Stability Analysis of a Deterministic Mathematical Model for Transmission Dynamics of Tuberculosis

Despite all efforts to curb and exterminate the menace of Tuberculosis (TB) epidemics on the human population, the disease still remains one of the major causes of death, with one –third of the world’s population infected. In this paper, we study a deterministic mathematical model to have a better insight in the transmission dynamics of TB. The model is shown to have disease-free and endemic equilibria and their local stabilities are established using the basic reproduction number, Ro. If Ro < 1, the infection can be controlled and then eradicated and when Ro > 1, the disease will persist. Numerical simulations are performed to validate the theoretical results. KeywordsMathematical Model, Tuberculosis, Infectious Disease, Disease-free, Endemic, Equilibrium, Epidemics, Local Stability, Basic Reproduction Number.