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.
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