Abstract
A new two-parameter kinetic equation model is proposed to describe the spatial spread of the virus in the current pandemic COVID-19. The migration of infection carriers from certain foci inherent in some countries is considered. The one-dimensional model is applied to three countries: Russia, Italy, and Chile. Both their geographical location and their particular shape stretching in the direction from the centers of infection (Moscow, Lombardy, and Santiago, respectively) make it possible to use such an approximation. The dynamic density of the infected is studied. Two parameters of the model are derived from known data. The first is the value of the average spreading rate associated with the transfer of infected persons in transport vehicles. The second is the frequency of the decrease in numbers of the infected as they move around the country, associated with the arrival of passengers at their destination. An analytical solution is obtained. Simple numerical methods are also used to perform a series of calculations. Calculations us to make some predictions, for example, about the time of recovery in Russia, if the beginning of recovery in Moscow is known.
Highlights
We study the movement of the wave of infections along the selected direction, but we do not consider the entire time evolution of the epidemic in a given area, since a few weeks after the first infections, it is already determined by local infections
We propose a two-parameter model, but these parameters have strict physical meaning: the speed of migration of infected individuals and resistance value that depends on various factors, for instance, the quarantine measures
The proposed model is determined by the following parameters: U is the average speed of transport coming from the center of infection and σ is the “resistance” to the movement of carriers of the virus by vehicles. In this kinetic-figurative approach we consider the early days of the COVID-19 pandemic in the spring of 2020
Summary
The COVID-19 pandemic is a serious challenge for medicine, and for other scientific disciplines including physics and mathematics. In the present case the equation is quite simple; we suggest a one-dimensional advection-kinetic type model of the spatial movement of infected carriers in Russia, Italy, and Chile. For these countries, the migration of carriers of the virus occurred from the designated centers: Moscow (the spread of the virus eastward from the capital is confirmed), the province of Lombardy, in. The proposed model is determined by the following parameters: U is the average speed of transport coming from the center of infection and σ is the “resistance” to the movement of carriers of the virus by vehicles In this kinetic-figurative approach we consider the early days of the COVID-19 pandemic in the spring of 2020. Some predictions according to the present model are discussed, namely, the data of the recovery for the whole country, as we know that the velocity of recovery is approximately equal to the velocity of infection
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