Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains
by
Nikolai Bessonov 1
, Gennady Bocharov 2,3, Andreas Meyerhans 2,4,5, Vladimir Popov 6 and Vitaly Volpert 2,6,7,8,*
Nikolai Bessonov 1, Gennady Bocharov 2,3, Andreas Meyerhans 2,4,5, Vladimir Popov 6 and Vitaly Volpert 2,6,7,8,*
1
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia
2
Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 199333 Moscow, Russia
3
Key Center of Excellence on Experimental immunophysiology and immunochemistry, Ural Federal University, 620002 Ekaterinburg, Russia
4
ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
5
Infection Biology Laboratory, Universitat Pompeu Fabra, 08003 Barcelona, Spain
6
Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
7
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
8
INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 117; https://doi.org/10.3390/math8010117
Received: 2 December 2019 / Revised: 8 January 2020 / Accepted: 9 January 2020 / Published: 12 January 2020
(This article belongs to the Special Issue Mathematical Modelling in Biomedicine)
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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Bessonov, N.; Bocharov, G.; Meyerhans, A.; Popov, V.; Volpert, V. Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains. Mathematics 2020, 8, 117.
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