We study the modern scenario of a rapid spread of a pandemic in space (traditional methods are as a rule based on diffusion-type equations used for a relatively slow spatial spread of epidemics associated with contacts). We study the movement of infected people by transport. It leads to a repetition of the pattern of propagation of pandemic waves because the average speed of propagation does not depend on the intensity of infection with viruses, but only on the average speed of the vehicle. The corresponding kinetic-advection equations with suitable initial and boundary conditions for the problems are used. The model has two parameters, which are calculated by comparing with real data. Namely, the mentioned average speed and the frequency of the decrease in the number of infected when moving around the country, associated with the arrival of passengers at their destination. The main assumption is related to the original sources of the first wave pandemic for specific countries: Lombardy for Italy, Moscow for Russia and Santiago for Chile. So, it is possible to determine the delay in the development of the disease both in individual regions and in the country as a whole. It is assumed that recovery is “symmetrical” and can be determined by the maximum number of infections per day. A calculation was obtained according to which the difference between this maximum for Moscow and Russia is about 3 weeks. For the next waves, specific forecasts were made with the calculation of this time shift and these forecasts were confirmed. In the second wave for Moscow, the recovery corresponded to the beginning of December 2020, and for Russia – the end of December 2020. For the third wave these data were the last decade of June 2021 and the mid-July 2021 respectively. For the fourth wave the maximums of infections occurred in the middle of the last decade of October 2021 for Moscow and mid-November 2021 for Russia as a whole. This allows us to predict the analogous character of events for the next waves as well. The model is generalized for two-dimensional geometry.