Stability Analysis of Epidemic Model with Time Delay In the Interaction of Susceptible and Infected Individuals

Abstract

In this paper, athree-compartment epidemic model with time delay  introduced in the interaction of susceptibleand infected individuals is considered and discussed local, global stability at its equilibrium points. Hopf bifurcation is used to identify the point at which system becomes unstable to stable. Numerical simulation is carried out to support the results using MATLAB. Numerical examples are presented in support of the increase in the transmission rate at a particular critical time delay parameter the system becomes unstable. Further, observed that due to increase in the additional transaction rate subject to fixed time delay, the system becoming unstable.