Stochastic modeling of population dynamics taking into account spatial heterogeneity and local constraints on reproduction of individuals
K.K. Loginov, N.V. Pertsev, V.A. Topchii
S.L. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia
Keywords: population dynamics, compartmental system, oriented graph, branching random process, local reproduction sites of individuals, Monte Carlo method, computational experiment
Abstract
A continuous-discrete stochastic model describing the dynamics of a spatially heterogeneous population is presented. The individuals of the population are located in a system consisting of two interconnected compartments. The individuals move between the compartments along unidirectional pipes. The duration of individual motion along the pipes is specified by constants or functions depending on time. The individuals located in the second compartment can contact one of the reproduction centers located in this compartment. As a result of contact with a reproduction center, an individual begins the process of fission. The reproduction of the individuals arising due to fission occurs until the number of descendants exceeds a threshold level, otherwise the reproduction of individuals ends. The population formed after the completion of fission contains descendant individuals that are not subject to fission and leave the system over time. The assumptions of the model are formulated, a probabilistic formalization of the model and an algorithm of numerical modeling based on the Monte Carlo method are given. The results of a computational experiment to simulate the dynamics of the population depending on the parameters of the model are presented.
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