Near-optimal control of a stochastic SICA model with imprecise parameters

TL;DR

This paper develops a near-optimal control framework for a stochastic SICA epidemic model of HIV transmission, accounting for parameter uncertainties using advanced stochastic analysis tools.

Contribution

It introduces a novel approach to control HIV spread in a stochastic setting with imprecise parameters, providing necessary and sufficient conditions for near-optimal control.

Findings

Established bounds for state and co-state variables.

Derived necessary and sufficient conditions for control.

Applied stochastic inequalities like Burkholder-Davis-Gundy.

Abstract

An adequate near-optimal control problem for a stochastic SICA (Susceptible-Infected-Chronic-AIDS) compartmental epidemic model for HIV transmission with imprecise parameters is formulated and investigated. We prove some estimates for the state and co-state variables of the stochastic system. The established inequalities are then used to prove a necessary and a sufficient condition for near-optimal control with imprecise parameters. The proofs involve several mathematical and stochastic tools, including the Burkholder-Davis-Gundy inequality.