Emergence and competition of virus variants in respiratory viral infections - Bessonov, Nikolai; Neverova, Daria; Popov, Vladimir; Volpert, Vitaly (Frontiers in Immunology, 2023)
Emergence of new variants of concern (VOC) of the SARS-CoV-2 infection is one of the main factors of epidemic progression. Their development can be characterized by three critical stages: virus mutation leading to the appearance of new viable variants; competition of different variants leading to the production of sufficiently large number of copies; infection transmission between individuals and its spreading in the population. The first two stages take place at the individual level (infected individual), while the third one at the population level with possible competition between different variants. This work is devoted to mathematical modelling of the first two stages of this process: emergence of new variants and their progression in the epithelial tissue with a possible competition between them. Emergence of new virus variants is modeled with nonlocal reaction-diffusion equations describing virus evolution and immune escape in the space of genotypes. Conditions of the emergence of new virus variants are determined by the mutation rate, cross reactivity of the immune response, the rates of virus replication and death. Once different variants emerge, they spread in the infected tissue with certain speed and viral load which can be determined through the parameters of the model. Competition of different variants for uninfected cells leads to the emergence of a single dominant variant and elimination of the others due to competitive exclusion. The dominant variant is the one with the maximal individual spreading speed. Thus, emergence of new variants at the individual level is determined by the immune escape and by the virus spreading speed in the infected tissue.