Integral inflow and outflow model and its applications

The article describes a general integral model of the inflow and outflow of a dynamic system, the parameters of which are stochastic in nature. For this type of dynamic systems, the general principle of dynamic balance is formulated, and the concepts of interval dynamic balance of integral volumes of inflow and outflow as well as the concept of dynamic balance characteristic are introduced. The class of stochastic dynamic processes and systems of inflow and outflow that satisfy the principle of dynamic balance is quite wide (the spread of viral epidemics and the dynamics of morbidity in medicine, processes of changes in the size and structure of the population in demography, the dynamics of supply and demand in the economy, etc.). The possibilities of using the proposed model for constructing short-term and long-term forecasts are demonstrated using examples of the spread of the COVID-19 epidemic in Moscow and Saint Petersburg, as well as using the example of forecasting the growth of the Earth population and population of countries. The results of computational experiments on constructing retrospective forecasts of the state of dynamic systems using the method of dynamic trends of stochastic parameters of the integral model and using the classical ARIMA method are presented. A comparative analysis of forecasting accuracy is provided.