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.
Highlights
Viral infections are often accompanied by rapid virus mutations, leading to the emergence of virus quasispecies [1–5] and their evolution [6–8]
Viral infection development in the tissues of the host organism depends on many factors determined by the pathogen and by the immune response to the infection
We study the influence of virus genotype distribution on spatial infection spreading
Summary
Viral infections are often accompanied by rapid virus mutations, leading to the emergence of virus quasispecies [1–5] and their evolution [6–8]. Virus quasispecies are characterized by the presence of different but related genotypes [9–12], facilitating their adaptation to the environment, facilitating more efficient infection of host cells and tissues [13–15], escaping the immune system [16–19] and resisting antiviral drugs [20,21]. Mutations that are not detrimental and still lead to escape are limited in number and mathematically can be described by a confined domain in the genotype space. The diversity of the HIV quasispecies observed during HIV infection increases at rate of about. Immune system can adapt to virus evolution [26], resulting in the increase of target regions and in the shift in the immunodominance [27,28]
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