Modeling the Impact of case detection on the transmission dynamics of tuberculosis

Abstract

Tuberculosis (TB) is a contagious disease which can cause death. In this paper, a non-linear model is proposed and analyzed by assuming reduction in transmission due to case detection. The dampening in the transmission term is modelled as Holling type II function. Additionally, impact of media is incorporated by including an exponential decay factor in the movement of individuals from exposed class to the class of undetected infectives. The basic reproduction number R0 is computed. All possible equilibria of the models are obtained and stability of these equilibria are discussed in details. The proposed model exhibits backward bifurcation for some set of parameters, which suggests that reducing R0 below one is not enough to make disease-free equilibrium to be globally stable. Parameter estimation is performed using real-life data of different states of India where TB is endemic. Numerical simulations are presented to illustrate our analytical findings.