A Consideration on an Optimal Control Strategy of SIR Model on the Basis of the Maximum Principle

Abstract

In the present paper, we shall put forward an optimal control scheme to suppress the susceptible population as well as the involved economic loss with a fundamental SIR model on the basis of the Pontryagin's maximum principle theory. From the present numerical simulation results, it will be elucidated that there exists an optimal control scheme concerned with the control variable related to a ratio between the basic reproduction number and effective one under maximization scheme in terms of an appropriate objective function defined in the maximum principle approach. As a special case apart from the economic loss, it is found that the present results are reduced to the previous ones in which the economic loss was ignored in the objective function. Furthermore one may elucidate the dependence of the susceptible population and the economic loss on model parameters related to the degree the economic loss in the objective function as well as on the minimal ratio under optimal control. Then one may conclude that the susceptible populations are properly proportional to the economic loss under the presently proposed optimal control based on the maximum principle.