Mathematical Modeling of TB - HIV Co Infection, Case Study of Tigania West Sub County, Kenya

Abstract

TB is one of the leading causes of death among individuals infected with HIV/AIDS. A deterministic model for HIV/TB co-infection is presented and analyzed. The analysis of the model carried out includes the reproduction number, local stability of the disease free equilibrium, unique endemic equilibrium point, bifurcation analysis and sensitivity analysis of the model. The stability of the model shows that the model is stable if R0 < 1 and unstable otherwise. The research seeks to investigate the impact of HIV/AIDS on TB infections. Numerical simulation shows that HIV infection speeds the progression from exposed to infectious/active TB. The two diseases exhibit synergistic relationship where the infection of one disease accelerates the progression of the other. The model also seeks to confirm the need of HIV testing of all TB patients. From the sensitivity analysis and simulation, treatment reduces the spread of TB in the population among the TB infected and HIV/TB infected individuals. Numerical simulation was carried out using data from Tigania West Sub County Hospital.