Vol. 8, No. 2, 2020

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Genotype-dependent virus distribution and competition of virus strains

Nikolai Bessonov, Gennady A. Bocharov, Cristina Leon, Vladimir Popov and Vitaly Volpert

Vol. 8 (2020), No. 2, 101–126
Abstract

Virus density distribution as a function of genotype considered as a continuous variable and of time is studied with a nonlocal reaction-diffusion equation taking into account virus competition for the host cells and its elimination by the immune response and by the genotype-dependent mortality. The existence of virus strains, that is, of positive stable stationary solutions decaying at infinity, is determined by the admissible intervals in the genotype space where the genotype-dependent mortality is less than the virus reproduction rate, and by the immune response under some appropriate assumptions on the immune response function characterizing virus elimination by immune cells. The competition of virus strains is studied, first, without immune response and then with the immune response. In the absence of immune response, the strain dynamics is different in a short time scale where they converge to some intermediate slowly evolving solutions depending on the initial conditions, and in a long time scale where their distribution converges to a stationary solution. Immune response can essentially influence the strain dynamics either stabilizing them or eliminating one of the strains. An antiviral treatment can also influence the competition of virus strains, and it can lead to the emergence of resistant strains, which were absent before the treatment because of the competition with susceptible strains.

Keywords
virus density distribution, genotype, nonlocal interaction, competition of strains
Mathematical Subject Classification 2010
Primary: 35K57, 92C30
Milestones
Received: 13 September 2019
Revised: 9 January 2020
Accepted: 18 February 2020
Published: 19 May 2020

Communicated by Francesco dell'Isola
Authors
Nikolai Bessonov
Institute of Problems of Mechanical Engineering
Russian Academy of Sciences
Saint Petersburg
Russia
Marchuk Institute of Numerical Mathematics
Russian Academy of Sciences
Moscow
Russia
Gennady A. Bocharov
Marchuk Institute of Numerical Mathematics
Russian Academy of Sciences
Moscow
Russia
Gamaleya Center of Epidemiology and Microbiology
Moscow
Russia
Cristina Leon
Peoples’ Friendship University of Russia
Moscow
Russia
Vladimir Popov
Peoples’ Friendship University of Russia
Moscow
Russia
Vitaly Volpert
Institut Camille Jordan
UMR 5208 CNRS
University Lyon 1
Villeurbanne
France
Team Dracula
Institut National de Recherche en Informatique et en Automatique
Lyon La Doua
Villeurbanne
France
Marchuk Institute of Numerical Mathematics
Russian Academy of Sciences
Moscow
Russia
Peoples’ Friendship University of Russia
Moscow
Russia