUN
cord-326631-7gd3hjc3	341	25	for	for	ADP
cord-326631-7gd3hjc3	341	26	htlv	htlv	PROPN
cord-326631-7gd3hjc3	341	27	-	-	PUNCT
cord-326631-7gd3hjc3	341	28	iii	iii	PROPN
cord-326631-7gd3hjc3	341	29	/	/	SYM
cord-326631-7gd3hjc3	341	30	lav	lav	NOUN
cord-326631-7gd3hjc3	341	31	infection	infection	NOUN
cord-326631-7gd3hjc3	341	32	asymptotic	asymptotic	ADJ
cord-326631-7gd3hjc3	341	33	final	final	ADJ
cord-326631-7gd3hjc3	341	34	size	size	NOUN
cord-326631-7gd3hjc3	341	35	distribution	distribution	NOUN
cord-326631-7gd3hjc3	341	36	for	for	ADP
cord-326631-7gd3hjc3	341	37	some	some	DET
cord-326631-7gd3hjc3	341	38	chain	chain	NOUN
cord-326631-7gd3hjc3	341	39	-	-	PUNCT
cord-326631-7gd3hjc3	341	40	binomial	binomial	NOUN
cord-326631-7gd3hjc3	341	41	processes	process	VERB
cord-326631-7gd3hjc3	341	42	asymptotic	asymptotic	ADJ
cord-326631-7gd3hjc3	341	43	final	final	ADJ
cord-326631-7gd3hjc3	341	44	size	size	NOUN
cord-326631-7gd3hjc3	341	45	distribution	distribution	NOUN
cord-326631-7gd3hjc3	341	46	of	of	ADP
cord-326631-7gd3hjc3	341	47	the	the	DET
cord-326631-7gd3hjc3	341	48	multitype	multitype	NOUN
cord-326631-7gd3hjc3	341	49	reed	reed	NOUN
cord-326631-7gd3hjc3	341	50	-	-	PUNCT
cord-326631-7gd3hjc3	341	51	frost	frost	NOUN
cord-326631-7gd3hjc3	341	52	process	process	NOUN
cord-326631-7gd3hjc3	341	53	an	an	DET
cord-326631-7gd3hjc3	341	54	age	age	NOUN
cord-326631-7gd3hjc3	341	55	-	-	PUNCT
cord-326631-7gd3hjc3	341	56	structured	structure	VERB
cord-326631-7gd3hjc3	341	57	model	model	NOUN
cord-326631-7gd3hjc3	341	58	of	of	ADP
cord-326631-7gd3hjc3	341	59	pre	pre	ADJ
cord-326631-7gd3hjc3	341	60	-	-	ADJ
cord-326631-7gd3hjc3	341	61	and	and	CCONJ
cord-326631-7gd3hjc3	341	62	post	post	ADJ
cord-326631-7gd3hjc3	341	63	-	-	ADJ
cord-326631-7gd3hjc3	341	64	vaccination	vaccination	ADJ
cord-326631-7gd3hjc3	341	65	measles	measles	NOUN
cord-326631-7gd3hjc3	341	66	transmission	transmission	NOUN
cord-326631-7gd3hjc3	341	67	infinite	infinite	ADJ
cord-326631-7gd3hjc3	341	68	subharmonic	subharmonic	ADJ
cord-326631-7gd3hjc3	341	69	bifurcation	bifurcation	NOUN
cord-326631-7gd3hjc3	341	70	in	in	ADP
cord-326631-7gd3hjc3	341	71	an	an	DET
cord-326631-7gd3hjc3	341	72	seir	seir	ADJ
cord-326631-7gd3hjc3	341	73	model	model	NOUN
cord-326631-7gd3hjc3	341	74	reproduction	reproduction	NOUN
cord-326631-7gd3hjc3	341	75	numbers	number	NOUN
cord-326631-7gd3hjc3	341	76	and	and	CCONJ
cord-326631-7gd3hjc3	341	77	subthreadold	subthreadold	ADJ
cord-326631-7gd3hjc3	341	78	endemic	endemic	ADJ
cord-326631-7gd3hjc3	341	79	equilibria	equilibrium	NOUN
cord-326631-7gd3hjc3	341	80	for	for	ADP
cord-326631-7gd3hjc3	341	81	compartmental	compartmental	NOUN
cord-326631-7gd3hjc3	341	82	models	model	NOUN
cord-326631-7gd3hjc3	341	83	fo	fo	ADP
cord-326631-7gd3hjc3	341	84	disease	disease	NOUN
cord-326631-7gd3hjc3	341	85	transmission	transmission	NOUN
cord-326631-7gd3hjc3	341	86	threshold	threshold	NOUN
cord-326631-7gd3hjc3	341	87	limit	limit	NOUN
cord-326631-7gd3hjc3	341	88	theorems	theorem	NOUN
cord-326631-7gd3hjc3	341	89	for	for	ADP
cord-326631-7gd3hjc3	341	90	some	some	DET
cord-326631-7gd3hjc3	341	91	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	341	92	processes	process	VERB
cord-326631-7gd3hjc3	341	93	different	different	ADJ
cord-326631-7gd3hjc3	341	94	epidemic	epidemic	NOUN
cord-326631-7gd3hjc3	341	95	curves	curve	NOUN
cord-326631-7gd3hjc3	341	96	for	for	ADP
cord-326631-7gd3hjc3	341	97	severe	severe	ADJ
cord-326631-7gd3hjc3	341	98	acute	acute	ADJ
cord-326631-7gd3hjc3	341	99	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	341	100	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	341	101	reveal	reveal	VERB
cord-326631-7gd3hjc3	341	102	similar	similar	ADJ
cord-326631-7gd3hjc3	341	103	impacts	impact	NOUN
cord-326631-7gd3hjc3	341	104	of	of	ADP
cord-326631-7gd3hjc3	341	105	control	control	NOUN
cord-326631-7gd3hjc3	341	106	measures	measure	NOUN
cord-326631-7gd3hjc3	341	107	from	from	ADP
cord-326631-7gd3hjc3	341	108	mathworld	mathworld	NOUN
cord-326631-7gd3hjc3	341	109	-	-	PUNCT
cord-326631-7gd3hjc3	341	110	a	a	DET
cord-326631-7gd3hjc3	341	111	wolfram	wolfram	NOUN
cord-326631-7gd3hjc3	341	112	web	web	NOUN
cord-326631-7gd3hjc3	341	113	resource	resource	NOUN
cord-326631-7gd3hjc3	341	114	.	.	PUNCT
cord-326631-7gd3hjc3	342	1	http:\math	http:\math	PROPN
cord-326631-7gd3hjc3	342	2	world.wolfram.com/lambertw-function.html	world.wolfram.com/lambertw-function.html	PART
cord-326631-7gd3hjc3	342	3	severe	severe	ADJ
cord-326631-7gd3hjc3	342	4	acute	acute	ADJ
cord-326631-7gd3hjc3	342	5	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	342	6	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	342	7	(	(	PUNCT
cord-326631-7gd3hjc3	342	8	sars	sar	NOUN
cord-326631-7gd3hjc3	342	9	)	)	PUNCT
cord-326631-7gd3hjc3	342	10	,	,	PUNCT
cord-326631-7gd3hjc3	342	11	multi	multi	ADJ
cord-326631-7gd3hjc3	342	12	-	-	ADJ
cord-326631-7gd3hjc3	342	13	country	country	ADJ
cord-326631-7gd3hjc3	342	14	outbreak	outbreak	NOUN
cord-326631-7gd3hjc3	342	15	severe	severe	ADJ
cord-326631-7gd3hjc3	342	16	acute	acute	ADJ
cord-326631-7gd3hjc3	342	17	respiratory	respiratory	ADJ
cord-326631-7gd3hjc3	342	18	syndrome	syndrome	NOUN
cord-326631-7gd3hjc3	342	19	(	(	PUNCT
cord-326631-7gd3hjc3	342	20	sars	sar	NOUN
cord-326631-7gd3hjc3	342	21	)	)	PUNCT
cord-326631-7gd3hjc3	342	22	,	,	PUNCT
cord-326631-7gd3hjc3	342	23	multi	multi	ADJ
cord-326631-7gd3hjc3	342	24	-	-	ADJ
cord-326631-7gd3hjc3	342	25	country	country	ADJ
cord-326631-7gd3hjc3	342	26	outbreak	outbreak	NOUN
cord-326631-7gd3hjc3	342	27	gonorrhea	gonorrhea	NOUN
cord-326631-7gd3hjc3	342	28	:	:	PUNCT
cord-326631-7gd3hjc3	342	29	transmission	transmission	NOUN
cord-326631-7gd3hjc3	342	30	dynamics	dynamic	NOUN
cord-326631-7gd3hjc3	342	31	and	and	CCONJ
cord-326631-7gd3hjc3	342	32	control	control	VERB
cord-326631-7gd3hjc3	342	33	an	an	DET
cord-326631-7gd3hjc3	342	34	explicit	explicit	ADJ
cord-326631-7gd3hjc3	342	35	solution	solution	NOUN
cord-326631-7gd3hjc3	342	36	for	for	ADP
cord-326631-7gd3hjc3	342	37	z	z	NOUN
cord-326631-7gd3hjc3	342	38	expressed	express	VERB
cord-326631-7gd3hjc3	342	39	in	in	ADP
cord-326631-7gd3hjc3	342	40	terms	term	NOUN
cord-326631-7gd3hjc3	342	41	of	of	ADP
cord-326631-7gd3hjc3	342	42	elementary	elementary	ADJ
cord-326631-7gd3hjc3	342	43	functions	function	NOUN
cord-326631-7gd3hjc3	342	44	is	be	AUX
cord-326631-7gd3hjc3	342	45	not	not	PART
cord-326631-7gd3hjc3	342	46	possible	possible	ADJ
cord-326631-7gd3hjc3	342	47	,	,	PUNCT
cord-326631-7gd3hjc3	342	48	but	but	CCONJ
cord-326631-7gd3hjc3	342	49	eq	eq	X
cord-326631-7gd3hjc3	342	50	.	.	PUNCT
cord-326631-7gd3hjc3	342	51	(	(	PUNCT
cord-326631-7gd3hjc3	342	52	4	4	NUM
cord-326631-7gd3hjc3	342	53	)	)	PUNCT
cord-326631-7gd3hjc3	342	54	can	can	AUX
cord-326631-7gd3hjc3	342	55	be	be	AUX
cord-326631-7gd3hjc3	342	56	solved	solve	VERB
cord-326631-7gd3hjc3	342	57	explicitly	explicitly	ADV
cord-326631-7gd3hjc3	342	58	for	for	ADP
cord-326631-7gd3hjc3	342	59	z	z	NOUN
cord-326631-7gd3hjc3	342	60	in	in	ADP
cord-326631-7gd3hjc3	342	61	terms	term	NOUN
cord-326631-7gd3hjc3	342	62	of	of	ADP
cord-326631-7gd3hjc3	342	63	the	the	DET
cord-326631-7gd3hjc3	342	64	lambert	lambert	PROPN
cord-326631-7gd3hjc3	342	65	w	w	PROPN
cord-326631-7gd3hjc3	342	66	function	function	PROPN
cord-326631-7gd3hjc3	342	67	(	(	PUNCT
cord-326631-7gd3hjc3	342	68	weisstein	weisstein	PROPN
cord-326631-7gd3hjc3	342	69	)	)	PUNCT
cord-326631-7gd3hjc3	342	70	,	,	PUNCT
cord-326631-7gd3hjc3	342	71	when	when	SCONJ
cord-326631-7gd3hjc3	342	72	the	the	DET
cord-326631-7gd3hjc3	342	73	infectious	infectious	ADJ
cord-326631-7gd3hjc3	342	74	period	period	NOUN
cord-326631-7gd3hjc3	342	75	is	be	AUX
cord-326631-7gd3hjc3	342	76	exponentially	exponentially	ADV
cord-326631-7gd3hjc3	342	77	distributed	distribute	VERB
cord-326631-7gd3hjc3	342	78	,	,	PUNCT
cord-326631-7gd3hjc3	342	79	i.e.	i.e.	X
cord-326631-7gd3hjc3	342	80	,	,	PUNCT
cord-326631-7gd3hjc3	342	81	f	f	PROPN
cord-326631-7gd3hjc3	342	82	(	(	PUNCT
cord-326631-7gd3hjc3	342	83	t	t	NOUN
cord-326631-7gd3hjc3	342	84	)	)	PUNCT
cord-326631-7gd3hjc3	343	1	=	=	PRON
cord-326631-7gd3hjc3	343	2	γ	γ	X
cord-326631-7gd3hjc3	343	3	e	e	NOUN
cord-326631-7gd3hjc3	343	4	−γ	−γ	PROPN
cord-326631-7gd3hjc3	343	5	t	t	PROPN
cord-326631-7gd3hjc3	343	6	,	,	PUNCT
cord-326631-7gd3hjc3	343	7	we	we	PRON
cord-326631-7gd3hjc3	343	8	have	have	VERB
cord-326631-7gd3hjc3	343	9	l(τ	l(τ	NOUN
cord-326631-7gd3hjc3	343	10	,	,	PUNCT
cord-326631-7gd3hjc3	343	11	t	t	PROPN
cord-326631-7gd3hjc3	343	12	)	)	PUNCT
cord-326631-7gd3hjc3	343	13	=	=	NOUN
cord-326631-7gd3hjc3	344	1	f	f	PROPN
cord-326631-7gd3hjc3	345	1	(	(	PUNCT
cord-326631-7gd3hjc3	345	2	t	t	NOUN
cord-326631-7gd3hjc3	345	3	)	)	PUNCT
cord-326631-7gd3hjc3	345	4	.	.	PUNCT
cord-326631-7gd3hjc3	346	1	thus	thus	ADV
cord-326631-7gd3hjc3	346	2	eq	eq	PROPN
cord-326631-7gd3hjc3	346	3	.	.	PUNCT
cord-326631-7gd3hjc3	346	4	(	(	PUNCT
cord-326631-7gd3hjc3	346	5	11f	11f	NUM
cord-326631-7gd3hjc3	346	6	)	)	PUNCT
cord-326631-7gd3hjc3	346	7	can	can	AUX
cord-326631-7gd3hjc3	346	8	be	be	AUX
cord-326631-7gd3hjc3	346	9	writtenlet	writtenlet	VERB
