Optimal control strategies for an ecological model including infection and competition

Abstract

This contribution is concerned with the application of optimal control theories and methods to an ecosystem. There are four major ingredients. The first ingredient is to present an optimal control problem for an ecosystem including infection and competition. The second ingredient is the existence results, which assert that in a given Hilbert space the controlled system admits a unique strong solution and the optimal control problem has at least one optimal pair. The third, which is the main new ingredient of this paper, is a maximum principle for the optimal control problem. The first-order necessary optimality condition for the optimal control is established by employing dual techniques. It provides a theoretical basis for the design of the optimal control strategy. The fourth ingredient is an example and its numerical simulation, which further confirm the results of this paper.