Mathematical modelling and simulation of HIV dynamics

TL;DR

This paper develops and analyzes a mathematical model of HIV within-host dynamics, incorporating treatment effects, to understand how therapy timing and strength influence viral suppression and disease progression.

Contribution

It introduces a nonlinear differential equation model with treatment extensions, analyzing stability and simulating therapy scenarios to explore HIV dynamics under various treatment strategies.

Findings

Therapy strength and timing significantly affect viral suppression.

Model stability depends on specific equilibrium conditions.

Simulations show potential for sustained viral suppression with optimal treatment timing.

Abstract

We study within-host HIV dynamics using a three--component nonlinear ordinary differential equation model for healthy CD4$^{+}$ T cells, infected CD4$^{+}$ T cells, and free virus. In addition to the baseline model without treatment, we consider two treatment extensions that incorporate antiretroviral therapy: (i) separate efficacy terms for Reverse Transcriptase inhibitors and Protease inhibitors acting on infection and virus production, and (ii) a simplified formulation using a single combined efficacy parameter. For each model we determine equilibrium points and apply linearization to obtain the Jacobian matrix and local stability conditions near equilibrium. We perform numerical simulations using the classical fourth--order Runge--Kutta method to illustrate the evolution of cell populations and viral load under different therapy levels and treatment start times, including continuous treatment scenarios. The simulations highlight how therapy strength and timing shape transient behavior and can lead to sustained viral suppression.