Nonlocal reaction–diffusion model of viral evolution: emergence of virus strains

Bessonov, Nickolay; Bocharov, Gennady A.; Meyerhans, Andreas; Popov, Vladimir; Volpert, Vitaly

doi:http://dx.doi.org/10.3390/math8010117

Nonlocal reaction–diffusion model of viral evolution: emergence of virus strains

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Bessonov N, Bocharov G, Meyerhans A, Popov V, Volpert V. Nonlocal reaction–diffusion model of viral evolution: emergence of virus strains. Mathematics. 2020; 8(1):117. DOI: 10.3390/math8010117

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.