Volume 56, Number 3, May-June 2022
|Page(s)||791 - 814|
|Published online||25 April 2022|
Infection spreading in cell culture as a reaction-diffusion wave
Laboratoire déquations aux dérivées partielles non linéaires et histoire des mathématiques, Ecole Normale Supérieure, B.P. 92, Vieux Kouba, 16050 Algiers, Algeria
2 Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia
3 Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, Poland
4 Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie, CNRS UMR 6085, Avenue de l’Université, BP 12, F-76801 Saint-Étienne-du-Rouvray, France
5 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
6 INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
7 Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation
* Corresponding author: email@example.com
Accepted: 14 February 2022
Infection spreading in cell culture occurs due to virus replication in infected cells and its random motion in the extracellular space. Multiplicity of infection experiments in cell cultures are conventionally used for the characterization of viral infection by the number of viral plaques and the rate of their growth. We describe this process with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells, virus, and interferon. Time delay corresponds to the duration of viral replication inside infected cells. We show that infection propagates in cell culture as a reaction-diffusion wave, we determine the wave speed and prove its existence. Next, we carry out numerical simulations and identify three stages of infection progression: infection decay during time delay due to virus replication, explosive growth of viral load when infected cells begin to reproduce it, and finally, wave-like infection progression in cell culture characterized by a constant or slowly growing total viral load. The modelling results are in agreement with the experimental data for the coronavirus infection in a culture of epithelial cells and for some other experiments. The presence of interferon produced by infected cells decreases the viral load but does not change the speed of infection progression in cell culture. In the 2D modelling, the total viral load grows faster than in the 1D case due to the increase of plaque perimeter.
Mathematics Subject Classification: 35K52 / 92C30
Key words: Viral infection / cell culture / reaction-diffusion equations / time delay
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.