SENSITIVITY ANALYSIS OF A TUBERCULOSIS (TB) MATHEMATICAL MODEL

Abstract In this work, we have constructed a Mathematical model for the transmission dynamics of tuberculosis TB. Feasibility and positivity of solutions of the model are determined and it is established that the model is well posed and that the solutions are all positive. The disease-free equilibrium (DFE) is also determined and the basic reproduction number R 0 is computed. Sensitivity analysis of the basic reproduction number is conducted to find parameters of the model that are most sensitive and should be targeted by intervention strategies. It was therefore, observed through sensitivity analysis that TB induced death (d) has a high impact on R 0 and varies inversely with R 0 . Graphical simulation of the model parameters was performed. It was observed that model parameters such as infection rate ( β ), recruitment rate ( π ) and rate of movement from latent to active TB ( α ) are directly proportional to the basic reproduction number R 0 . Finally, it is observed that the basic reproduction number R 0 is a decreasing function of the recovery rate ( γ ) and natural death rate ( μ ).