STABILITY ANALYSIS OF A DELAYED SIR MODEL WITH NONLINEAR INCIDENCE RATE

In this paper a delayed SIR model with exponential demographic structure and the nonlinear incidence rate is formulated. We show if the basic reproductive number, denoted, is less than unity, disease free equilibrium is stable. Moreover, we prove that the endemic equilibrium is locally stable without delay and the endemic equilibrium is stable if the delay is under some condition. Finally a numerical example is also included to illustrate the effectiveness of the proposed model.