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342 DOI: 10.37398/JSR.2020.640247 Abstract: In this article, A SIR epidemic model with bilinear incidence rate has been proposed and the existing threshold requirements of all classifications of equilibrium points are obtained. Further, we study the global and local stability of the disease-free and endemic equilibriums of the model. An optimal control problem is formed and solved. Some numerical simulations works are carried out to demonstrate our results. In this process, our results generalized and improved any results in existing literature.

Stability Analysis of a Complex Dynamics of a SIR Epidemic Model with Bilinear Incidence Rate and Treatment