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

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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/}
}
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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/