Modeling the transmission dynamics of tuberculosis in Khyber Pakhtunkhwa Pakistan

Abstract

This article addresses the dynamics of the bacterial disease tuberculosis in Khyber Pakhtunkhwa, Pakistan, through a mathematical model. In this work, the latent compartment is divided into slow and fast kinds of progresses. The model is parameterized based on the reported tuberculosis-infected cases in Khyber Pakhtunkhwa for the period 2002–2017. We obtain the basic reproduction number R0 of the model using the next-generation method. The estimated value of R0 for the given period is approximately 1.38. Furthermore, it is shown that the model has two types of equilibria: disease-free and endemic equilibriums. The global stability analysis of the model equilibria is shown via Lyapunov functions. We also perform the sensitivity analysis of R0 and present their corresponding graphical results to examine the relative importance of various model parameters to tuberculosis transmission and prevalence. Finally, some numerical simulations are done for the estimated parameters and the key parameters effects are considered on the curtailing tuberculosis disease. From the numerical results and model sensitivity analysis, it is found that the spread of tuberculosis can be minimized by increasing the treatment rate ℽ of infected people and decreasing the effective disease transmission rate β and the rate δ at which the individuals leave treated class reenter infected classes.