National characteristics of changes in the hazard of development of the COVID-19 coronavirus pandemic: mathematical modeling and statistical analysis

The article develops models and methods for calculating quantitative indicators of the response of the national state and society to the hazard of spreading COVID-19 coronavirus infection in different countries. There are used the concepts, models and methods in reliability theory to describe the development of the epidemiological situation with probability functions (possibilities) of no-failure operations (survival, health protection), probability density (distribution) of the failure (infection rates), integrated hazard of infection, failure rate (risk to take ill), acceptable risk, and manageability of the epidemic situation. Government control is carried out through pressure on the acceptable risk. Based on the results of statistical processing of data on the number of confirmed cases of the disease in different countries, a comparative analysis of the epidemic process in different national circumstances of the fight against the world pandemic was conducted. The reliability functions are based on a double interpretation of the equation of changes in the hazard measure over time and on the factors of development of the epidemic process, in particular, the age structure of the population is taken into account. The mathematical and statistical analyses are based on the exponential hazard equation, which is represented in a semi-logarithmic scale by a linear dependence on time. Nonlinear distortions are due to variations in the controlled value of acceptable risk and show national features of regulating the epidemic load on the population. The results obtained confirm the model's efficiency in clear terms of reliability theory and determine the direction of its improvement in the context of an ongoing global pandemic on the basis of newly emerging data and circumstances for a better understanding of the features of current processes across countries and continents.