Traveling waves in delayed reaction-diffusion equations in biology

Trofimchuk, Sergeĭ; Volpert, Vitaly

doi:10.3934/mbe.2020339

Cited by 8 publications

(3 citation statements)

References 121 publications

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“…This condition is related to the location of the essential spectrum, and we do not know whether the waves exist if it not satisfied. It is possible that oscillating waves emerge instead of monotone waves as it is the case for some other models [18].…”

Section: Discussionmentioning

confidence: 96%

“…Existence of waves described by monotone reaction-diffusion systems is studied in the case without time delay (see [20] and the references therein). In general, the introduction of time delay essentially complicates the analysis of wave existence, as reviewed in [18]. In some cases, when the maximum principle remains applicable, the wave existence can be proved by conventional methods, though it may be more technically difficult and some additional conditions can be necessitated to be imposed.…”

Section: Discussionmentioning

confidence: 99%

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Infection spreading in cell culture as a reaction-diffusion wave

et al. 2022

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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.

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

Infection spreading in cell culture as a reaction-diffusion wave

et al. 2022

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“…Periodic recurrent waves occur in out of equilibrium dynamics for propagation into unstable states in viral epidemics [1] , [2] , [3] , [4] , in population dynamics, ecology, cyclic predator-prey systems, spreading fires, ferroelectrics and membranes [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] . The viral pandemic Influenza A appearing in 1918 (called Spanish flu) has shown three main waves in its first two years [1] followed by seasonal waves of influenza variants for many years [2] .…”

Section: Introductionmentioning

confidence: 99%