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Invasion of new territories by alien organisms is of primary concern forenvironmental and health agencies and has been a core topic in mathematicalmodeling, in particular in the intents of reconstructing the past dynamics ofthe alien organisms and predicting their future spatial extents. Partialdifferential equations offer a rich and flexible modeling framework that hasbeen applied to a large number of invasions. In this article, we arespecifically interested in dating and localizing the introduction that led toan invasion using mathematical modeling, post-introduction data and an adequatestatistical inference procedure. We adopt a mechanistic-statistical approachgrounded on a coupled reaction-diffusion-absorption model representing thedynamics of an organism in an heterogeneous domain with respect to growth.Initial conditions (including the date and site of the introduction) and modelparameters related to diffusion, reproduction and mortality are jointlyestimated in the Bayesian framework by using an adaptive importance samplingalgorithm. This framework is applied to the invasion of \textit{Xylellafastidiosa}, a phytopathogenic bacterium detected in South Corsica in 2015,France.

Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption model