OPTIMAL CONTROL PROBLEM FOR HOST-PATHOGEN MODEL

Abstract

In this paper, we study the distributed optimal control problem of a coupled system of the host-pathogen model. The system consists of the density of the susceptible host, the density of the infected host, and the density of pathogen particles. Our main goal is to minimize the infected density and also to decrease the cost of the drugs administered. First, we prove the existence and uniqueness of solutions for the proposed problem. Then, the existence of the optimal control is established and necessary optimality conditions are also derived.