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Global asymptotic stability of an age-structured tuberculosis model: An analytical method to determine kernel coefficients in Lyapunov functional

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  • Chen, Yi
  • Wang, Lianwen
  • Zhang, Jinhui

Abstract

Tuberculosis (TB) is a slowly progressive and chronic long-lasting communicable disease and several significant age-dependent heterogeneous factors are involved in TB transmission. To be specific, the individual susceptibility to TB varies with the ages during their life time, the current BCG vaccine effectiveness wanes since vaccination. And the rate of progression from latent TB infection to active TB, and the infectiousness of TB patients, the rate of treatment success for the patients and the risk of relapse for recovered individuals are also dependent on the sojourn time elapsed since the individuals enter into related compartmental classes. Based on the model framework developed by Li et al. (2022) a novel PDE TB model structured by ages of susceptibility, vaccination, latency, infection, treatment and relapse is formulated to evaluate the influences of the class-age structure on TB transmission. Global dynamical properties, including local stability, uniform persistence and global asymptotic stability, are systematically investigated and worked out by application of some new analytical techniques. Meanwhile, we develop an analytical method to determine kernel coefficients in Lyapunov functional. Our theoretical findings manifest that the age-structured PDE TB model remains global threshold stability characterized by the basic reproduction number. Some numerical simulations underscore the need for substantially improving vaccination rate for susceptible adolescents and adults population to effectively contain even end TB spread if new effective vaccines are available.

Suggested Citation

  • Chen, Yi & Wang, Lianwen & Zhang, Jinhui, 2024. "Global asymptotic stability of an age-structured tuberculosis model: An analytical method to determine kernel coefficients in Lyapunov functional," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002005
    DOI: 10.1016/j.chaos.2024.114649
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    References listed on IDEAS

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    1. Li, Yong & Liu, Xianning & Yuan, Yiyi & Li, Jiang & Wang, Lianwen, 2022. "Global analysis of tuberculosis dynamical model and optimal control strategies based on case data in the United States," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Fang, Bin & Li, Xue-Zhi & Martcheva, Maia & Cai, Li-Ming, 2015. "Global asymptotic properties of a heroin epidemic model with treat-age," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 315-331.
    3. Li, Yingke & Teng, Zhidong & Hu, Cheng & Ge, Qing, 2017. "Global stability of an epidemic model with age-dependent vaccination, latent and relapse," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 195-207.
    4. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    5. Adrian Roderick Escombe & David A J Moore & Jon S Friedland & Carlton A Evans & Robert H Gilman, 2007. "Natural Ventilation for Prevention of Airborne Contagion: Authors' Reply," PLOS Medicine, Public Library of Science, vol. 4(5), pages 1-2, May.
    6. Wang, Jinliang & Wang, Jing & Kuniya, Toshikazu, 2019. "Analysis of an age-structured multi-group heroin epidemic model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 78-100.
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