# Global Stability for a HIV/AIDS Model

## TL;DR

This paper analyzes the global stability of a HIV/AIDS population model with constant recruitment and mass action incidence, establishing conditions for disease-free and endemic equilibrium stability using Lyapunov methods.

## Contribution

It provides new theoretical results on the existence, uniqueness, and global stability of equilibria in a HIV/AIDS model with variable population size.

## Key findings

- Existence and uniqueness of disease-free and endemic equilibria.
- Global stability of these equilibria established.
- Conditions under which the disease persists or dies out.

## Abstract

We investigate global stability properties of a HIV/AIDS population model with constant recruitment rate, mass action incidence, and variable population size. Existence and uniqueness results for disease-free and endemic equilibrium points are proved. Global stability of the equilibria is obtained through Lyapunov's direct method and LaSalle's invariance principle.