Geodesic
Numerical stochastic modeling of dynamics of interacting populations
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 135-153.

Voir la notice de l'article provenant de la source Math-Net.Ru

A continuous-discrete stochastic model of the dynamics of populations of interacting individuals is considered. The model is interpreted as a multidimensional random process for the number of different populations. The model description is based on a combination of both the Markov approach for the influx of individuals from an external source, the death of individuals under the influence of natural causes, the interaction of individuals, entailing their simultaneous death, transformation and generation of offspring in different populations, and the presence of non-Markov restrictions on the duration of stay of individuals in some populations. A formal probability-theoretic description of the model is given, taking into account the current state of populations and the prehistory of their development. The algorithm of direct statistical modeling of the dynamics of the components of the constructed random process is presented. Based on the algorithm, a numerical study of the stage-dependent stochastic model of the epidemic process was carried out.
Keywords: population dynamics, development of populations dependent on the past, continuous-discrete random process, Monte-Carlo method, stage-dependent model, epidemiology. 
@article{SJIM_2022_25_3_a11,
     author = {N. V. Pertsev and V. A. Topchii and K. K. Loginov},
     title = {Numerical stochastic modeling of dynamics of interacting populations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {135--153},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a11/}
}
TY  - JOUR
AU  - N. V. Pertsev
AU  - V. A. Topchii
AU  - K. K. Loginov
TI  - Numerical stochastic modeling of dynamics of interacting populations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2022
SP  - 135
EP  - 153
VL  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a11/
LA  - ru
ID  - SJIM_2022_25_3_a11
ER  - 
%0 Journal Article
%A N. V. Pertsev
%A V. A. Topchii
%A K. K. Loginov
%T Numerical stochastic modeling of dynamics of interacting populations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2022
%P 135-153
%V 25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a11/
%G ru
%F SJIM_2022_25_3_a11
N. V. Pertsev; V. A. Topchii; K. K. Loginov. Numerical stochastic modeling of dynamics of interacting populations. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 135-153. http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a11/

[1] M. S. Bartlett, Vvedenie v teoriyu sluchainykh protsessov, Izd-vo inostr. lit., M., 1958

[2] A. T. Barucha-Rid, Elementy teorii markovskikh sluchainykh protsessov i ikh prilozheniya, Nauka, M., 1969

[3] B. A. Sevastyanov, Vetvyaschiesya protsessy, Nauka, M., 1971

[4] P. Jagers, Branching Processes with Biological Applications, Wiley and Sons, London, 1975

[5] R. Nisbet, W. Garney, Modelling Fluctuating Populations, Wiley and Sons, London, 1982

[6] N. V. Pertsev, Veroyatnostnaya model infektsionnogo zabolevaniya, Preprint VTs SO AN SSSR, No 107, Novosibirsk, 1984

[7] G. I. Marchuk, Matematicheskie modeli v immunologii, Nauka, M., 1985

[8] N. V. Pertsev, B. Yu. Pichugin, “Primenenie metoda Monte-Karlo dlya modelirovaniya dinamiki soobschestv vzaimodeistvuyuschikh individuumov”, Vestn. Voronezh. gos. tekhn. un-ta, 2:5 (2006), 70–76

[9] A. D. Barbour, M. J. Luczak, “Individual and patch behaviour in structured metapopulation models”, J. Math. Biol., 71:3 (2015), 713–733

[10] O. Hyrien, S. A. Peslak, N. Yanev, J. Palis, “Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration”, J. Math. Biol., 70:7 (2015), 1485–1521

[11] T. Chou, C. D. Greenman, “A hierarchical kinetic theory of birth, death and fission in age-structured interacting populations”, J. Stat. Phys., 164:1 (2016), 49–76

[12] B. J. Pichugin, N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modeling of age-structed population with time and size dependence of immigration rate”, Russ. J. Numer. Anal. Math. Modelling, 33:5 (2018), 289–299

[13] K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Stokhasticheskoe modelirovanie kompartmentnykh sistem s trubkami”, Mat. biologiya i bioinformatika, 14:1 (2019), 188–203

[14] N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Stokhasticheskii analog modeli dinamiki VICh-1 infektsii, opisyvaemoi differentsialnymi uravneniyami s zapazdyvaniem”, Sib. zhurn. industr. matematiki, 22:1 (2019), 74–89

[15] N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analiz stadiya-zavisimoi modeli epidemii, postroennoi na osnove nemarkovskogo sluchainogo protsessa”, Sib. zhurn. industr. matematiki, 23:3 (2020), 105–122

[16] K. K. Loginov, N. V. Pertsev, “Pryamoe statisticheskoe modelirovanie rasprostraneniya epidemii na osnove stadiya-zavisimoi stokhasticheskoi modeli”, Mat. biologiya i bioinformatika, 16:2 (2021), 169–200

[17] G. A. Bocharov, K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Pryamoe statisticheskoe modelirovanie dinamiki VICh-1 infektsii na osnove nemarkovskoi stokhasticheskoi modeli”, Zhurn. vychisl. matematiki i mat. fiziki, 61:8 (2021), 1245–1268

[18] M. A. Marchenko, G. A. Mikhailov, “Parallel realization of statistical simulation and random number generators”, Russ. J. Numer. Anal. Math. Modelling, 17 (2002), 113–124

[19] M. Marchenko, “PARMONC a software library for massively parallel stochastic simulation”, Parallel Computing Technologies, Lecture Notes in Computer Science, 6873, Springer-Verl., Berlin–Heidelberg, 2011, 302–316

[20] G. A. Mikhailov, A. V. Voitishek, Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo, Akademiya, M., 2006

[21] G. A. Mikhailov, “Zamechaniya o prakticheski effektivnykh algoritmakh chislennogo statisticheskogo modelirovaniya”, Sib. zhurn. vychisl. matematiki, 17:2 (2014), 177–190

[22] G. Kramer, Matematicheskie metody statistiki, Mir, M., 1975