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Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics

Author

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  • Sergey Kabanikhin

    (Sobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Olga Krivorotko

    (Sobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Andrei Neverov

    (Sobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
    These authors contributed equally to this work.)

  • Grigoriy Kaminskiy

    (State Health Organization Tula Regional Center for Control and Prevention of AIDS and Infectious Diseases, 300002 Tula, Russia
    These authors contributed equally to this work.)

  • Olga Semenova

    (Federal State Budgetary Institution “Novosibirsk TB Research Institute” of the Ministry of Health Russian Federation, 630040 Novosibirsk, Russia)

Abstract

This paper proposes and analyzes a mathematical model of tuberculosis and HIV co-infection that specifies for Russian Federation regions, based on mass balance law and described by eight ordinary differential equations. A sensitivity-based identifiability analysis of this mathematical model was performed, which revealed the sensitivity of the averaged parameters of the models to statistical real data of infectious individuals based on the Sobol method. The problem of identifying the sensitive epidemiological parameters (contagiousness, the rate of tuberculosis activation, additional mortality rate, etc.) for the model was reduced to the problem of minimization of the quadratic misfit function. The numerical results of the modeling of the number of people expected to be infected with tuberculosis and HIV were shown and discussed for the Sverdlovsk and Moscow regions of the Russian Federation. It has been shown that increasing the capacity of the medical system by 10% will make it possible to reduce the number of diagnosed cases of active tuberculosis by 2 times over the next 3 years in some regions of Russian Federation.

Suggested Citation

  • Sergey Kabanikhin & Olga Krivorotko & Andrei Neverov & Grigoriy Kaminskiy & Olga Semenova, 2024. "Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics," Mathematics, MDPI, vol. 12(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3636-:d:1525817
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    References listed on IDEAS

    as
    1. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    2. Andrei I. Vlad & Alexei A. Romanyukha & Tatiana E. Sannikova, 2024. "Parameter Tuning of Agent-Based Models: Metaheuristic Algorithms," Mathematics, MDPI, vol. 12(14), pages 1-21, July.
    3. R M Lebcir & R A Atun & R J Coker, 2010. "System Dynamic simulation of treatment policies to address colliding epidemics of tuberculosis, drug resistant tuberculosis and injecting drug users driven HIV in Russia," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1238-1248, August.
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