Global stability and Hopf bifurcation of a delayed epidemiological model with logistic growth and disease relapse

Abstract

In this paper, an SIRI epidemiological model with relapse and a time delay describing the latent period of the disease is investigated. In the model, it is assumed that the susceptible population is subject to logistic growth in the absence of the disease. We show that the dynamic of the model are determined by the basic reproduction number. If the basic reproduction number is less than unity, then the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, Hopf bifurcation occurs as the time delay passes through a critical value. Numerical simulations are carried out to support our theoretical conclusion.