Solving the inverse problem of an SIS epidemic reaction-diffusion model by optimal control methods

In this contribution, a novel inverse problem on an SIS epidemic reaction-diffusion model is investigated by employing the optimal control methods. By setting a proper regular cost functional and choosing the coefficients to be identified as control variables, we embed the original inverse problem which is very difficult to solve into an optimal control problem. The existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established, respectively. In particular, the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques.