Nonlinear Dynamics and Bifurcation Analysis in TB Models with Endogenous Reactivation and Exogenous Reinfection

Abstract

Tuberculosis (TB) is an airborne, contagious disease that poses a significant global health challenge. Despite being preventable and curable disease, it ranks as the 13th leading cause of mortality worldwide and the second deadliest infectious killer, following COVID-19. Exogenous reinfection plays a crucial role in TB dynamics as it significantly impacts the progression and persistence of the disease in a population. In TB-endemic regions, a large proportion of individuals remain in the latent phase. However, exogenous reinfection can destabilize latency and trigger progression to active TB, increasing the number of infectious cases. Research indicates that individuals previously infected with TB are at a higher risk of reinfection upon contact with infectious persons. In real life, most people take precautionary measures to protect themselves from reinfection, particularly if they have been exposed to or recovered from the disease. This behavior is often driven by increased awareness due to the dissemination of disease-related information. As a result of these information-induced behavioral changes, people tend to limit their interactions with infectious individuals to reduce the risk of both infection and reinfection. Firstly, a nonlinear mathematical model for TB transmission is proposed and analyzed, incorporating multiple saturated exogenous reinfections. Additionally, the model accounts for the progression of exposed individuals to active TB through endogenous reactivation. A sensitivity analysis of the basic reproduction number is performed to identify the parameters that have a pivotal role in controlling the disease. The study rigorously examines the existence and the stability of equilibrium points, providing valuable insights into the dynamics of the system. Numerical simulations further reveal complex nonlinear behaviors, such as Hopf-bifurcation, backward bifurcation, and the occurrence of endemic bubbles.