Stochastic optimal control of pre-exposure prophylaxis for HIV infection

Abstract: In this paper, we study the stochastic optimal control problem for the PReP vaccine in the stochastic model for HIV/AIDS with PReP. By using the stochastic maximum principle, we derive the stochastic optimal control of PReP for the unconstrained control problem, as well as for two different types of budget constrains. We illustrate the results by a numerical example. We first study the PReP stochastic differential equation dynamics with a constant, deterministic PReP treatment rate. Then, we compare this to the stochastic optimal control in the unconstrained case.