Infection spreading in cell culture as a reaction-diffusion wave

Abstract

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.

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

“…We describe the infection progression in a cell culture by the system of equations for the concentrations of uninfected cells , infected cells , and virus [2] . The right-hand side of the first equation in (2.1) describes the rate of infection of uninfected cells, and there is a similar term in the second equation for infected cells.…”

“…Here, constant is a given initial concentration of uninfected cells, while the final concentration of uninfected cells is unknown. First, we will determine , viral load and the wave speed following the method from [2] . Then we will use them to construct the approximate analytical solution.…”

“…(2.2) – (2.4) (cf. [2] ): Excluding the integrals from these equations, we obtain the equation with respect to . Here, is the virus replication number.…”

“…Right: wave speed in numerical simulations and analytical formula (curves coincide) for the values of parameters: (upper curve), (middle curve) and (lower curve). Note that the wave exists for , but viral load grows linearly in time [2] . …”

“…From the modelling point of view, viral infection spreading can be described as a reaction–diffusion wave [1] , [2] . The wave speed and the viral load can be determined analytically through the model parameters, including the rate of cell infection and the rate of virus replication [3] .…”