Methodology of selection and synthesis of mathematical models of the epizootic process

Abstract

The epizootic process (EP) is a continuous process of the emergence and spread of explicit and latent infections of animals. In some zoonoses, the study of EP by experimental studies can have negative consequences for human health. Therefore, the development of mathematical models of EP is of great practical importance. The purpose of the work is to consider the principles of the methodology for selecting and synthesizing EP models based on the mathematical theory of epidemics (MTE). Of the existing two main types of models are considered - deterministic and stochastic, their advantages and disadvantages are noted in connection with the main parameters used in the modeling of EP. An analytical review of mathematical models of Kermack (W.O.Kermack) and McKendrick; Weiss (George H. Weiss) for the study of EP is presented. Of the existing two main types of models are considered - deterministic and stochastic, their advantages and disadvantages are noted in connection with the main parameters used in the simulation of the EP. The issue of the methodology of selection and synthesis of models of the epizootic process for further forecasting of the most common viral and bacterial diseases of animals using models existing in the mathematical theory of epidemics is considered. The principles of the methodology for the selection and synthesis of MTE models using state graphs and tables of transition intensity models are considered. It is established that the method of selecting a stochastic MTE model for a specific disease or model synthesis uses a table of transition intensity models. It is concluded that the choice between deterministic and stochastic models is determined by the population size, the stage of epizootic/epidemic development, and the requirements for the accuracy of mathematical modeling. The proposed methodology for the selection and synthesis of mathematical models of EP allows you to build a mathematical model for predicting the distress of farms at the regional level. In recent years, there has been a tendency to switch to the use of simulation models and the creation of a bank of mathematical models for predicting epizootic situation indicators based on time series analysis.