Stability and Optimal Control of a Delayed HIV Model

TL;DR

This paper models HIV infection dynamics with delays, analyzes stability criteria, and formulates an optimal control problem to improve treatment strategies while minimizing drug use.

Contribution

It introduces a delayed HIV model with stability analysis and formulates an optimal control framework considering incubation and pharmacological delays.

Findings

Derived stability conditions for infected and viral free states.

Formulated an optimal control problem balancing immune response and drug minimization.

Provided insights into effective treatment timing considering delays.

Abstract

We propose and investigate a delayed model that studies the relationship between HIV and the immune system during the natural course of infection and in the context of antiviral treatment regimes. Sufficient criteria for local asymptotic stability of the infected and viral free equilibria are given. An optimal control problem with time delays both in state variables (incubation delay) and control (pharmacological delay) is then formulated and analyzed, where the objective consists to find the optimal treatment strategy that maximizes the number of uninfected $CD4^{+}$ T cells as well as CTL immune response cells, keeping the drug therapy as low as possible.