id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3727	Oumarou, Abba Mahamane; Bisso, Saley	Modelling and Simulating a Transmission of COVID-19 Disease: Niger Republic Case	2020	18	.pdf	application/pdf	4808	254	70	On the definition and compu- tation of the basic reproduction ratio r0 in the model of infectious disease in hetero- geneous populations. Pλ = (µ+ λ)(λ5 + a1λ 4 + a2λ 3 + a3λ 2 + a4λ+ a5), (17) with: a1 = 5µ+ µ1 + α+ α1 + α2 + γ + θ1 + θ2 + θd > 0, (18) a2 = (µ+α)(µ+α1 +α2) + (2µ+α+α1 +α2)(2µ+ γ + θ1 + θ2) + (2µ+α+α1 +α2)× (µ+ µ1 + θd) + (µ+ γ)(µ+ θ1 + θ2) + (2µ+ γ + θ1 + θ2)(µ+ µ1 + θd) + αβ > 0 (19) a3 = (µ+α)(µ+α1 +α2)(2µ+γ+θ1 +θ2)+(µ+α)(µ+α1 +α2)(µ+µ1 +θd)+(µ+γ)× (µ+θ1 +θ2)(2µ+α+α1 +α2)+(2µ+α+α1 +α2)(2µ+γ+θ1 +θ2)(µ+µ1 +θd)+(µ+γ)× (µ+ θ1 + θ2)(µ+ µ1 + θd) + αβ(3µ+ µ1 + γ + θ1 + θ2 + θd − α1 − 1) > 0 (20) a4 = (µ+ α)(µ+ α1 + α2)(µ+ γ)(µ+ θ1 + θ2) + (µ+ α)(µ+ α1 + α2)(µ+ µ1 + θd)× (2µ+γ+θ1+θ2)+(µ+γ)(µ+θ1+θ2)(µ+µ1+θd)(2µ+α+α1+α2)+αβ(µ+θ1+θ2)(µ+µ1+θd) + αβ(2µ+ µ1 + θ1 + θ2 + θd)(µ+ γ)− αβθ2α2 − αβα1(2µ+ µ1 + θ1 + θ2 + θd) − αβ(2µ+ µ1 + γ + θd) > 0 (21) A. M. Oumarou, S. Bisso / Eur.	cache/ejpam-3727.pdf	txt/ejpam-3727.txt