An application of the Maximum Principle to design control strategies for disease outbreaks
We investigate an application of the Pontryagin Maximum Principle to control the severity of an epidemic, described by the well-known SIR compartment model of spreading disease. Our main objective is to demonstrate how an optimal control problem can be formulated, with the goal of minimizing the total infected population at minimal cost. We consider a control which decreases the basic reproduction number in the SIR equations as a means to model mask usage and social distancing. Solutions for both a linear and non-linear running cost are derived by applying the Maximum Principle. The resulting system of ODE’s is then solved numerically via the shooting method to find the optimal control and associated SIR trajectory. This is a joint work with Colin Clark.