Abstract
Abstract In this paper, we study an SIRI epidemic model with nonlinear incidence rate and latent period, namely k I ( t − τ ) S 1 + α I h ( t − τ ) , which describes the psychological effect of certain serious diseases on the community when the size of the set of infective individuals is getting larger. We first obtain the threshold dynamics on the global stability of the equilibria for the model without latent period, and then we analyze the stability and Hopf bifurcation for the model with the latent period. The results show the influence of nonlinear incidence rate and latent period on the dynamical behaviors of the SIRI model. The examples and its simulations are given to illustrate the obtained results.
Highlights
An SIRI epidemiological model in a population was formulated by Tudor [ ], which consists of a system with three compartments: susceptible, infective, and removed individuals, labeled by S, I, R
It can be seen that the nonlinear incidence rate and latent period influence the dynamical behaviors of the SIRI model
It follows from the Lyapunov-Lasalle invariant principle in [, ] that the disease-free equilibrium (DFE) E is globally asymptotically stable
Summary
An SIRI epidemiological model in a population was formulated by Tudor [ ], which consists of a system with three compartments: susceptible, infective, and removed individuals, labeled by S, I, R. In Section , we obtain the threshold dynamics on stability for the model without the latent period (i.e., τ = ). It can be seen that the nonlinear incidence rate and latent period influence the dynamical behaviors of the SIRI model.
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