CONTROLLED SINGULAR EVOLUTION EQUATIONS AND PONTRYAGIN TYPE MAXIMUM PRINCIPLE WITH APPLICATIONS

Due to the propagation of new coronavirus (COVID-19) on the community, global researchers are concerned with how to minimize the impact of COVID-19 on the world. Mathematical models are effective tools that help to prevent and control this disease. This paper mainly focuses on the optimal control problems of an epidemic system governed by a class of singular evolution equations. The mild solutions of such equations of RiemannLiouville or Caputo types are special cases of the proposed equations. We firstly discuss well-posedness in an appropriate functional space for such equations. In order to reduce the cost caused by control process and vaccines, and minimize the total number of susceptible people and infected people as much as possible, an optimal control problem of an epidemic system is presented.

Automated summary

This paper focuses on the optimal control problems of an epidemic system governed by a class of singular evolution equations, aiming to minimize the impact of the COVID-19 pandemic on the world. By using mathematical models, the study explores well-posedness in an appropriate functional space and presents an optimal control problem to reduce costs and minimize the total number of susceptible and infected individuals.