Parameter identification for a PDE model representing scrapie transmission in a sheep flock

In this paper a strategy for the identification of the parameters in a mathematical model which describes the dynamics of a scrapie outbreak in a sheep flock is proposed. Scrapie is a transmissible spongiform encephalopathy that affects sheep, characterised by a genetic susceptibility factor and a long incubation period. To represent the outbreak, demographic and epidemiological processes need to be taken into account in the model, as well as seasonality in breeding and scrapie transmission. The eflock is hence structured according to scrapie status (susceptible or infected), genotype, time, age, and infection load (related to the incubation period), resulting into a PDE model. We built a hierarchy of two aggregated models and take advantage of the hyperbolic structure of the PDEs to part the parameters of the model into three groups, which can theoretically be separately identified. The problem of identifiability and identification is addressed and tests with data from a natural scrapie outbreak are performed.