Abstract
Under study is an individual-based stochastic model of the spread of tuberculosis. We present a probability theory formalization of the model which rests on a characterization of individuals in distinct groups (uninfected, infected, and sick people). Some results of computational experiments concern the selecting parameters of the model based on approximation of actual data. We study how the distributions of the sizes of the groups change in dependence on the variation of the parameters of the model.
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K. K. Avilov and A. A. Romanyukha, “Mathematical Models of the Spreading and Checking of Tuberculosis (A Survey),” Mat. Biologiya i Bioinformatika 2(2), 188–318 (2007).
M. I. Perelman,G. I. Marchuk, S. E. Borisov, B. Y. Kazennykh, K. K. Avilov, A. S. Karkach, and A. A. Romanyukha, “Tuberculosis Epidemiology in Russia: a Mathematical Model and Data Analysis,” Russian J. Numer. Anal.Math. Modelling 19(4), 305–314 (2004).
K. K. Avilov and A. A. Romanyukha, “Mathematical Modeling of Tuberculosis Propagation and Patient Detection,” Avtomatika i Telemekhanika, No. 9, 145–160 (2007) [Automation and Remote Control 68 (9), 1604–1617 (2007)].
A. O. Melnichenko and A. A. Romanyukha, “A Model of Tuberculosis Epidemiology: Estimation of Parameters and Analysis of Factors Influencing the Dynamics of an Epidemic Process,” Russian J. Numer. Anal. Math. Modelling 23(1), 1–13 (2008).
V. S. Kasatkina and N. V. Pertsev, “Comparison of Solutions of the Stochastic and Deterministic Models of the Tuberculosis Spread,” in Proceedings of the 2nd Conference on Analytic and Numerical Methods for Modeling the Natural-Science and Social Science Problems (Penza, 2007), pp. 171–174.
N. V. Pertsev, A. A. Romanyukha, and V. S. Kasatkina, “A Nonlinear Stochastic Model of the Tuberculosis Spread,” Sistemy Upravleniya i Inform. Tekhnologii, No. 1–2(31), 246–250 (2008).
B. Yu. Pichugin, “AStochasticModel of an Association of Interacting Individuals Characterized by a Parameter Set,” in Proceedings of the International Conference on ComputationalMathematicsMKVM-2004, Vol. 1 (Inst. Comput. Math. Comput. Geophys., Novosibirsk, 2004), pp. 303–309.
N. V. Pertsev and B. Yu. Pichugin, “Monte-Carlo Method Application for Modeling the Dynamics of an Association of Interacting Individuals,” Vestnik. Voronezh. Gos. Tekh. Univ., Ser. Vychisl. Telekommun. Sist. 2(5), 70–77 (2006).
B. Yu. Pichugin, “The Code pm.exe,” URL: http://iitam.omsk.net.ru/~pichugin/.
G. I. Marchuk, V. N. Anisimov, A. A. Romanyukha, and A. I. Yashin, Gerontology in silico: Formation of a New Discipline. Mathematical Models, Data Processing, and Computational Experiments (BINOM, Moscow, 2007) [in Russian].
G. A. Mikhailov and A. V. Voitishek, Computational Statistical Modeling. Monte-Carlo Methods (Akademiya, Moscow, 2006) [in Russian].
J. Wallinga, W. J. Edmunds, and M. Kretzschmar, “Perspective: Human Contact Patterns and the Spread of Airbone Infectious Diseases,” Trends in Microbiology 7(9), 372–377 (1999).
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Original Russian Text © N.V. Pertsev, B.Yu. Pichugin, 2009, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2009, Vol. XII, No. 2, pp. 85–98.
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Pertsev, N.V., Pichugin, B.Y. An individual-based stochastic model of the spread of tuberculosis. J. Appl. Ind. Math. 4, 359–370 (2010). https://doi.org/10.1134/S1990478910030087
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DOI: https://doi.org/10.1134/S1990478910030087