A Mathematical Model of Tuberculosis with Respect to Drug Resistance to the First and Second Line of the Treatment

Abstract

In this research paper work, we developed a mathematical model for tuberculosis (TB). Disease was formulated and rigorously analyzed. The model sub-divided into six compartments. The model has equilibria; the diseases-free equilibrium. The equilibrium states were obtained and analyzed for their stability relatively to the effective reproduction number. The result shows that the disease-free equilibrium state was stable state is established. We able to show that the TB disease free equilibrium is locally and globally asymptotically stable R0<1. Using the number of treatment, individual increases as the rate at which recovery rate of which makes them recovery back from disease. The analytical solution was obtained using homotopy perturbation method and effective reproduction number was computed to measure the relative impact for individual or combined intervention for effective disease control. Numerical simulations of the model show that lose their immunity at the rate decreases at immunity wanes of which makes them susceptible back to disease is the most effective way to combat the epidemiology of TB.