| مستخلص: |
This paper deals with the diffusive epidemic model with saturated incidence and logistic growth, ∂S/∂t = dSΔS - βSI/1 + αI + rS (1 - S/K), x ∈ Ω, t > 0, ∂I/∂t = dIΔI - βSI/1 + αI - γS, x ∈ Ω, t > 0, where Ω ⊂ ℝN (N ∈ ℕ) is a bounded domain with smooth boundary and dS, dI, K, r, α, β, γ > 0 are constants. Setting R0 := Kβ/γ, Avila-Vales et al. [1] succeeded in showing that if R0 ≤ 1, then the disease-free equilibrium (K, 0) of the model with saturated treatment is globally asymptotically stable, whereas in the case R0 > 1 the model admits a constant endemic equilibrium (S*, I*) (S*, I * > 0), and it is unknown whether (S*, I*) is globally asymptotically stable or not. The purpose of this paper is to establish that the constant endemic equilibrium of the above model is globally asymptotically stable by constructing a strict Lyapunov functional. The construction is carried out by optimizing a function of two real variables through straightforward calculations, division into some cases and arrangement of several conditions. Moreover, to show that the functional is strict, some auxiliary function is introduced. [ABSTRACT FROM AUTHOR] |