  We study the problem of optimal control of the stochastic SIR model. Models
of this type are used in mathematical epidemiology to capture the time
evolution of highly infectious diseases such as COVID-19. Our approach relies
on reformulating the Hamilton-Jacobi-Bellman equation as a stochastic minimum
principle. This results in a system of forward backward stochastic differential
equations, which is amenable to numerical solution via Monte Carlo simulations.
We present a number of numerical solutions of the system under a variety of
scenarios.
