Numerical Solution of a Mathematical Model of HIV/AIDS on Progression from Latent Tuberculosis to Infectious Tuberculosis

Abstract

In this study, a Mathematical Model on the effects of HIV/AIDS on the progression from Latent Tuberculosis to infectious Tuberculosis was formulated using a modified Susceptible-Infected-Susceptible (SIS) model. Parameters for speedy progression from latently infected tuberculosis to infectious tuberculosis resulting from immunosuppressive condition caused by HIV/AIDS were incorporated into the model given rise to a system of four non-linear differential equations which was solved using fourth order Runge-Kutta method and the resulted algorithm was coded using Mapple software. The result shows that Tuberculosis progress faster from Latent Tuberculosis to Infectious Tuberculosis when there is high compromise of immune system of TB patients by HIV. Effective administration of Antiretroviral drugs to HIV patients will decrease the rate of progression from Latent Tuberculosis to Infectious Tuberculosis. However, high Latent TB treatment was also found to eradicate Tuberculosis with time despite the immunosuppressive condition caused by HIV