Virus replication and competition in a cell culture: Application to the SARS-CoV-2 variants

Mahiout, Latifa Ait; Mozokhina, Anastasia; Tokarev, Alexey; Volpert, Vitaly

doi:10.1016/j.aml.2022.108217

Cited by 12 publications

(41 citation statements)

References 8 publications

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“…A one-equation model of the emergence of new quasispecies was studied in (22,24) with a non-local reactiondiffusion equation. This model is qualitatively similar to the model describing the emergence of biological species on the basis of mutations, reproduction, and intraspecific competition (25,26). In this work, we suggest a more detailed model of the emergence of new variants due to the immune escape.…”

Section: Emergence Of New Variantssupporting

confidence: 67%

“…It can be modeled with non-local reaction–diffusion equations for the virus density distribution in the genotype space. Similar to the emergence of biological species, it is based on competition, reproduction, and mutations ( 25 , 26 ). Compared to the previous studies, we will consider a more detailed and biologically realistic model including the concentrations of uninfected cells, infected cells, viruses and the immune response (Section 2).…”

Section: Introductionmentioning

confidence: 99%

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Emergence and competition of virus variants in respiratory viral infections

et al. 2023

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The emergence of new variants of concern (VOCs) of the SARS-CoV-2 infection is one of the main factors of epidemic progression. Their development can be characterized by three critical stages: virus mutation leading to the appearance of new viable variants; the competition of different variants leading to the production of a sufficiently large number of copies; and infection transmission between individuals and its spreading in the population. The first two stages take place at the individual level (infected individual), while the third one takes place at the population level with possible competition between different variants. This work is devoted to the mathematical modeling of the first two stages of this process: the emergence of new variants and their progression in the epithelial tissue with a possible competition between them. The emergence of new virus variants is modeled with non-local reaction–diffusion equations describing virus evolution and immune escape in the space of genotypes. The conditions of the emergence of new virus variants are determined by the mutation rate, the cross-reactivity of the immune response, and the rates of virus replication and death. Once different variants emerge, they spread in the infected tissue with a certain speed and viral load that can be determined through the parameters of the model. The competition of different variants for uninfected cells leads to the emergence of a single dominant variant and the elimination of the others due to competitive exclusion. The dominant variant is the one with the maximal individual spreading speed. Thus, the emergence of new variants at the individual level is determined by the immune escape and by the virus spreading speed in the infected tissue.

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Section: Emergence Of New Variantssupporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Emergence and competition of virus variants in respiratory viral infections

et al. 2023

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“…This conclusion seems unexpected because

does not depend on either D or

, see Equation ( 4 ). Mahiout et al [ 14 ] obtained the same condition for autowave propagation,

, but their model included time-delay instead of “exposed” cells, and

was also independent on the delay. This means that general results are robust concerning variations in particular model details.…”

Section: Discussionmentioning

confidence: 99%

“…Recent studies of autowave spatial infection spreading in cell cultures were also based on delay reaction–diffusion equations [ 14 ]. There, the conditions for infection propagation in terms of viral replication number and the formulas for the propagation speed were derived involving time delay as a parameter.…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, using time delays simplifies model equations, but on the other hand delays are the greatest drawbacks of such models as they hamper both analytical and numerical studies. Recent studies of autowave spatial infection spreading in cell cultures were also based on delay reaction-diffusion equations [14]. There, the conditions for infection propagation in terms of viral replication number and the formulas for the propagation speed were derived involving time delay as a parameter.…”

mentioning

confidence: 99%

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Competition of SARS-CoV-2 Variants in Cell Culture and Tissue: Wins the Fastest Viral Autowave

2022

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Replication of viruses in living tissues and cell cultures is a “number game” involving complex biological processes (cell infection, virus replication inside infected cell, cell death, viral degradation) as well as transport processes limiting virus spatial propagation. In epithelial tissues and immovable cell cultures, viral particles are basically transported via Brownian diffusion. Highly non-linear kinetics of viral replication combined with diffusion limitation lead to spatial propagation of infection as a moving front switching from zero to high local viral concentration, the behavior typical of spatially distributed excitable media. We propose a mathematical model of viral infection propagation in cell cultures and tissues under the diffusion limitation. The model is based on the reaction–diffusion equations describing the concentration of uninfected cells, exposed cells (infected but still not shedding the virus), virus-shedding cells, and free virus. We obtain the expressions for the viral replication number, which determines the condition for spatial infection progression, and for the final concentration of uninfected cells. We determine analytically the speed of spatial infection propagation and validate it numerically. We calibrate the model to recent experimental data on SARS-CoV-2 Delta and Omicron variant replication in human nasal epithelial cells. In the case of competition of two virus variants in the same cell culture, the variant with larger individual spreading speed wins the competition and eliminates another one. These results give new insights concerning the emergence of new variants and their spread in the population.

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Airway obstruction in respiratory viral infections due to impaired mucociliary clearance

Bessonov

Volpert

2023

Numer Methods Biomed Eng

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Respiratory viral infections, such as SARS‐CoV‐2 or influenza, can lead to impaired mucociliary clearance in the bronchial tree due to increased mucus viscosity and its hyper‐secretion. We develop in this work a mathematical model to study the interplay between viral infection and mucus motion. The results of numerical simulations show that infection progression can be characterized by three main stages. At the first stage, infection spreads through the most part of mucus producing airways (about 90% of the length) without significant changes in mucus velocity and thickness layer. During the second stage, when it passes through the remaining generations, mucus viscosity increases, its velocity drops down, and it forms a plug. At the last stage, the thickness of the mucus layer gradually increases because mucus is still produced but not removed by the flow. After some time, the thickness of the mucus layer in the small airways becomes comparable with their diameter leading to their complete obstruction.

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Virus replication and competition in a cell culture: Application to the SARS-CoV-2 variants

Cited by 12 publications

References 8 publications

Emergence and competition of virus variants in respiratory viral infections

Emergence and competition of virus variants in respiratory viral infections

Competition of SARS-CoV-2 Variants in Cell Culture and Tissue: Wins the Fastest Viral Autowave

Airway obstruction in respiratory viral infections due to impaired mucociliary clearance

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