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

Nikolai Bessonov, Gennady Bocharov, Andreas Meyerhans, Vladimir Popov and Vitaly Volpert
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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
Andreas Meyerhans: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 199333 Moscow, Russia
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

Mathematics, 2020, vol. 8, issue 1, 1-20

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.

Keywords: virus density distribution; genotype; virus infection; immune response; resistance to treatment; nonlocal interaction; quasi-species diversification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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