Bessonov, NickolayBocharov, Gennady A.Meyerhans, AndreasPopov, VladimirVolpert, Vitaly2020-04-202020-04-202020Bessonov 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/math80101172227-7390http://hdl.handle.net/10230/44276This 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.application/pdfeng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).info:eu-repo/semantics/articlehttp://dx.doi.org/10.3390/math8010117Virus density distributionGenotypeVirus infectionImmune responseResistance to treatmentNonlocal interactionQuasi-species diversificationinfo:eu-repo/semantics/openAccess