STABILITY ANALYSIS OF AN SIR EPIDEMIC MODEL WITH SPECIFIC NONLINER INCIDENCE RATE

Abstract

We study an SIR epidemic model with a specific non linear incidence rate function. The stability of the disease-free equilibrium and the endemic equilibrium are found and an appropriate Dulac function was constructed for investigating the global stability of an endemic equilibrium. We illustrate the theoretical results by carrying numerical simulation.

Keywords: epidemic, nonlinear incidence, inhibitory effect, disease-free equilibrium, endemic equilibrium, global stability.

2010 AMS Subject Classification: 92D30, 93A30, 93D30, 34D23.