Towards Modeling HIV Long Term Behavior

TL;DR

This paper introduces a mathematical model to predict HIV progression to AIDS, analyzing long-term dynamics and equilibria, providing insights into disease progression and stability conditions.

Contribution

It presents a novel dynamical model for HIV/AIDS progression, identifying conditions for stable and unstable disease states, advancing understanding of long-term infection behavior.

Findings

Two equilibria identified: one stable (long-term HIV without AIDS), one unstable (progression to AIDS).

Model sensitivity indicates parameter variations significantly affect disease trajectory.

Provides a framework for understanding long-term HIV/AIDS dynamics.

Abstract

The precise mechanism that causes HIV infection to progress to AIDS is still unknown. This paper presents a mathematical model which is able to predict the entire trajectory of the HIV/AIDS dynamics, then a possible explanation for this progression is examined. A dynamical analysis of this model reveals a set of parameters which may produce two real equilibria in the model. One equilibrium is stable and represents those individuals who have been living with HIV for at least 7 to 9 years, and do not develop AIDS. The other one is unstable and represents those patients who developed AIDS in an average period of 10 years. However, further work is needed since the proposed model is sensitive to parameter variations.