Mathematical Analysis of Transmission Dynamics of Tuberculosis with Recurrence based on Treatment

In this paper, a mathematical model for the transmission dynamic of tuberculosis (TB) with recurrence based on treatment is proposed and analyzed for the stability of infected states. The disease free and endemic equilibrium are locally stable if they are less than unity and unstable if greater than unity. The reproduction number is also derived and used to explore the existence and stability of equilibrium points of the proposed model. It has been shown that the timely treatment to tuberculosis lead to the effective control of TB disease. Further the sensitivity analysis suggests that the efficacy of the treatment has a significant impact in the prevention and controlling of TB disease in the community.