AN SIR EPIDEMIC MODEL WITH NONLINEAR BIRTH PULSES

Abstract. An SIR epidemic model with logistic population dynamics and nonlinear birth pulses is considered in this paper. The basic reproductive number R0 is defined. We obtain the exact infection-free periodic solution of the impulsive epidemic system. By using the discrete dynamical system generated by a monotone, concave map for the population, we prove that the infection-free periodic solution is globally asymptotically stable if R0 < 1. We use standard bifurcation theory to show the existence of positive periodic solution if R0> 1. Numerical simulation is given in the paper