A dual delays epidemic model for TB with adaptive mobility behavior

Qun Dai; Longkun Zhang; Qun Dai; Longkun Zhang

doi:10.3934/math.2025683

AIMS Mathematics

2025, Volume 10, Issue 7: 15231-15263. doi: 10.3934/math.2025683

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Research article

A dual delays epidemic model for TB with adaptive mobility behavior

Qun Dai ,
Longkun Zhang ^,

School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China

Received: 11 April 2025 Revised: 13 June 2025 Accepted: 24 June 2025 Published: 02 July 2025
MSC : 34C23, 93A30

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.
- mobility-adaptive behavior,
- tuberculosis,
- nonlinear transmission rate,
- time delays,
- stability,
- Hopf bifurcation
Citation: Qun Dai, Longkun Zhang. A dual delays epidemic model for TB with adaptive mobility behavior[J]. AIMS Mathematics, 2025, 10(7): 15231-15263. doi: 10.3934/math.2025683

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Abstract

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.

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