Global stability of a stage-structured epidemic model with a nonlinear incidence

摘要

In this paper, a stage-structured epidemic model with a nonlinear incidence with a factor Sp is investigated. By using limit theory of differential equations and Theorem of Busenberg and van den Driessche, global dynamics of the model is rigorously established. We prove that if the basic reproduction number R0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out; if R0 is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable. Numerical simulations support our analytical results and illustrate the effect of p on the dynamic behavior of the model.