Stability Analysis of a Deterministic Compartmental Model of Tuberculosis with Effect of HIV/AIDS on the Progression from Latent Class to Infectious Class.

Abstract

In 2015, there were an estimated 10.4 million new (incident) Tu- berculosis cases worldwide, of which 5.9 million (56%) were among men, 3.5 million (34%) among women and 1.0 million (10%) among children. People living with HIV accounted for 1.2 million (11%) of all new TB cases. Six countries accounted for 60% of the new cases: India, Indonesia, China, Nigeria, Pakistan and South Africa [3]. In this study we present a deterministic compartmental mathematical model for the dynamics of tuberculosis and incorporate parameters for slow and fast progression from latently infected tuberculosis to in- fectious tuberculosis using a modified SIS model to show the effect of HIV/AIDS on the spread of Tuberculosis. The disease free and endemic equilibrium states were established. The disease free equi- librium state was analyzed for stability using a modified version of Bellman and Cooke theorem [1].