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

Mathematics

Nikolai Bessonov¹  Gennady Bocharov²  Andreas Meyerhans²  Vitaly Volpert²  Vladimir Popov³ 

[1] Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia;Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 199333 Moscow, Russia;Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia;

关键词: virus density distribution;    genotype;    virus infection;    immune response;    resistance to treatment;    nonlocal interaction;    quasi-species diversification;   

DOI  :  10.3390/math8010117

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown