Mathematical Analysis of a Tuberculosis Model Incorporating Vaccination, Treatment and Re-Infection

Tuberculosis (TB) remains to be a major global health challenge with complex dynamics influenced by various factors including transmission, vaccination, treatment and re-infection. In this paper, we formulate and analyze a mathematical model of TB transmission that incorporates vaccination, treatment and re-infection. The equilibrium points exist. The basic reproduction number R0 of the model was established. Both local and global stability analyses of the equilibrium points were conducted. In contrast to the endemic equilibrium, which displays a local and global stable state anytime R0 > 1, the disease-free equilibrium is locally and globally stable when R0 < 1. The system undergoes a forward bifurcation when R0 = 1. The graphical solutions illustrated that incorporating vaccination, treatment and re-infection in a TB transmission model is pivotal in determining the correct thresholds for controlling and finally curbing this disease in the population.