Space and Genotype-Dependent Virus Distribution during Infection Progression

Nicholas Bessonov, Gennady Bocharov and Vitaly Volpert
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Nicholas Bessonov: Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia
Gennady Bocharov: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
Vitaly Volpert: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2021, vol. 10, issue 1, 1-17

Abstract: The paper is devoted to a nonlocal reaction-diffusion equation describing the development of viral infection in tissue, taking into account virus distribution in the space of genotypes, the antiviral immune response, and natural genotype-dependent virus death. It is shown that infection propagates as a reaction-diffusion wave. In some particular cases, the 2D problem can be reduced to a 1D problem by separation of variables, allowing for proof of wave existence and stability. In general, this reduction provides an approximation of the 2D problem by a 1D problem. The analysis of the reduced problem allows us to determine how viral load and virulence depend on genotype distribution, the strength of the immune response, and the level of immunity.

Keywords: virus density distribution; genotype; nonlocal interaction; wave propagation; infection progression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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