Bifurcation and Stability Analysis of Delayed SIR Model

Abstract

In this paper, an SIR epidemic model is investigated and analysed by incorporating an incubation time delay in identification of infected population. The state variables considered are:susceptible, infected and recovered host individuals. The non-zero interior equilibrium is calculated. By applying the time delay as a bifurcation parameter, the local stability of the endemic equilibrium is studied and the condition which is absolutely stable or conditionally stable is established. Furthermore, a Hopf bifurcation occurs under certain conditions. Numerical simulations are carried out using MATLAB. to illustrate the main results.