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Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains

Author

Listed:
  • Nikolai Bessonov

    (Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia)

  • Gennady Bocharov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 199333 Moscow, Russia
    Key Center of Excellence on Experimental immunophysiology and immunochemistry, Ural Federal University, 620002 Ekaterinburg, Russia)

  • Andreas Meyerhans

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 199333 Moscow, Russia
    Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluis Companys 23, 08003 Barcelona, Spain
    Infection Biology Laboratory, Universitat Pompeu Fabra, 08003 Barcelona, Spain)

  • Vladimir Popov

    (Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

  • Vitaly Volpert

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 199333 Moscow, Russia
    Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
    Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
    INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France)

Abstract

This work is devoted to the investigation of virus quasi-species evolution and diversification due to mutations, competition for host cells, and cross-reactive immune responses. The model consists of a nonlocal reaction–diffusion equation for the virus density depending on the genotype considered to be a continuous variable and on time. This equation contains two integral terms corresponding to the nonlocal effects of virus interaction with host cells and with immune cells. In the model, a virus strain is represented by a localized solution concentrated around some given genotype. Emergence of new strains corresponds to a periodic wave propagating in the space of genotypes. The conditions of appearance of such waves and their dynamics are described.

Suggested Citation

  • Nikolai Bessonov & Gennady Bocharov & Andreas Meyerhans & Vladimir Popov & Vitaly Volpert, 2020. "Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:117-:d:307997
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    References listed on IDEAS

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    1. Marco Vignuzzi & Jeffrey K. Stone & Jamie J. Arnold & Craig E. Cameron & Raul Andino, 2006. "Quasispecies diversity determines pathogenesis through cooperative interactions in a viral population," Nature, Nature, vol. 439(7074), pages 344-348, January.
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