New Results of Epidemic Models on the Example of COVID-19

Abstract

The current research considered new results of epidemic models used to study the COVID-19 epidemic. In the integro-differential model, a method for obtaining a core for an integral operator is proposed. From the analysis of hospitalization statistics, a statistical curve was determined for the number of recovered patients depending on the duration of treatment. Gaussian and Lorentzian (in physical terminology) approximations of the statistical curve are proposed. Approximation coefficients are determined by the least squares method. The Lorentz approximation as the best one is used to obtain an analytical expression for the core of the integral operator in the integro-differential model. It is proposed to shift the approximating curve by the duration of the latent incubation period of the disease. It is shown that the core of the integral operator can be determined using incomplete statistical data. For the differential model of an epidemic with a source of infection, we continued to use an approach based on solving an inverse problem to determine the source and a direct problem with an identified source for comparison with disease statistics for the city of Moscow for 796 days of the epidemic. This approach was used to study the lethality of the epidemic, obtain a parametric graph describing epidemic waves and calculate the reproduction rate of the virus, which makes it possible to analyze the degree of development of the epidemic and the need to introduce or weaken sanitary standards.