  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.
