Genotype-dependent virus distribution and competition of virus strains

Abstract

Virus density distribution as a function of genotype considered as a continuous variable and of time is studied with a nonlocal reaction-diffusion equation taking into account virus competition for the host cells and its elimination by the immune response and by the genotype-dependent mortality. The existence of virus strains, that is, of positive stable stationary solutions decaying at infinity, is determined by the admissible intervals in the genotype space where the genotype-dependent mortality is less than the virus reproduction rate, and by the immune response under some appropriate assumptions on the immune response function characterizing virus elimination by immune cells. The competition of virus strains is studied, first, without immune response and then with the immune response. In the absence of immune response, the strain dynamics is different in a short time scale where they converge to some intermediate slowly evolving solutions depending on the initial conditions, and in a long time scale where their distribution converges to a stationary solution. Immune response can essentially influence the strain dynamics either stabilizing them or eliminating one of the strains. An antiviral treatment can also influence the competition of virus strains, and it can lead to the emergence of resistant strains, which were absent before the treatment because of the competition with susceptible strains.Communicated by Francesco dell'Isola. MSC2010: 35K57, 92C30.

On a quarantine model of coronavirus infection and data analysis

“…Considering, for simplicity, the unbounded space (or a bounded interval with no-flux boundary conditions), we introduce the total size of infected as J(t) = ∞ −∞ I(x, t)dx. Integrating equation (6) with respect to x, for variable J we then obtain an equation similar to (3).…”

“…Finally, we mention virus mutations that can have a strong influence on the disease progression and treatment [3]. At the moment, there are no available data on mutations of coronavirus, it will take some time before this aspect can be convincingly confirmed or ruled out.…”

Existence of solutions for a nonlocal reaction-diffusion equation in biomedical applications

“…Such equations arise in various biological and biomedical applications where u(x) corresponds to the density of some population (animals, cells, viruses) [4,5].…”

“…The population density distribution as a function of its genotype describes the existence and the evolution of biological species, cell lineages and cell clones in cancer, or virus strains. In this case, a conventional mathematical question about the existence of solutions acquires a clear and important biological significance allowing the determination of the conditions of the existence of biological species (clones, strains) (see [4,5]). Mathematical analysis of equation (1.1) has some specific features because it is considered in an unbounded domain, and also because of the presence of the integral term and possibly discontinuous coefficients.…”

Space and Genotype-Dependent Virus Distribution during Infection Progression

“…for y ∈ R. This equation describes virus distribution with respect to its genotype, taking into account its reproduction and its elimination by the immune response and due to the genotype-dependent mortality. A positive solution to this equation decaying at infinity corresponds to a virus quasi-species concentrated around some of the most frequent genotypes and decaying as the genotype goes away from this value [37]. The goal of this work is to study infection spread in the tissue or organ, taking into account the virus distribution with respect to its genotype.…”