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Backward bifurcation and optimal control problem for a tuberculosis model incorporating LTBI detectivity and exogenous reinfection

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  • Huang, Song
  • Liu, Zhijun
  • Wang, Lianwen

Abstract

The detection of latent tuberculosis infection (LTBI) is one of the vital means in controlling the spread of TB. The dynamical properties of a mathematical model with LTBI detectivity and exogenous reinfection are analyzed and their impacts on TB control are explored. By applying the center manifold theory, it is revealed that the model may exhibit the phenomenon of backward bifurcation caused by exogenous reinfection. Furthermore, sensitivity analysis for the basic reproduction number R0 is performed and an optimal control problem is further formulated by incorporating TB prevention and education propaganda, timely treatment and enhancing therapy efficacy. Finally, our analysis and numerical results show that an increase in detection rate of LTBI cases reduces the value of R0 as well as the possibility that backward bifurcation occurs and the joint implementation of all three strategies effectively contains TB transmission.

Suggested Citation

  • Huang, Song & Liu, Zhijun & Wang, Lianwen, 2024. "Backward bifurcation and optimal control problem for a tuberculosis model incorporating LTBI detectivity and exogenous reinfection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 1104-1123.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:1104-1123
    DOI: 10.1016/j.matcom.2023.11.018
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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. 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).
    3. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Akgül, Ali & Baleanu, Dumitru, 2022. "Dynamics of HIV-TB coinfection model using classical and Caputo piecewise operator: A dynamic approach with real data from South-East Asia, European and American regions," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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    5. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. 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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