Mechanistic-statistical model for the expansion of ash dieback.

Hymenoscyphus fraxineus is an invasive forest fungal pathogen that induces severe dieback in European ash populations. The spread of the disease has been closely monitored in France by the forest health survey system which has made it possible to record the symptoms observed in the plots visited. We have developed a mechanistic-statistical model using a partial differential equation (PDE) that describes the spread of the disease. It is particularly adapted for pathogen population dynamics driven by propagation of airborn spores and it allows us to take into account climate (summer temperature and spring rainfall), Allee effect induced by limited sexual partner encounters and host density. We fitted this model using available disease reports. We estimated the parameters of our model by a bayesian method, first identifying the appropriate ranges for the parameters, which led to a model reduction, and then using an adaptive multiple importance sampling algorithm for fitting. The model reproduces well the propagation observed in France over the last 20 years. In particular, it predicts the absence of disease impact in the south east of the country and its weak development in the Garonne valley in south-west France. Summer temperature is the factor with the highest overall effect on disease spread and explains its limited impact in southern France. However, the Allee effect and the heterogeneity of spring precipitation did not have a significant impact on the expansion of H. fraxineus across France and could be disregarded for this large-scale modeling. The model can be used to infer the average annual dispersal of H. fraxineus in France.