MATHEMATICAL MODEL FORECASTING DEVELOPMENT OF DEPENDENCE IN SOCIETY FROM PSYCHOACTIVE SUBSTANCES

Abstract

In order to achieve a slowdown in the rate of dependence on psychoactive substances (PSS), scientific development of effective territorial prophylaxis programs should be carried out on the basis of the combined efforts of interested state, scientific, medical, law enforcement, pedagogical, sports institutions, and community groups. The dynamics of dependence on psychoactive substances development in the society in recent years has been analyzed. analysis of existing methods of mathematical and geometric modeling of biological systems for the description of epidemic processes associated with the spread of dependence on drugs and other PSSs in predicting the dynamics of morbidity in drug addiction and alcoholism in Ukraine as a whole and in its individual regions. When analyzing methods, it is necessary to take into account the specificity of the perception of modeling results by medical personnel, which requires an expanded and adequate visualization of the results of simulation. Thus, the dynamics of the development of populations dependent on PSS varies with time depending on the set of social and medical factors. The choice of a mathematical model was carried out on the basis of the initial analysis of the system. In accordance with the object and goals, mathematical models in biology can be divided into two large classes. The incompleteness of data and a significant number of external factors of the biological system under study does not allow the use of simulation models. In this regard, basic regressive models are subject to study. One of the fundamental assumptions underlying all growth models is the proportionality of the population growth rate of its population. For complex biological systems, reproduction occurs under a more complicated law, but in the simplest model one can assume that the rate of reproduction of a population is proportional to its size. The basic regression models of biological systems are considered. The choice of the model of interpopulation interactions as the basis for modeling an epidemic of dependence on psychoactive substances is substantiated. The evaluation of the presented model is carried out. The methods of elimination of model shortcomings are proposed. An algorithm and program for the MatLab package are developed. The obtained results are presented in the form of graphs and fuccits of curves of the second order. Extrapolation of output data was carried out. The direction of further research is determined.