Stability and Bifurcation Analysis of Logistically Grown SIR Model with External Infection Effect of the Susceptible Class and Effect of Loss of Immunity of the Recovered Class

Abstract

In this paper we consider an SIR model with logistic growth rate of susceptible where rate of incidence is directly affected by inhibitory factors or social or psychological factors and infection through interaction and external source also taken into consideration. In our model three equilibrium points are obtained under different conditions. One of them is trivial equilibrium point which always exists and unstable in nature in all circumstance. The other two are endemic equilibrium points exist under certain conditions and one of them becomes non-feasible under another condition. Here we examine the hopf-bifurcation depending on carrying capacity. Finally numerical simulations are done.