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Matematicheskaya Biologiya i Bioinformatika, 2019, Volume 14, Issue 1, Pages 188–203
DOI: https://doi.org/10.17537/2019.14.188
(Mi mbb379)
 

This article is cited in 9 scientific papers (total in 9 papers)

Mathematical Modeling

Stochastic Modeling of Compartmental Systems with Pipes

K. K. Loginov, N. V. Pertsev, V. A. Topchii

Sobolev Institute of Mathematics SB RAS, Omsk Branch, Omsk, Russia
Full-text PDF (800 kB) Citations (9)
References:
Abstract: An approach to the construction of a stochastic model of population dynamics distributed over a compartmental system with pipes is proposed. Population dynamics is described in terms of a multidimensional random process of birth and death, supplemented by taking into account point distributions reflecting different types of particles. In this model, the belonging of a particle to a certain type is determined by the time of its transition between compartments. The duration of particle transitions through the pipes are not random, but are set as parameters of the environment in which the population develops. Graph theory is used for formalization and compact representation of the model. On the basis of the Monte Carlo method the algorithm of numerical simulation of population dynamics is constructed. The results of computational experiments for a system consisting of five compartments are presented.
Key words: compartmental system with pipes, population dynamics, birth and death random process, random graph, Monte Carlo method, stochastic model of HIV-1 infection.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 0314-2019-0009
Russian Science Foundation 18-71-10028
Received 11.03.2019, 30.04.2019, Published 06.05.2019
Document Type: Article
UDC: 519.248:57
Language: Russian
Citation: K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Stochastic Modeling of Compartmental Systems with Pipes”, Mat. Biolog. Bioinform., 14:1 (2019), 188–203
Citation in format AMSBIB
\Bibitem{LogPerTop19}
\by K.~K.~Loginov, N.~V.~Pertsev, V.~A.~Topchii
\paper Stochastic Modeling of Compartmental Systems with Pipes
\jour Mat. Biolog. Bioinform.
\yr 2019
\vol 14
\issue 1
\pages 188--203
\mathnet{http://mi.mathnet.ru/mbb379}
\crossref{https://doi.org/10.17537/2019.14.188}
Linking options:
  • https://www.mathnet.ru/eng/mbb379
  • https://www.mathnet.ru/eng/mbb/v14/i1/p188
  • This publication is cited in the following 9 articles:
    1. N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical Stochastic Simulation of Spatially Heterogeneous Population”, Numer. Analys. Appl., 17:2 (2024), 174  crossref
    2. V. A. Topchii, N. V. Pertsev, “Critical multitype branching processes on a graph and the model of the HIV infection development”, Sib. elektron. matem. izv., 20:1 (2023), 465–476  mathnet  crossref
    3. N. V. Pertsev, K. K. Loginov, “Stochastic modeling in immunology based on a stage-dependent framework with non-Markov constraints for individual cell and pathogen dynamics”, Matem. biologiya i bioinform., 18:2 (2023), 543–567  mathnet  crossref
    4. N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Chislennoe stokhasticheskoe modelirovanie dinamiki vzaimodeistvuyuschikh populyatsii”, Sib. zhurn. industr. matem., 25:3 (2022), 135–153  mathnet  crossref
    5. 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  crossref
    6. N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical modelling of the transition of infected cells and virions between two lymph nodes in a stochastic model of HIV-1 infection”, Russ. J. Numer. Anal. Math. Model, 36:5 (2021), 293–302  crossref  mathscinet  zmath  isi
    7. G. A. Bocharov, K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Direct statistical modeling of HIV-1 infection based on a non-Markovian stochastic model”, Comput. Math. Math. Phys., 61:8 (2021), 1229–1251  mathnet  mathnet  crossref  crossref  isi  scopus
    8. Loginov K., Pertsev N., International Conference Mathematical Modelling in Biomedicine 2019, Itm Web of Conferences, 31, eds. Volpert V., Syomin F., E D P Sciences, 2020  crossref  isi
    9. N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of a stage-dependent epidemic model based on a non-Markov random process”, J. Appl. Industr. Math., 14:3 (2020), 566–580  mathnet  crossref  crossref  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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