Numerical Stochastic Modeling of Dynamics of Interacting Populations

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 sizes of different populations. The model description is based on combining the Markov approach for the influx of indi...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics 2022, Vol.16 (3), p.524-539
Main Authors: Pertsev, N. V., Topchii, V. A., Loginov, K. K.
Format: Article
Language:English
Subjects:
Algorithms
Mathematics
Mathematics and Statistics
Populations
Random processes
Statistical analysis
Statistical models
Stochastic models
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Summary: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 sizes of different populations. The model description is based on combining the Markov approach for the influx of individuals from an exogenous source, the death of individuals due to natural causes, the interaction of individuals implying their simultaneous death, and transformation and generation of offspring in different populations and the presence of non-Markov constraints 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 is carried out.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478922030164