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

Abstract

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.