On the SEIR Model Based on the Maximum Principle to Suppress Simultaneously the Susceptible Population as well as the Economic Loss

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 SEIR model on the basis of 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 a maximization scheme in terms of an appropriate objective function. Furthermore one may elucidate the dependence of the susceptible population and the economic loss on a model parameter related to the degree of the economic loss in the objective function as well as on the minimal ratio under optimal control. In conclusion one may find that there exists a tradeoff relation between the suppress effect and the corresponding economic loss under the optimal control based on the maximum principle scheme.