Accounting for biological variability and sampling scale: a multi-scale approach to building epidemic models.

When one considers the fine-scale spread of an epidemic, one usually knows the sources of biological variability and their qualitative effect on the epidemic process. The force of infection on a susceptible unit depends on the locations and the strengths of the infectious units, and on the environmental and intrinsic factors affecting infectivity and/or susceptibility. The infection probability for the susceptible unit can then be modelled as a function of these factors. Thus, one can build a conceptual model at the fine scale. However, the epidemic is generally observed at a larger scale and one has to build a model adapted to this larger scale. But how can the sources of variation identified at the fine scale be integrated into the model at the larger scale? To answer this question, we present, in the context of plant epidemiology, a multi-scale approach which consists of defining a base model built at the fine scale and upscaling it to match the scale of the sampling and the data. This approach will enable comparing experiments involving different observational processes.