The thesis research aims to provide a generic methodology that improves the predictions of an invasive species dynamics for which no dedicated model is available and whose initial conditions are unknown. In order to achieve this goal, we proceed in two complementary lines of research. The first one is to propose a model&data-based inference method of biological invasions, in the framework of the so-called mechanistic-statistical approach. This method allows us to jointly estimate the introduction point and other parameters of the dynamics related to diffusion, reproduction and death. It is hinged on (i) a partial differential equation (PDE) that offers a concise description of the invasive species dynamics in a heterogeneous domain, (ii) a stochastic model that represents the observation process and (iii) a statistical Bayesian inference procedure for estimating model parameters. We propose to replace the PDE by a model issued from the framework of Piecewise-deterministic Markov Process to balance the trade-off between model realism and estimation easiness. The second research line consists on accounting for the uncertainty about models form using the Bayesian model-averaging. This method consists of combining predictions drawn from competing models in order to obtain a unique and ameliorated prediction. This technique is not widespread in the field of epidemiology. One of the methodological goals of the PhD is to investigate its application and usefulness in predictive epidemiology. The case study of my thesis is the phytopathogenic bacterium Xylella fastidiosa which is susceptible to cause in France a major sanitary crisis as the one caused in Italy since 2013