Influence of routine slaughtering on the evolution of BSE: example of British and French slaughterings

The aim of this article is to build a methodology allowing the study and the comparison of the potential spread of BSE at the scale of countries under different routine slaughtering conditions in order to evaluate the risk of nonextinction due to this slaughtering. We first model the evolution in discrete time of the proportion of animals in the latent period and that of infectives, assuming a very large branching population not necessarily constant in size, two age classes, less than 1-year-old animals, and adult animals. We analytically derive a bifurcation parameter rho(0) allowing us to predict either endemicity or extinction of the disease, which has the meaning of an epidemiological reproductive rate. We show that the classical reproductive number R(0) cannot be used for prediction if the size of the population, when healthy, does not remain stable throughout time. We illustrate the qualitative results by means of simulations with either the British routine slaughtering probabilities or the French ones, the other conditions being assumed identical in both countries. We show that the French probabilities lead to a higher risk of spread of the disease than the British ones, this result being mainly due to a smaller value of the routine slaughtering probability of the adult animals in France than in Great Britain.