Backward Bifurcation and the Endemic Equilibrium for an HIV/AIDS - Tuberculosis Co infection Model

Abstract

This study proposes a model that describes the dynamics of HIV/AIDS Co infection with Tuberculosis (TB) using systems of nonlinear ordinary differential equations. A characteristic of nonlinear oscillating systems is the sudden change in behavior which occurs as a parameter passes through a critical value called a bifurcation point. A bifurcation point is a point in parameter space where the number of equilibrium points, or their stability properties, or both, change. The results of the study shows that the Co infection model  has a diseases-free equilibrium (DFE) which is globally asymptotically unstable implying that the stable  endemic state co-exists with the DFE. Numerical simulations are carried out to illustrate the backward bifurcation phenomenon.

Keywords: Backward bifurcation,  Equilibria, Co-infection, Stability .

DOI: 10.7176/MTM/9-4-05

Publication date: April 30^th 2019.