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Space and Genotype-Dependent Virus Distribution during Infection Progression

Author

Listed:
  • Nicholas Bessonov

    (Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia
    Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia)

  • Gennady Bocharov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
    Moscow Center of Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute of Computer Science and Mathematical Modelling, Sechenov First Moscow State Medical University, 119991 Moscow, Russia)

  • Vitaly Volpert

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
    Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
    INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
    Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia)

Abstract

The paper is devoted to a nonlocal reaction-diffusion equation describing the development of viral infection in tissue, taking into account virus distribution in the space of genotypes, the antiviral immune response, and natural genotype-dependent virus death. It is shown that infection propagates as a reaction-diffusion wave. In some particular cases, the 2D problem can be reduced to a 1D problem by separation of variables, allowing for proof of wave existence and stability. In general, this reduction provides an approximation of the 2D problem by a 1D problem. The analysis of the reduced problem allows us to determine how viral load and virulence depend on genotype distribution, the strength of the immune response, and the level of immunity.

Suggested Citation

  • Nicholas Bessonov & Gennady Bocharov & Vitaly Volpert, 2021. "Space and Genotype-Dependent Virus Distribution during Infection Progression," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:96-:d:712774
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