Choice of spatial discretisation influences the progression of viral infection within multicellular tissues

There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that, if rates of viral diffusion are small, then the choice of spatial discretisation of the viral surface can have quantitative and even qualitative influence on model outputs. We investigate in detail the mechanisms driving these phenomena and discuss the constraints on the design and implementation of multicellular viral dynamics models for different parameter configurations. Author summary Here we analyse the impact that the resolution of spatial discretisation has on the behaviour of spatial models of viral dynamics. We show that the extent of this influence depends on the size of the diffusion coefficient, and that, if the diffusion coefficient is sufficiently small - for example, small enough to describe tight plaque-forming dynamics - the choice of discretisation of the viral surface relative to the cell grid can appreciably change key predictions of the model. We show that the resolution of spatial discretisation modulates the timescale of infection, and identify the mechanisms by which this occurs. This work provides theory to inform the development of multicellular models of viral dynamics, which is in short supply in the literature.