About one stochastic model of coexistence of various population groups into the urban environment

Abstract

The problem of the interaction of various population groups in the framework of urban environment is of current interest this time. The population is divided into different strata according to their economic and social characteristics. For example, a population could be classified according to genetic and phenotypic characteristics, belonging to a ethnic group and, first of all, according to income level. In several countries, the co-existence of population groups belonging to different social strata gives rise to serious problems and therefore has been studied from different points of view, mainly from a sociological. Due to the qualitative analysis of various situations, it becomes possible to predict and prevent possible conflicts and problems. The significance of this problem is obvious, but reasonable proposals for its solution have not been put forward. In this regard, the construction of a qualitative, but general mathematical model of the dynamics of various groups of the population is of interest. Such a mathematical model should be built within the framework of the concept of spatial economics. This paper discusses the first version of the model for a situation where there are only two groups of people. The corresponding system of equations includes two nonlinear diffusion equations with terms describing the interaction of the population groups in model. Of course, the basic difficulty is the selection of coefficients, which will provide the picture as close as possible to reality, so it makes sense to add to the model and stochastic terms that will be responsible for random environmental factors. Thus, a two-dimensional stochastic model of the temporal dynamics of the distribution of two population groups in an urban environment was presented and numerically investigated. As a result of the mathematical modeling certain estimates were obtained regarding the feasibility of considering stochastic factors in the proposed mathematical model.