Fractional differential model of physical processes with saturation and its application to the description of the dynamics of COVID-19

In this article, a fractional differential model of physical processes with saturation was used to describe the dynamics of lethal outcomes of COVID-19 infection. The mathematical description of the model is given by the integro-differential Riccati equation with a derivative of a fractional variable order of the Gerasimov-Caputo type. This description makes it possible to take into account the effects of saturation and memory in the dynamics of the spread of COVID-19 among the population. Here, the saturation effect consists in reaching a plateau in the number of cases and deaths, which indicates the stabilization of the dynamics of the spread of COVID-19. The memory effect is that the symptoms of infection in infected people do not appear immediately, but with some delay. The article examines observational data on new cases of infection and the total number of deaths over a period of 2.5 years (from March to September 2022) in the Russian Federation and the Republic of Uzbekistan. Further, the parameters of the model are refined based on the studied data on the dynamics of COVID-19. With the help of the refined model, a preliminary forecast for the next six months is made with subsequent verification. Good agreement is shown between the model curves and the data curves for the total number of deaths from COVID-19.