A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs

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A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs. / Kabanikhin, Sergey ; Krivorotko, Olga; Kashtanova, Victoriya.

In: Eurasian Journal of Mathematical and Computer Applications, Vol. 26, No. 1, 01.02.2018, p. 121-131.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{fde9e0e018de47e28a16592842dbecd8,

title = "A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs",

abstract = "A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model describe particular qualities of the population and the development of the disease. The inverse problem of parameter identification in a mathematical model is reduced to the problem of minimizing an objective function characterizing the square deviation of the statistical data from the experimental data. The combination of statistical and optimization algorithms demonstrates the identification of parameters with an appropriate relative accuracy of 30%. The results can be used by public health organizations to predict the infectious disease epidemic in a given region by comparing the data of simulation with historical data.",

keywords = "65L09, reconstruction of model parameters, simulated annealing method, numerical method, Model of tuberculosis transmission, gradient descent method, system of ordinary differential equations, parameter identification, CONTROL STRATEGIES, SENSITIVITY, IMPACT, DYNAMICS, EPIDEMIOLOGY",

author = "Sergey Kabanikhin and Olga Krivorotko and Victoriya Kashtanova",

year = "2018",

month = feb,

day = "1",

doi = "10.1515/jiip-2017-0019",

language = "English",

volume = "26",

pages = "121--131",

journal = "Eurasian Journal of Mathematical and Computer Applications",

issn = "2306-6172",

publisher = "L. N. Gumilyov Eurasian National University",

number = "1",

}

RIS

TY - JOUR

T1 - A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs

AU - Kabanikhin, Sergey

AU - Krivorotko, Olga

AU - Kashtanova, Victoriya

PY - 2018/2/1

Y1 - 2018/2/1

N2 - A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model describe particular qualities of the population and the development of the disease. The inverse problem of parameter identification in a mathematical model is reduced to the problem of minimizing an objective function characterizing the square deviation of the statistical data from the experimental data. The combination of statistical and optimization algorithms demonstrates the identification of parameters with an appropriate relative accuracy of 30%. The results can be used by public health organizations to predict the infectious disease epidemic in a given region by comparing the data of simulation with historical data.

AB - A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model describe particular qualities of the population and the development of the disease. The inverse problem of parameter identification in a mathematical model is reduced to the problem of minimizing an objective function characterizing the square deviation of the statistical data from the experimental data. The combination of statistical and optimization algorithms demonstrates the identification of parameters with an appropriate relative accuracy of 30%. The results can be used by public health organizations to predict the infectious disease epidemic in a given region by comparing the data of simulation with historical data.

KW - 65L09

KW - reconstruction of model parameters

KW - simulated annealing method

KW - numerical method

KW - Model of tuberculosis transmission

KW - gradient descent method

KW - system of ordinary differential equations

KW - parameter identification

KW - CONTROL STRATEGIES

KW - SENSITIVITY

KW - IMPACT

KW - DYNAMICS

KW - EPIDEMIOLOGY

UR - http://www.scopus.com/inward/record.url?scp=85037569184&partnerID=8YFLogxK

U2 - 10.1515/jiip-2017-0019

DO - 10.1515/jiip-2017-0019

M3 - Article

AN - SCOPUS:85037569184

VL - 26

SP - 121

EP - 131

JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

SN - 2306-6172

IS - 1

ER -

ID: 9154289