scholarly journals Existence and Dynamics of Strains in a Nonlocal Reaction-Diffusion Model of Viral Evolution

2021 ◽  
Vol 81 (1) ◽  
pp. 107-128
Author(s):  
Nikolai Bessonov ◽  
Gennady Bocharov ◽  
Andreas Meyerhans ◽  
Vladimir Popov ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Model ◽  
Viral Evolution ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Nonlocal Reaction

scholarly journals Convection effect on two-dimensional dynamics in the nonlocal reaction-diffusion model

2011 ◽  
Vol 3 (1) ◽  
pp. 55-61
Author(s):  
Aleksandr Vasilievich Shapovalov ◽  
Andrey Yur'evich Trifonov ◽  
Aleksei Vladimirovich Borisov
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Two Dimensional ◽  
Reaction Diffusion Model ◽  
Nonlocal Reaction

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

2019 ◽  
Author(s):  
Nikolai Bessonov ◽  
Gennady Bocharov ◽  
Andreas Meyerhans ◽  
Vladimir Popov ◽  
Vitaly Volpert
Keyword(s):  
Viral Evolution ◽  
Reaction Diffusion ◽  
Periodic Wave ◽  
Continuous Variable ◽  
Host Cells ◽  
Reaction Diffusion Equation ◽  
Nonlocal Effects ◽  
Reaction Diffusion Model ◽  
Nonlocal Reaction ◽  
Quasispecies Evolution

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.

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

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 117 ◽  
Author(s):  
Nikolai Bessonov ◽  
Gennady Bocharov ◽  
Andreas Meyerhans ◽  
Vladimir Popov ◽  
Vitaly Volpert
Keyword(s):  
Viral Evolution ◽  
Reaction Diffusion ◽  
Periodic Wave ◽  
Continuous Variable ◽  
Host Cells ◽  
Reaction Diffusion Equation ◽  
Nonlocal Effects ◽  
Reaction Diffusion Model ◽  
Species Evolution ◽  
Nonlocal Reaction

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.

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