id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5122	Pooda, Mathieu; Simpore , Yacouba; Traore , Oumar	Modeling and Multi-objective Optimal Control of Thedynamics of Counterterrorism in the Sahel Region in Africa	2024	35	.pdf	application/pdf	15231	551	66	Math, 17 (2) (2024), 870-904 896 dλ9 dt = −w5 + (λ9 − λ1)γ8 + (λ1 − λ5)c1π1 C(N −D) N2 + (λ1 − λ4)c1α1 C(C +A+ V ) (C + I)2 + (λ8 − λ1)c4α2 BC (C + I)2 +(λ2 − λ5)c1π5 R(N −D) N2 + (λ2 − λ9)c5ω3 R(R+A+ V +B) (R+ I)2 + (λ8 − λ2)c4ω4 BR (R+ I)2 +(λ3 − λ5)c1π3 A(N −D) N2 + (λ8 − λ3)c4ν3 BA I2 + (λ3 − λ9)c5ω2 A(A+ V +B) I2 + λ3ζ1 A(A+ V ) I2 +(λ4 − λ5)c1π2 V (N −D) N2 + λ4ζ2 V (A+ V ) I2 + (λ5 − λ6)c2β2 S ( N − (E + F + T ) ) N2 +(λ6 − λ7)c3β3 E ( N − (F + T ) ) N2 + (λ10 − λ7)τ1 F (A+ V ) (F + I)2 + (λ7 − λ10)c5β4 F (N − T ) N2 − λ7ζ3 F (A+ V ) (F + I)2 +(λ8 − λ10)c4θ2 PB (P + I)2 + (λ8 − λ5)c1π4 B(N −D) N2 + (λ8 − λ9)c5ω1 B(A+ V +B) I2 − λ8ζ4 B(A+ V ) I2 +(λ10 − λ8)τ2 B(A+ V ) I2 + (λ10 − λ9)c5θ1 P (P +A+ V +B) (P + I)2 + (λ9 − λ10)τ3 (A+ V )(A+ V +B) I2 +λ9 + (λ10 − λ5)c1π6 P (N −B) N2 + λ9ζ5 (A+ V )(A+ V +B) I2 dλ10 dt = −w6 + (λ10 − λ1)γ5 + (λ5 − λ1)c1π1 DC N2 + (λ5 − λ2)c1π5 DR N2 + (λ5 − λ3)c1π3 DA N2 + (λ5 − λ4)c1π2 DV N2 +(λ5 − λ8)c1π4 DB N2 + (λ10 − λ5)c1π6 D(N − P ) N2 + (λ6 − λ5)c2β2 S(E + F + T ) N2 + (λ7 − λ6)c3β3 E(F + T ) N2 +(λ9 − λ7)c5β4 TF N2 + (λ10 − λ8)c4θ2 BI (P + I)2 + (λ10 − λ9)c5θ1 TI (P + I)2 + λ10µ+ λ10η with transversality conditions λi(Tf ) Math, 17 (2) (2024), 870-904 878 dN dt = Λ− µN − δ1V − δ2A− δ3B − δ4T − δ5F − ηP Since A, V,B, T, F, P are positive functions and using the positivity of the functions δ1, δ2, δ3, δ4, δ5, given that the constants ζ1, ζ2, ζ3, ζ4, ζ5 and η are strictly positive as well, we get: dN dt ≤ Λ− µN Then d dt ( N − Λ µ ) ≤ −µ ( N − Λ µ )	cache/ejpam-5122.pdf	txt/ejpam-5122.txt