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

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 perf...

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Main Authors: Sergey Kabanikhin, Olga Krivorotko, Andrei Neverov, Grigoriy Kaminskiy, Olga Semenova
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/23/3636
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author Sergey Kabanikhin
Olga Krivorotko
Andrei Neverov
Grigoriy Kaminskiy
Olga Semenova
author_facet Sergey Kabanikhin
Olga Krivorotko
Andrei Neverov
Grigoriy Kaminskiy
Olga Semenova
author_sort Sergey Kabanikhin
collection DOAJ
description 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.
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spelling doaj-art-ed573123c9ca481e90c179d8efed860a2024-12-13T16:27:15ZengMDPI AGMathematics2227-73902024-11-011223363610.3390/math12233636Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection DynamicsSergey Kabanikhin0Olga Krivorotko1Andrei Neverov2Grigoriy Kaminskiy3Olga Semenova4Sobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, RussiaSobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, RussiaSobolev Institute of Mathematics Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, RussiaState Health Organization Tula Regional Center for Control and Prevention of AIDS and Infectious Diseases, 300002 Tula, RussiaFederal State Budgetary Institution “Novosibirsk TB Research Institute” of the Ministry of Health Russian Federation, 630040 Novosibirsk, RussiaThis 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.https://www.mdpi.com/2227-7390/12/23/3636mathematical modelepidemiologytuberculosis and HIV co-infectioninverse problemidentifiabilityoptimization
spellingShingle Sergey Kabanikhin
Olga Krivorotko
Andrei Neverov
Grigoriy Kaminskiy
Olga Semenova
Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics
Mathematics
mathematical model
epidemiology
tuberculosis and HIV co-infection
inverse problem
identifiability
optimization
title Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics
title_full Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics
title_fullStr Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics
title_full_unstemmed Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics
title_short Identification of the Mathematical Model of Tuberculosis and HIV Co-Infection Dynamics
title_sort identification of the mathematical model of tuberculosis and hiv co infection dynamics
topic mathematical model
epidemiology
tuberculosis and HIV co-infection
inverse problem
identifiability
optimization
url https://www.mdpi.com/2227-7390/12/23/3636
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AT olgakrivorotko identificationofthemathematicalmodeloftuberculosisandhivcoinfectiondynamics
AT andreineverov identificationofthemathematicalmodeloftuberculosisandhivcoinfectiondynamics
AT grigoriykaminskiy identificationofthemathematicalmodeloftuberculosisandhivcoinfectiondynamics
AT olgasemenova identificationofthemathematicalmodeloftuberculosisandhivcoinfectiondynamics