Application of a Kinetic Model for Studying the Spatial Spread of COVID-19

A one-dimensional model based on a kinetic-type equation is proposed for studying the dynamic distribution density of virus carriers in time and space while taking into account their distribution from a dedicated center. This model is new and fundamentally different from known models of the diffusion–reaction type. The analytical solution is built;for obtaining a series of calculations, numerical methods are also used. The model and real data from Italy, Russia, and Chile are compared. In addition to the rate of infection, the “rate of recovery” is considered. When the wave of recovery passes through a territory with the greater part of the commonwealth, a conclusion is made about the onset of global recovery, which corresponds to real data. The predictions are proved to have been accurate also for the second wave of the pandemic in Russia. The model is expected to be able also to describe adequately subsequent epidemics instead of only the development of COVID-19.

Application of the kinetic type model for study of a spatial spread of COVID-19

A simple model based on a kinetic-type equation is proposed to describe the spread of a virus in space through the migration of virus carriers from a certain center. The consideration is carried out on the example of three countries for which such a one-dimensional model is applicable: Russia, Italy and Chile. The geographical location of these countries and their elongation in the direction from the centers of infection (Moscow, Milan and Lombardia in general, as well as Santiago, respectively) makes it possible to use such an approximation. The aim is to determine the dynamic density of the infected in time and space. The model is two-parameter. The first parameter is the value of the average spreading rate associated with the transfer of infected moving by transport vehicles. The second parameter is the frequency of the decrease of the infected as they move through the country, which is associated with the passengers reaching their destination, as well as with quarantine measures. The parameters are determined from the actual known data for the first days of the spatial spread of the epidemic. An analytical solution is being built;simple numerical methods are also used to obtain a series of calculations. The geographical spread of the disease is a factor taken into account in the model, the second important factor is that contact infection in the field is not taken into account. Therefore, the comparison of the calculated values with the actual data in the initial period of infection coincides with the real data, then these data become higher than the model data. Those no less model calculations allow us to make some predictions. In addition to the speed of infection, a similar “speed of recovery” is possible. When such a speed is found for the majority of the country's population, a conclusion is made about the beginning of a global recovery, which coincides with real data. © 2021 Vladimir V. Aristov, Andrey V. Stroganov, Andrey D. Yastrebov This work is licensed under the Creative Commons Attribution-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nd/3.0/or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.