Analysis of models of the mathematical theory of epidemics and recommendations on the use of deterministic and stochastic models

Abstract

The model of the epidemic/epizootic process, in principle, should reflect the interaction of all its components: the source of the causative agent of infection, the mechanism of its transmission and susceptible individuals. The purpose of the article is to analyze models of the mathematical theory of epidemics (MTE) and provide recommendations on the areas of use of deterministic and stochastic models of MTE. Depending on the research objectives, relatively simple deterministic, stochastic models or more complex computer simulation models are used. Since each stochastic model of the mathematical theory of epidemics/epizootics has its deterministic counterpart, it is of interest to analyze the errors associated with ignoring the stochastic essence of the epidemic/epizootic process using deterministic models in various situations. As an example for error analysis, a widely used general stochastic model was chosen, the deterministic analogue of which is the Kermak model (W.O. Kermak) and Mc Kendrick (A.G. Mc Kendrik) [6]. The article discusses the principles of constructing deterministic and stochastic models of the mathematical theory of epidemics/epizootics (MTE). A comparative study of the results of the use of deterministic and stochastic models using simulation modeling is carried out. Recommendations on the areas of application of deterministic and stochastic models are given. The results of the conducted studies have shown that the choice between deterministic and stochastic models is determined by the population size, the stage of epidemic development, a set of parameters and requirements for the accuracy of mathematical modeling. It is concluded that mathematical modeling systems are designed to obtain a quantitative forecast of the development of the epidemic / epizootic process in order to assess the effectiveness of antiepidemic / antiepizootic measures, to analyze the risk and assess possible economic damage. The possibilities of predictive or retrospective modeling of the spread of infectious diseases are shown.