Semi-Analytic Solution of HIV and TB Co-Infection Model

Abstract

In this work we developed and analyzed a mathematical model of HIV and TB coinfection. The model is a first order Ordinary Differential Equations, in which the human population is divided into six mutually- exclusive compartments namely; TB- Susceptible individuals (S), TB-Infected individuals (I), TB-Recovered individuals (R), HIV-Infected individuals (P1), Co- Infected individuals ( P2) and individuals with AIDS (A). The analytical solution is obtained using Homotopy Perturbation Method (HPM). The result of the numerical simulation shows that at high HIV and TB treatment rates; TB, AIDS and HIV/TB co-infection will be eradicated completely in the population. Also, early detection of HIV and TB cases and provision of early treatments can reduce the rate of infection, reduce the rate of progression of HIV infected individuals to AIDS and lowers co-infection.

Keywords: Tuberculosis, Human Immunodeficiency Virus, Co-infection, Treatment and Homotopy Perturbation Method (HPM).