title: Global stability analysis of a delayed susceptible-infected-susceptible epidemic model.
abstract: We study a susceptible-infected-susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0>1, then the endemic equilibrium is globally asymptotically stable. It is remarkable that the model dynamics is independent of the probability of immunity lost.
authors: a Department of Mathematics , Southeast Missouri State University , Cape Girardeau , MO 63701 , USA.
authors: Calah
authors: C
authors: Paulhus
authors: Xiang-Sheng
authors: XS
authors: Wang
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D004198:Disease Susceptibility / Q000453:epidemiology*; D058872:Epidemics; D006801:Humans; D008954:Models, Biological
keywords: 34K20; 92D30; Lyapunov functional; Lyapunov–LaSalle invariance principle; SIS model; distributed delay; global stability