Enumerative numerical solution for optimal control using treatment and vaccination for an SIS epidemic model

Abstract

Optimal control problems in mathematical epidemiology are often solved by Hamiltonian methods. However, these methods require conditions on the problem to guarantee that they give global solutions. Because of the improved computational power of modern computers, numerical approximate solutions that systematically try a large number of possibilities have become practical. In this paper we give an efficient implementation of an enumerative numerical solution method for an optimal control problem, which applies to cases where standard methods cannot guarantee global optimality. We demonstrate the method on a model where vaccination and treatment are used to control the level of prevalence of an infectious disease. We describe the solution algorithm in detail, and verify the method with simulations. We verify that the enumerative numerical method produces solutions that are locally optimal.