GLOBAL ANALYSIS FOR A DELAYED SIV MODEL WITH DIRECT AND ENVIRONMENTAL TRANSMISSIONS

Abstract

In this paper, we propose a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions. For such model, we first introduce the basic reproduction number <i>R</i> by using the next generation matrix. And then global stability of the equilibria is discussed by means of Lyapunov functionals and LaSalle's invariance principle for delay differential equations, which shows that the infection-free equilibrium of the system is globally asymptotically stable if <i>R</i><1 and the epidemic equilibrium of the system is globally asymptotically stable for <i>R</i>>1: