Modeling the Spread of Viral Infection in a Local Atmosphere Infected with the SARS-CoV-2 Virus: Constant Virion Concentration

A mathematical model of human infection with the COVID-19 virus by the absorption of virions from the local atmosphere is presented. The standard cellular model includes new terms that account for the initial immunity and a flux of pathogen microparticles from the environment into the organism. It is shown that immunity reduces the degree of invasion of body cells and increases the time interval between the onset of infection and the explosive increase in the concentration of pathogenic microparticles. The results of calculations using the modified model are compared with the experimental data of the time dependence of the virus concentration in the organism of infected patients. At the initial stage of infection, an analytical solution describing the growth of the pathogen concentration at a constant flux of virions from the atmosphere is found. The existence of a critical initial concentration of virions in the organism, exceeding which leads to an intensive increase in the concentration of virions, has been established. When the initial concentration of virions becomes less than a critical value, the virus in the organism degenerates. The critical initial concentration of virions in the organism rises with the increasing degree of immunity. The critical value of the constant flux of virions from the atmosphere, exceeding which leads to an irreversible increase in the concentration of pathogenic cells, is found. If the value of virion flux is less than the critical value, a constant concentration of pathogen microparticles is established in the organism. A mathematical model of vaccination, which reduces the likelihood of damage to the body’s cells by microparticles of the virus, is proposed. Various scenarios for the development of a viral infection in the body of an individual evacuated from an atmosphere contaminated with a virus are illustrated.