Mathematical Modeling of Tuberculosis Transmission Dynamics with Vaccination and Drug Resistance

Abstract

The spread of tuberculosis, a disease that is communicable and caused by the Bacillus mycobacterium, is the main topic of this study. Vaccination and drug-resistant patients are the subjects of particular attention. Patients who are freshly infected with tuberculosis undergo an average treatment duration of 6–8 months; however, for those who are multidrug resistant, the treatment can extend up to 2.5 years. Despite decades of study, widespread use of a vaccine, and an apparent push by the WHO to promote a single global management strategy in recent years, tuberculosis continues to be the second most prevalent infectious killer, following COVID-19. In 2021, experts estimate that 10.6 million people worldwide contracted tuberculosis, either latently or actively. Using a mathematical model, we performed an investigation to investigate the dynamics of tuberculosis transmission in humans. We conducted sensitivity analysis on the model to identify the primary parameters impacting the disease's propagation and establish the fundamental reproduction number. The analysis's findings can inform the proposal of effective intervention techniques. The research looked at the tuberculosis endemic equilibrium point and assessed the stability on a local and global scale related to the disease-free equilibrium point. We examined the effects of the transmission rate on the backward bifurcation of the model. Global stable endemic equilibrium coexists with stable disease-free equilibrium (DFE). It has been demonstrated that vaccine efficacy and a small percentage of the population who receive vaccinations contribute equally to reducing the burden of disease. The drug-resistant group is a bigger concern than the infected group, which shows that health workers and government agencies need to be extra careful to keep an eye on this silent source of tuberculosis transmission. Based on the numerical simulation, it can be demonstrated that, if vaccination coverage and efficacy are both quite high, it is possible to effectively control tuberculosis in a population by using an imperfect vaccination. Health professionals and government organizations should monitor this covert method of tuberculosis transmission, as these findings indicate that the group resistant to drugs poses a greater threat than those who are afflicted.