Numerical stochastic modeling of a spatially heterogeneous population
N.V. Pertsev, V.A. Topchii, K.K. Loginov
S. L. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia
Keywords: population dynamics, compartmental system, oriented graph, branching random process, queuing system, Poisson distribution, Monte Carlo method, computational experiment
Abstract
A continuous-discrete stochastic model is constructed to describe the evolution of a spatially heterogeneous population. The population structure is defined in terms of a graph with two vertices and two unidirectional edges. The graph describes the presence of individuals in the population at the vertices and their transitions between the vertices along the edges. Individuals enter the population from an external source at each of the vertices of the graph. The duration of movement of individuals along the edges of the graph is constant. Individuals may die or turn into individuals of other populations not considered in the model. The assumptions of the model are formulated, the probabilistic formalization of the model and the numerical simulation algorithm based on the Monte Carlo method are given. Distribution patterns of the population are studied. The results of a computational experiment are presented.
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