Sensitivity Analysis Of A Tuberculosis (TB) Mathematical Model
Vaachia, V.; Terna, M. T.
Show 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 R0 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 R0 and varies inversely with R0. Graphical simulation of the model parameters was performed. It was observed that model parameters such as infection rate ({beta}), recruitment rate ({pi}) and rate of movement from latent to active TB () are directly proportional to the basic reproduction numberR0. Finally, it is observed that the basic reproduction number R0 is a decreasing function of the recovery rate ({gamma}) and natural death rate ().
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