The possibility of applying the kinetic theory of aging of biological species published earlier by the authors of this work to assess and predict changes in the number of specific populations is evaluated. The populations of the USA, China and Russia, as well as the population of mice observed in the experiment "mouse paradise" of the American scientist John Calhoun are considered. To this end, a historically consistent analysis of the main previously proposed multi-scenario mathematical models describing demographic data and predicting the dynamics of the population was performed. The results of these models show a decrease in the population growth rate, a tendency toward a limit with an increase in historical time, the achievement of such a limit in some developed countries with a relatively high level of social security, a subsequent decrease in the number and further uncertainty of the final population outlook in the distant future. In addition, these models made it possible to establish that the observed population growth in developed countries is unambiguously accompanied by its aging - a relative predominant increase in the number of elderly people compared to the number of the younger generation (people are aging, the population of countries is aging). In this work, the assumption was made and confirmed that the dynamics of the aging of the population of the countries of the World corresponds to the dynamics of aging of a person of one generation and is mathematically described by the differential equation of the kinetic theory of aging of living systems of the same type with close values of the parameters. The biophysical meaning of the parameters of the kinetic equation reflects G. Selye's concept of the determining role of stress in human life and populations. An analysis of the changes in the numbers of the considered populations of humans and mice at various stages of their development is qualitatively commented on from the standpoint of comparative tension according to G. Selye. To assess the degree of aging of a biological object of one population in kinetic theory, the probability of death during life is selected as an indicator of aging. In this work, the probability of reaching the maximum population size was chosen as an indicator of the aging of a biological object of various populations. The published literature predicts various options for changing the population after reaching a maximum - maintaining the reached maximum level and decreasing to a certain limit, less than the maximum achieved. In this paper, based on an analysis of its results and an analogy with the complete degeneration of mice in the “mouse paradise” experiment, a conclusion is drawn about a hypothetically possible third variant of the limiting decrease in the population - its complete degeneration.

On the basis of the basic model of the kinetic theory of aging of living systems, mathematical modeling of various characteristics of aging of mankind, state, generation, human body, organs and cells has been carried out. These results are compared with experimental and calculated data of other authors. The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging, as a manifestation of the fractality property of living systems.

An original mathematical model, previously tested by the authors on other non-demographic objects, is proposed for describing and forecasting demographic systems — the population of the countries of the World using the examples of the USA, China and Russia, as well as the number of mice in the “mouse paradise” experiment of the American scientist John Calhoun. The proposed approach allows us to describe the stages and features of this dynamics: population growth in the USA, growth and possible decrease in the population in China, loss of a part of the population of the Russian Empire and the USSR due to two world wars and the collapse of the USSR, biological degradation of the “mouse paradise” up to its complete extinction. The use of the kinetic model of aging of various types of living systems to predict the development of the number of demographic systems is based on the assumptions that the aging and development processes are related to each other and have the same statistical regularity, reflecting the fractal principle of Nature - the unity of structure and function. The results obtained suggest that a person, a population of the World, humanity and other biological species develop and simultaneously age like each other under the conditions of the always existing syndrome of general adaptation (stress) and according to the same pattern corresponding to the mathematical model proposed here.