A theoretical study on mathematical modelling of an infectious disease with application of optimal control

In this paper, we propose and analyze an epidemic problem which can be controlled by vaccination as well as treatment. In the first part of our analysis we study the dynamical behavior of the system with fixed control for both vaccination and treatment. Basic reproduction number is obtained in all possible cases and it is observed that the simultaneous use of vaccination and treatment control is the most favorable case to prevent the disease from being epidemic. In the second part, we take the controls as time dependent and obtain the optimal control strategy to minimize both the infected populations and the associated costs. All the analytical results are verified by simulation works. Some important conclusions are given at the end of the paper.