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Dynamics of Delayed Sirs Epidemic Model with a Non-Linear Incidence Rate

Appa Rao Dokala*, Shaik Kalesha Vali S. **, Papa Rao A. V.***

* Department of Mathematics, IIIT Srikakulam, RGUKT, Andhra Pradesh, India.

**-*** Department of Mathematics, JNTUK, University College of Engineering, Vizianagaram, Andhra Pradesh, India.

Periodicity:July - September'2019
DOI : https://doi.org/10.26634/jmat.8.3.16707

Abstract

In this work, we consider an SIRS epidemic model with a non-linear incidence rate with time delay. The time delay is incorporated in susceptible population with the interaction of susceptible (S) and removable (R) population. We also induce the saturated incidence rate in S, R population. By analyzing the model, the local stability of an endemic equilibrium point is discussed. The system undergoes Hopf bifurcation. The analytical results are supported with numerical simulation using MATLAB and it is shown that the system is locally asymptotically stable and exhibit Hopf bifurcation.

Keywords

Disease Free, Endemic Equilibrium Point, Local Stability, Hopf Bifurcation.

How to Cite this Article?

Dokala, A. R., Vali, S. K., and Rao, P. A. V. (2019). Dynamics of Delayed Sirs Epidemic Model with a Non-Linear Incidence Rate. i-manager's Journal on Mathematics, 8(3), 17-27. https://doi.org/10.26634/jmat.8.3.16707

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