A dual delays epidemic model for TB with adaptive mobility behavior

Tuberculosis is a chronic infectious disease caused by Mycobacterium tuberculosis, primarily transmitted through the air. It has a long incubation period and complex infection dynamics, with its transmission characteristics significantly influenced by population mobility and infection risk-responsive behavior. According to reports from the World Health Organization (WHO), tuberculosis remains a severe global public health issue, particularly in developing countries, where its high transmission rate and mortality pose substantial challenges to socioeconomic development and healthcare resources. Therefore, investigating the key factors driving tuberculosis transmission is of great significance for global public health management. This paper investigates a dual delays SEIRm epidemic model for tuberculosis that incorporates mobility-adaptive behavior and a nonlinear transmission rate. The stability of these equilibria and the existence of Hopf bifurcations are analyzed. Finally, numerical simulations are performed to examine the impact of population mobility and time-delay factors on disease transmission. The simulation results indicate that properly controlled population movement can significantly reduce the spread of the epidemic. Although mobility responsiveness does not affect the basic number of reproductions, it can mitigate the peak of infections, thereby protecting a larger proportion of the susceptible population.