Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 79, Issue 2, Pages 765-789Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-019-01376-x
Keywords
Partial differential equation; Reaction-diffusion; Diffusion-absorption; Bayesian inference; Mechanistic-statistical approach; Biological invasions; Disease dynamics; Xylella fastidiosa
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Funding
- Ph.D. grant INRA-Region PACA (Emplois Jeunes Doctorants)
- HORIZON 2020 XF-ACTORS Project [SFS-09-2016]
- INRA-DGAL Project [21000679]
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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.
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