Modeling and bifurcation analysis of tuberculosis with the multidrug-resistant compartment incorporating chemoprophylaxis treatment - Kitaro, Damtew Bewket; Bole, Boka Kumsa; Rao, Koya Purnachandra (Frontiers in Applied Mathematics and Statistics, 2023)
Tuberculosis is a big health issue that is a reason for infectious mortality throughout the world. A new challenge for society that demands extensive work towards the right control strategies for TB is the emergence of drug-resistant TB. In this work, we constructed a mathematical model to study the effect of chemoprophylaxis treatment on the transmission of tuberculosis with drug resistant compartment. An analysis of the stabilities is done along with an investigation into the possibility of endemic and disease-free equilibrium. The qualitative outcome of the model analysis shows that DFE is locally asymptotically stable for R less than 1, but the endemic equilibrium becomes globally asymptotically stable for R > 1. A bifurcation analysis is performed using the center manifold theorem, and it is found that the model shows evidence of forward bifurcation. Furthermore, sensitivity analysis of the model is thoroughly carried out, and numerical simulation is also performed. This study showed that the provision of chemoprophylaxis treatment for latently infected individuals significantly reduces the progression of exposed individuals to the infectious class and also to the drug resistant class, which in turn reduces the transmission of this disease at large.