Modeling and bifurcation analysis of tuberculosis with the multidrug-resistant compartment incorporating chemoprophylaxis treatment

Tuberculosis is a major health problem that contributes significantly to infectious disease mortality worldwide. A new challenge for society that demands extensive work toward implementing the right control strategies for Tuberculosis (TB) is the emergence of drug-resistant TB. In this study, we developed a mathematical model to investigate the effect of chemoprophylaxis treatment on the transmission of tuberculosis with the drug-resistant compartment. An analysis of stabilities is performed along with an investigation into the possibility of endemic and disease-free equilibrium. The qualitative outcome of the model analysis shows that Disease Free Equilibrium (DFE) is locally asymptotically stable for R 0 < 1, but the endemic equilibrium becomes globally asymptotically stable for R 0 > 1. A bifurcation analysis was performed using the center manifold theorem, and it was found that the model shows evidence of forward bifurcation. Furthermore, the sensitivity analysis of the model was thoroughly carried out, and numerical simulation was also performed. This study showed that administering chemoprophylaxis treatment to individuals with latent infections significantly reduces the progression of exposed individuals to the infectious and drug-resistant classes, ultimately leading to a reduction in the transmission of the disease at large.