A mathematical model of respiratory viral infections in cell cultures and body tissues has been developed to study the effect of the immune response on the rate of infection spread and viral load. This makes it possible to predict scenarios of the course of the disease depending on the initial viral load and the parameters of the immune response. The assessment of the duration of the disease was studied using real data on COVID-19. These results are important for epidemiologists, immunologists, and physicians and will allow them to predict the spread of viral infections, in particular COVID-19.

A computer program has been developed to simulate the current distribution in a weakly ionized plasma of vaporized tungsten. The simulation results obtained with its help have been tested at a number of leading international conferences on mathematical physics.

The first mathematical model of plasma confinement in a spiral magnetic field has been developed. This is necessary to prevent the plasma from cooling down or the reactor from collapsing due to the ingress of a large number of plasma particles.

A new mathematical model has been developed to study the occurrence and recurrence of epidemics caused by mutations of animal viruses. Analytical conditions for the occurrence of epidemics, the rate of infection spread in the genotype space, and the time interval between outbreaks are derived. It has been shown that the effectiveness of cross-immunity, the symmetry of its function and the initial configuration of strains significantly affect the dynamics of the epidemic. The weakening of the immune system leads to repeated outbreaks of existing strains.