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.
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
\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:
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical Stochastic Simulation of Spatially Heterogeneous Population”, Numer. Analys. Appl., 17:2 (2024), 174
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
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
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, V. A. Topchii, K. K. Loginov, “Numerical Stochastic Modeling of Dynamics of Interacting Populations”, J. Appl. Ind. Math., 16:3 (2022), 524
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
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
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
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
Citation in format AMSBIB
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