Stability Analysis of Mathematical Modeling on the Spread of Tuberculosis Case Detection

Abstract

In this study, a mathematical model on the transmission dynamics of tuberculosis was formulated and analyzed. The basic reproduction number ( ) for each model is calculated and determined using the next generation method and condition for elimination (disease free equilibrium) or persistence (endemic equilibrium) in a population. Stability analysis shows that disease free equilibrium is locally asymptotically stable whenever the reproduction is less than unity. Furthermore, tuberculosis case detection continued to persist whenever the reproduction number exceeds unity. However, the models consisting of system of first order nonlinear differential equations.