Modeling of spatial spread of COVID-19 pandemic waves in Russia using a kinetic-advection model

Objectives. COVID-19 has a number of specific characteristics that distinguish it from past pandemics. In addition to the high infection rate, the high spread rate is due to the increased mobility of contemporary populations. The aim of the present work is to construct a mathematical model for the spread of the pandemic and identify patterns under the assumption that Moscow comprises the main source of viral infection in Russia. For this purpose, a twoparameter kinetic model describing the spatial spread of the epidemic is developed. The parameters are determined using theoretical constructions alongside statistical vehicle movement and population density data from various countries, additionally taking into account the development of the first wave on the examples of Russia, Italy and Chile with verification of values obtained from subsequent epidemic waves. This paper studies the development of epidemic events in Russia, starting from the third and including the most recent fifth and sixth waves. Our twoparameter model is based on a kinetic equation. The investigated possibility of predicting the spatial spread of the virus according to the time lag of reaching the peak of infections in Russia as a whole as compared to Moscow is connected with geographical features: in Russia, as in some other countries, the main source of infection can be identified. Moscow represents such a source in Russia due to serving as the largest transport hub in the country.Methods. Mathematical modeling and data analysis methods are used.Results. A predicted time lag between peaks of daily infections in Russia and Moscow is confirmed. Identified invariant parameters for COVID-19 epidemic waves can be used to predict the spread of the disease. The checks were carried out for the wave sequence for which predictions were made about the development of infection for Russia and when the recession following peak would occur. These forecasts for all waves were confirmed from the third to the last sixth waves to confirm the found pattern, which can be important for predicting future events.Conclusions. The confirmed forecasts for the timing and rate of the recession can be used to make good predictions about the fifth and sixth waves of infection of the Omicron variant of the COVID-19 virus. Earlier predictions were confirmed by the statistical data.