Sensitivity Analysis of Mathematical Modeling of Tuberculosis Dynamics with a Control Measure

Abstract

Tuberculosis is a global threat to human existence. A model to investigate the transmission of tuberculosis was constructed and analysed. The threshold quantity ( R_0) that predicts the existence or extinction of the disease in a population was computed. It was found that the local stability is asymptotically stable when the basic reproduction number is less than unity at the disease-free – equilibrium point. A Lyapunov function was constructed in order to analyse the global stability which was proved to be globally asymptotically stable when the threshold quantity is less or equal to unity. Sensitivity analysis was conducted on the basic reproduction number in order to determine the parameters of the model that are most sensitive as a way to deduce suitable control measures. Numerical simulations are carried out, discussions were made and results are presented in graphical forms.