Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 2 December 2019 / Approved: 4 December 2019 / Online: 4 December 2019 (03:59:20 CET)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Mathematics 2020, 8, 117
DOI: 10.3390/math8010117

Abstract

The work is devoted to the investigation of virus quasispecies 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 as 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.

Subject Areas

virus density distribution; genotype; virus infection; immune response; resistance to treatment; nonlocal interaction; quasispecies diversification

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