Modeling the spread of viral infection in a local atmosphere infected with SARS-COV-2 virus. Constant virion concentration

I. V. Derevich ; A. A. Panova

Matematičeskoe modelirovanie, Tome 36 (2024) no. 3, pp. 67-86

Résumé

A mathematical model of human infection with COVID-19 virus by absorption of virions from the local atmosphere is presented. The standard cellular model includes new terms that account for initial immunity and the 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 experimental data of time dependence of 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 was 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 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, has been found. If the value of virion flux is less than a critical value, a constant concentration of pathogen microparticles is established in the organism.

Détail

Keywords: COVID-19 cell model, infected organism cell concentration, initial immunity
Mots-clés : pathogen microparticle concentration, target organism cell concentration, virion flux.