Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and predicting their future spatial extents. Partial differential equations offer a rich and flexible modeling framework that has been applied to a large number of invasions. In this article, we are specifically interested in dating and localizing the introduction that led to an invasion using mathematical modeling, post-introduction data and an adequate statistical inference procedure. We adopt a mechanistic-statistical approach grounded on a coupled reaction–diffusion–absorption model representing the dynamics of an organism in an heterogeneous domain with respect to growth. Initial conditions (including the date and site of the introduction) and model parameters related to diffusion, reproduction and mortality are jointly estimated in the Bayesian framework by using an adaptive importance sampling algorithm. This framework is applied to the invasion of Xylella fastidiosa , a phytopathogenic bacterium detected in South Corsica in 2015, France. Electronic supplementary material The online version of this article (10.1007/s00285-019-01376-x) contains supplementary material, which is available to authorized users.

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Forecasting invasive-pathogen dynamics is paramount to anticipate eradication and containment strategies. Such predictions can be obtained using a model grounded on partial differential equations (PDE; often exploited to model invasions) and fitted to surveillance data. This framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses and real observations. However, it may lead to models with overly rigid behavior and possible data-model mismatches. Hence, to avoid drawing a forecast grounded on a single PDE-based model that would be prone to errors, we propose to apply Bayesian model averaging (BMA), which allows us to account for both parameter and model uncertainties. Thus, we propose a set of different competing PDE-based models for representing the pathogen dynamics, we use an adaptive multiple importance sampling algorithm (AMIS) to estimate parameters of each competing model from surveillance data in a mechanistic-statistical framework, we evaluate the posterior probabilities of models by comparing different approaches proposed in the literature, and we apply BMA to draw posterior distributions of parameters and a posterior forecast of the pathogen dynamics. This approach is applied to predict the extent of Xylella fastidiosa in South Corsica, France, a phytopathogenic bacterium detected in situ in Europe less than 10 years ago (Italy 2013, France 2015). Separating data into training and validation sets, we show that the BMA forecast outperforms competing forecast approaches. Supplementary Information The online version contains supplementary material available at 10.1007/s11538-023-01169-w.

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