Dynamical behaviors of an SIRI epidemic model with nonlinear incidence and latent period

Abstract

Full list of author information is available at the end of the article Abstract In this paper, we study an SIRI epidemic model with nonlinear incidence rate and latent period, namely kI(t-τ)S/1+αIh(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. © 2014 Authors.