Multiscale modelling of scrapie epidemiology: II. Geographical level: hierarchical transfer of the herd model to the regional disease spread

Abstract

Geographical diffusion of scrapie disease is modelled as the outcome of two processes: intra-herd dynamic and regional spreading of genetic and infectious material between herds. The intra-herd dynamic of the disease is represented in this paper by an analytical iterative model with three state variables: the percentage of infected animals, the percentage of resistance alleles, and the percentage of hypersusceptibility alleles. Parameters of this analytical representation are estimated and validated using an existing intra-herd model. The main between-herd contamination path is known to be the trading of animals. Herds contacts on grazing grounds are also suspected to allow disease transmission. Exposure of herds to these contamination paths varies depending on local pastoral habits. We model these contamination paths as diffusion processes in three 1-D spaces: the first represents the situation in winter, where herds are stationed in farms, but when commercial exchanges are also active; the second represents the summer condition for sedentary herds, which are grazing in the vicinity of their farms, but are in contact with other neighbouring herds, and the third represents herds migrating in summer which are strongly exposed to other herds in mountain grazing grounds. We thus obtain a model for the disease diffusion at a regional scale. Using this model it is possible to analyse the influence of different pastoral habits and control measures on the geographic spread of the disease. Furthermore, using both the herd-level model and the regional-level model, we can test the consequences of individual-level hypotheses on regional-level dynamics; this is possible because of the hierarchical transfer of the herd model to the regional disease spread, and because both models are mechanistic.