On Models of Tuberculosis with Exogenous Reinfection

Abstract

A deterministic mathematical model by Feng et. al (2000) for the dynamics of tuberculosis with exogenous reinfection is modified. The old model and the modified model are studied qualitatively. The two models were analysed for existence and stability of disease-free states. It was found that a disease free state exists in each case, which is locally asymptotically stable, an indication that the disease is controllable. Numerical studies show that with treatment, the population of infected people is less in the modified model than the old model, this show that control of TB will be achieve faster with the modified model than with the old model.

Keywords: Locally asymptotically stable, Treatment, Disease-free-equilibrium, Tuberculosis