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Qualitative analysis of TB transmission dynamics considering both the age since latency and relapse

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  • Das, Riya
  • Das, Dhiraj Kumar
  • Kar, Tapan Kumar

Abstract

Since the beginning of time, tuberculosis (TB) has been a fatal illness that predominantly affects the human lungs before spreading to other organs including the brain, spine, etc. The main elements of TB mitigation are age-dependent heterogeneity, identifying those who are latently infected, and treating them using the right diagnostic strategy. In this present work, the complex transmission mechanism of this disease in a population is described by a coupled system of integro-partial differential equations (IDE-PDE). The system’s well-posedness requirement is confirmed. The proposed system’s basic reproduction number (R0) is obtained. This work provides a complete analysis of the qualitative properties of the model, including steady state existence, asymptotic smoothness of the solution semi-flow, uniform persistence of the endemic equilibrium, and the global asymptotic stability criterion. It is observed that in assessing the severity of the pandemic, the value of R0 is crucial. Additionally, the stability results are visually illustrated by solving the model equations numerically while assuming two hypothetical cases. The current work also suggests several methods for reducing the value of the basic reproductive number (R0) by manipulating a few parameter values, which may help to lessen the prevalence of TB in a community.

Suggested Citation

  • Das, Riya & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2024. "Qualitative analysis of TB transmission dynamics considering both the age since latency and relapse," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 939-967.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:939-967
    DOI: 10.1016/j.matcom.2023.09.021
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    References listed on IDEAS

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    1. Bentout, Soufiane & Djilali, Salih, 2023. "Asymptotic profiles of a nonlocal dispersal SIR epidemic model with treat-age in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 926-956.
    2. 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.
    3. 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).
    4. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
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