STABILITY AND BIFURCATION OF AN SIRS EPIDEMIC MODEL

In this paper we propose an analytical approach to obtain an exact global solution for the classical SIRS epidemic mathematical model. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and disease-free equilibrium is discussed. By comparison arguments, it is proved that if basic reproductive number R0 < 1, the disease-free equilibrium is globally asymptotically stable. If R0 > 1 by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the endemic equilibrium.