1). There exists a unique endemic equilibrium that is globally asymptotically stable when R0>1. Next, we use the Markov-chain Monte-Carlo (MCMC) method to acquire the model’s optimal parameters. From R0=1.3763, tuberculosis will not be eliminated without control measures taken in the United States. Through partial rank correlation analysis, the most sensitive parameters to the basic reproduction number are found. Based on this, we take the actual epidemic situation of tuberculosis in the United States into considerations to get the required conditions for optimal control using Pontryagin’s maximum principle and cost-effectiveness analysis. Implementation of three public health measures: tuberculosis prevention and control education, timely treatment, and enhanced efficacy can reduce the prevalence of tuberculosis in the United States. But at present, it is challenging for us to achieve the goal of eliminating tuberculosis by 2030 as called for by WHO."> 1). There exists a unique endemic equilibrium that is globally asymptotically stable when R0>1. Next, we use the Markov-chain Monte-Carlo (MCMC) method to acquire the model’s optimal parameters. From R0=1.3763, tuberculosis will not be eliminated without control measures taken in the United States. Through partial rank correlation analysis, the most sensitive parameters to the basic reproduction number are found. Based on this, we take the actual epidemic situation of tuberculosis in the United States into considerations to get the required conditions for optimal control using Pontryagin’s maximum principle and cost-effectiveness analysis. Implementation of three public health measures: tuberculosis prevention and control education, timely treatment, and enhanced efficacy can reduce the prevalence of tuberculosis in the United States. But at present, it is challenging for us to achieve the goal of eliminating tuberculosis by 2030 as called for by WHO.">
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Global analysis of tuberculosis dynamical model and optimal control strategies based on case data in the United States

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  • Li, Yong
  • Liu, Xianning
  • Yuan, Yiyi
  • Li, Jiang
  • Wang, Lianwen
Abstract
Tuberculosis is a chronic infectious disease with a high death rate, which has attracted worldwide attention. In this paper, we focus on the annual data of tuberculosis in the United States from 1988 to 2019. Firstly, we propose an SVEITR dynamical model with vaccination, fast and slow progression, incomplete treatment, and relapse. Mathematical analyses show that the disease-free equilibrium is globally asymptotically stable (unstable) if R0≤1 (if R0>1). There exists a unique endemic equilibrium that is globally asymptotically stable when R0>1. Next, we use the Markov-chain Monte-Carlo (MCMC) method to acquire the model’s optimal parameters. From R0=1.3763, tuberculosis will not be eliminated without control measures taken in the United States. Through partial rank correlation analysis, the most sensitive parameters to the basic reproduction number are found. Based on this, we take the actual epidemic situation of tuberculosis in the United States into considerations to get the required conditions for optimal control using Pontryagin’s maximum principle and cost-effectiveness analysis. Implementation of three public health measures: tuberculosis prevention and control education, timely treatment, and enhanced efficacy can reduce the prevalence of tuberculosis in the United States. But at present, it is challenging for us to achieve the goal of eliminating tuberculosis by 2030 as called for by WHO.

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  • 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).
    • Handle: RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000698
    DOI: 10.1016/j.amc.2022.126983
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    1. Lianwen Wang & Yong Li & Liuyong Pang, 2016. "Dynamics Analysis of an Epidemiological Model with Media Impact and Two Delays," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-9, January.
    2. Li, Yong & Wang, Lianwen & Pang, Liuyong & Liu, Sanhong, 2016. "The data fitting and optimal control of a hand, foot and mouth disease (HFMD) model with stage structure," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 61-74.
    3. Julia Grübler & Leon Podkaminer & Oliver Reiter, 2020. "Monthly Report No. 06/2020," wiiw Monthly Reports 2020-06, The Vienna Institute for International Economic Studies, wiiw.
    4. Yang, Yali & Li, Jianquan & Ma, Zhien & Liu, Luju, 2010. "Global stability of two models with incomplete treatment for tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 79-85.
    5. Torben M. Andersen & Giuseppe Bertola & Cecilia Garcia-Peñalosa & Clemens Fuest & Harold James & Jan-Egbert Sturm & Branko Uroševic, 2020. "EEAG Report 2020: Executive Summary," EEAG Report on the European Economy, CESifo, vol. 0, pages 7-9, March.
    6. Jia, Zhong-Wei & Tang, Gong-You & Jin, Zhen & Dye, Christopher & Vlas, Sake J. & Li, Xiao-Wen & Feng, Dan & Fang, Li-Qun & Zhao, Wen-Juan & Cao, Wu-Chun, 2008. "Modeling the impact of immigration on the epidemiology of tuberculosis," Theoretical Population Biology, Elsevier, vol. 73(3), pages 437-448.
    7. Amat Adarov & Ruslan Grinberg & Julia Grübler & Robert Stehrer, 2020. "Monthly Report No. 10/2020," wiiw Monthly Reports 2020-10, The Vienna Institute for International Economic Studies, wiiw.
    8. Seeley, Brien A. MD. & Seeley, Damon & Rakas, Jasenka PhD, 2020. "A Report on the Future of Electric Aviation," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4t76186k, Institute of Transportation Studies, UC Berkeley.
    9. Bibek Adhikari & James Alm & Timothy F. Harris, 2020. "Information Reporting and Tax Compliance," AEA Papers and Proceedings, American Economic Association, vol. 110, pages 162-166, May.
    10. Manohar Reddy YV & Reddy Mahesh N & Sandeep P & Divya G, 2020. "A Case Report on Rare Disease - Pemphigus Foliaceus," JOJ Dermatology & Cosmetics, Juniper Publishers Inc., vol. 2(2), pages 29-31, February.
    11. Andrei V. Belyi & Julia Grübler & Peter Havlik & Grzegorz W. Kolodko, 2020. "Monthly Report No. 04/2020," wiiw Monthly Reports 2020-04, The Vienna Institute for International Economic Studies, wiiw.
    12. Mantilla-Beniers, N.B. & Gomes, M.G.M., 2009. "Mycobacterial ecology as a modulator of tuberculosis vaccine success," Theoretical Population Biology, Elsevier, vol. 75(2), pages 142-152.
    13. Torben M. Andersen & Giuseppe Bertola & Cecilia Garcia-Peñalosa & Clemens Fuest & Harold James & Jan-Egbert Sturm & Branko Uroševic, 2020. "EEAG Report 2020: Recommendations for Europe," EEAG Report on the European Economy, CESifo, vol. 0, pages 1-06, March.
    14. , Nudesoc, 2020. "Reporte metodológico Encuesta Zona Cero," OSF Preprints 45j9m, Center for Open Science.
    15. Clemens Fuest, 2020. "EEAG Report 2020: Foreword," EEAG Report on the European Economy, CESifo, vol. 0, pages 01-02, March.
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    1. 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).

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