Abstract:
We present some stochastic model of an infection spread among the adult population of a certain region. The model bases on a random birth and death process supplemented by the point distributions that reflect the durations of stay of individuals at various stages of the disease. The durations of some stages of the disease are assumed constant.
The model is a stochastic analog of a system of delay differential equations and convolution integral equations describing the infection spread in the deterministic approach. We address the problem of the infection eradication over a time span comparable to the average lifetime of several generations of individuals.
The results of computational experiments are presented, where the dynamics of mathematical expectations of the size of certain groups of individuals is studied and the probability of the infection eradication over a finite time span is estimated using the Monte Carlo method.
Keywords:
stage-dependent epidemic model, random birth and death process, non-Markov random process, point distribution, Monte Carlo method, computational experiment,
eradication of infection.
.
N. V. Pertsev and K. K. Loginov were supported by the State Task to the Sobolev
Institute of Mathematics (project no. 0314-2019-0009). V. A. Topchii was supported by the
Russian Science Foundation (project no. 18-71-10028).
Citation:
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of a stage-dependent epidemic model based on a non-Markov random process”, Sib. Zh. Ind. Mat., 23:3 (2020), 105–122; J. Appl. Industr. Math., 14:3 (2020), 566–580
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\paper Analysis of a stage-dependent epidemic model based on a non-Markov random process
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 3
\pages 105--122
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\crossref{https://doi.org/10.33048/SIBJIM.2020.23.309}
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\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 3
\pages 566--580
\crossref{https://doi.org/10.1134/S1990478920030151}
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Linking options:
https://www.mathnet.ru/eng/sjim1102
https://www.mathnet.ru/eng/sjim/v23/i3/p105
This publication is cited in the following 11 articles:
G. A. Mikhailov, G. Z. Lotova, S. V. Rogasinsky, “Study of the Bias in Monte Carlo N-Particle Estimates for Problems with Particle Interaction”, Dokl. Math., 2025
G. Z. Lotova, G. A. Mikhailov, S. V. Rogasinsky, “Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation”, Comput. Math. and Math. Phys., 64:5 (2024), 1065
G. Z Lotova, G. A Mikhailov, S. V Rogazinsky, “INVESTIGATION AND OPTIMIZATION OF THE N-PARTIAL NUMERICAL STATISTICAL ALGORITHM FOR SOLVING THE BOLTZMANN EQUATION”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:5 (2024), 842
G. A. Mikhailov, G. Z. Lotova, S. V. Rogazinskii, “Study of the bias of $N$-particle estimates of the Monte Carlo method in problems with particle interaction”, Dokl. RAN. Math. Inf. Proc. Upr., 519 (2024), 33–38
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modeling of local by time and location contacts of individuals in the epidemic process”, J. Appl. Industr. Math., 17:2 (2023), 355–369
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stokhasticheskoe modelirovanie epidemicheskogo protsessa na osnove stadiya-zavisimoi modeli s nemarkovskimi ogranicheniyami dlya individuumov”, Matem. biologiya i bioinform., 18:1 (2023), 145–176
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Chislennoe stokhasticheskoe modelirovanie dinamiki vzaimodeistvuyuschikh populyatsii”, Sib. zhurn. industr. matem., 25:3 (2022), 135–153
N. V. Pertsev, K. K. Loginov, A. N. Lukashev, Yu. A. Vakulenko, “Stokhasticheskoe modelirovanie dinamiki rasprostraneniya Kovid-19 s uchetom neodnorodnosti naseleniya po immunologicheskim, klinicheskim i epidemiologicheskim kriteriyam”, Matem. biologiya i bioinform., 17:1 (2022), 43–81
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical Stochastic Modeling of Dynamics of Interacting Populations”, J. Appl. Ind. Math., 16:3 (2022), 524
G. Z. Lotova, V. L. Lukinov, M. A. Marchenko, G. A. Mikhailov, D. D. Smirnov, “Numerical-statistical study of the prognostic efficiency of the SEIR model”, Russ. J. Numer. Anal. Math. Model, 36:6 (2021), 337–345
K. K. Loginov, N. V. Pertsev, “Pryamoe statisticheskoe modelirovanie rasprostraneniya epidemii na osnove stadiya-zavisimoi stokhasticheskoi modeli”, Matem. biologiya i bioinform., 16:2 (2021), 169–200
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