Mathematical models based on ordinary differential equations (ODE) that describe the population dynamics of viruses and infected cells have been an essential tool to characterize and quantify viral infection dynamics. Although an important aspect of viral infection is the dynamics of viral spread, which includes transmission by cell-free virions and direct cell-to-cell transmission, models used so far ignored cell-to-cell transmission completely, or accounted for this process by simple mass-action kinetics between infected and uninfected cells. In this study, we show that the simple mass-action approach falls short when describing viral spread in a spatially-defined environment. Using simulated data, we present a model extension that allows correct quantification of cell-to-cell transmission dynamics within a monolayer of cells. By considering the decreasing proportion of cells that can contribute to cell-to-cell spread with progressing infection, our extension accounts for the transmission dynamics on a single cell level while still remaining applicable to standard population-based experimental measurements. While the ability to infer the proportion of cells infected by either of the transmission modes depends on the viral diffusion rate, the improved estimates obtained using our novel approach emphasize the need to correctly account for spatial aspects when analyzing viral spread.

Many bacteria have developed a possibility to recognise aspects of their environment or to communicate with each other by chemical signals. The so-called Quorum sensing (QS) is a special case of this kind of communication. Such an extracellular signalling via small diffusible compounds (called autoinducers) is known for many bacterial species, including pathogenic and beneficial bacteria. Using this mechanism allows them to regulate their behaviour, e.g. virulence. We will focus on the typical QS system of Gram negative bacteria of the so-called lux type, based on a gene regulatory system with a positive feedback loop. There is increasing evidence that autoinducer systems themselves are controlled by various factors, often reflecting the cells’ nutrient or stress state. We model and analyse three possible interaction patterns. Typical aspects are e.g. the range of bistability, the activation threshold and the long term behaviour. Additionally, we aim towards understanding the differences with respect to the biological outcomes and estimating potential ecological or evolutionary consequences, respectively.