Optimal control strategies for a reaction-diffusion epidemic system

This contribution mainly focuses on the optimal control problems of an epidemic system governed by reaction-diffusion equations. In order to reduce the cost caused by control process,vaccines and treatments, 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 firstly. Then the existence, uniqueness and some estimates of the positive strong solution to the controlled system are acquired by employing the theories of semigroups of operators. After that, the existence of the optimal control strategies are proved by virtue of minimal sequence techniques. Subsequently, the first order necessary optimality conditions satisfied by the optimal control strategies are established by applying the methods of convex perturbation. Finally, a numerical example is given to illustrate the concrete realization of the results obtained in this paper. (C) 2018 Elsevier Ltd. All rights reserved.