Infection spreading in cell culture as a reaction-diffusion wave

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. © 2022 The authors. Published by EDP Sciences, SMAI.

Ait Mahiout L. , Bessonov N.2 , Kazmierczak B.3 , Sadaka G.4 , Volpert V. 5, 6, 7
EDP Sciences
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  • 1 Laboratoire Dequations Aux Derivees Partielles Non Lineaires Et Histoire Des Mathematiques, Ecole Normale Supérieure, B.P. 92, Vieux Kouba, Algiers, 16050, Algeria
  • 2 Institute Of Problems Of Mechanical Engineering, Russian Academy Of Sciences, Saint Petersburg, 199178, Russian Federation
  • 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, Saint-Etienne-du-Rouvray, F-76801, France
  • 5 Institut Camille Jordan, Umr 5208 Cnrs, University Lyon 1, Villeurbanne, 69622, France
  • 6 Inria Team Dracula, Inria Lyon La Doua, Villeurbanne, 69603, France
  • 7 Peoples Friendship University Of Russia, Rudn University, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Ключевые слова
Cell culture; Reaction-diffusion equations; Time delay; Viral infection
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