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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 26, Issue 1


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

Sergey Kabanikhin
  • Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prosp. Akad. Lavrentyeva 6, 630090 Novosibirsk, Russia
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/ Olga Krivorotko
  • Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prosp. Akad. Lavrentyeva 6, 630090 Novosibirsk; and Novosibirsk State University, Pirogova Str. 2, 630090 Novosibirsk, Russia
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/ Victoriya Kashtanova
Published Online: 2017-09-06 | DOI: https://doi.org/10.1515/jiip-2017-0019


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 30Ṫhe 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: Model of tuberculosis transmission; reconstruction of model parameters; system of ordinary differential equations; parameter identification; numerical method; simulated annealing method; gradient descent method

MSC 2010: 65L09


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About the article

Received: 2017-02-18

Revised: 2017-07-31

Accepted: 2017-07-31

Published Online: 2017-09-06

Published in Print: 2018-02-01

This work is supported by the Scholarship of the President of Russian Federation MK-1214.2017.1 “Investigation and development of numerical algorithms of direct and inverse problems in immunology and epidemiology” and the Ministry of Education and Science of Russian Federation (4.1.3 The Joint Laboratories of NSU-NSC SB RAS).

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 26, Issue 1, Pages 121–131, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2017-0019.

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