Optimal control of a delayed HIV model

TL;DR

This paper develops an optimal control framework for a delayed HIV-1 infection model, incorporating drug delays and analyzing stability, with numerical solutions for minimizing virus load and treatment costs.

Contribution

It introduces a novel delayed HIV model with control and pharmacological delays, and formulates an optimal control problem with numerical solutions.

Findings

Stability of equilibrium points established.

Optimal control strategies reduce virus concentration.

Numerical simulations demonstrate effective treatment protocols.

Abstract

We propose a model for the human immunodeficiency virus type 1 (HIV-1) infection with intracellular delay and prove the local asymptotical stability of the equilibrium points. Then we introduce a control function representing the efficiency of reverse transcriptase inhibitors and consider the pharmacological delay associated to the control. Finally, we propose and analyze an optimal control problem with state and control delays. Through numerical simulations, extremal solutions are proposed for minimization of the virus concentration and treatment costs.