Numerical Stochastic Simulation of Spatially Heterogeneous Population

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 to each of the vertices of the graph from an external source. The duration of the migration 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, and a probabilistic formalization of the model and a numerical simulation algorithm based on the Monte Carlo method are given. The laws of population size distribution are studied. The results of a computational experiment are presented.