Stochastic optimal control of pre-exposure prophylaxis for HIV infection

TL;DR

This paper develops a stochastic optimal control framework for pre-exposure prophylaxis (PrEP) in HIV/AIDS, deriving optimal strategies under different constraints using stochastic maximum principle and illustrating with numerical examples.

Contribution

It introduces a novel stochastic control approach for PrEP treatment optimization considering budget constraints in HIV/AIDS models.

Findings

Optimal control strategies derived for different budget constraints.

Numerical example demonstrating the effectiveness of the control strategies.

Comparison between constant treatment rate and optimal stochastic control.

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.