OF THE
M ODEL & DATA - BASED PREDICTION FUTURE DYNAMICS OF Xylella fastidiosa
IN
F RANCE
Candy Abboud:
[email protected], Olivier Bonnefon, Éric Parent, Samuel Soubeyrand. Main Objectives of My PhD Introduction Use several spatio-temporal propagation models to estimate epidemiological parameters
‚ The spread of Xylella fastidiosa (Xf), detected in Corsica in 2015, might cause a major sanitary crisis in France. In particular, it might affect agricultural and horticultural productions through important direct or indirect costs
Make predictions from surveillance data of Xylella fastidiosa with flexible models and statistical tools
‚ Predicting Xf dynamics from surveillance data should help us in improving control and surveillance measures ‚ In this poster, we will present, as a work in progress, a model that describes the dynamics of Xf. This model was built following the mathematical approach presented bellow.
Take account of uncertainty about model forms Design control and surveillance based on model predictions Ha Ha
Methodology Data in South Corsica
HaHa The
> 8000 plants sampled since 2015 of which 800 have been diagnosed as infected (realtime PCR); > For those 8000 plants, geographic coordinates and sampling dates are available > We also consider T , the average of the minimum daily temperature over January and February
Mechanistic-statistical Approach
HaData
Model
Let I be a sample of size I that contains all the sampled plants. ‚ ti the sampling time of plant i ‚ xi its location ‚ Yi its sanitary state observed at time ti
Process Model We assume that the dynamics of Xf is described by the following model where upt, xq is the probability of a plant to be infected at time t in x $ Bu “ D∆u ` bupu ´ θqp1 ´ uqXΩ2 ´ αuXΩ1 , in Ω ’ ’ B t ’ ’ & ∇u.n “ 0, on BΩ ’ ’ ’ ’ % u0 pxq “ upτ0 , xq, in Ω Ω “ Ω1
D : dispersal rate
Ť
Bayesian Inference with AMIS The Adaptive Multiple Importance Sampling Algorithm
Ω2
b : intrinsic growth rate of Xf We divide South Corsica in two subdomains: 1- where T ď T˜ and Xf cannot grow 2- where T ą T˜ and Xf can grow
θ Ps0;
1 r: 2
reaction threshold in Ω2 which induces an Allee effect
α : absorption cœfficient in Ω1 XDom : characteristic function which is equal to 1 in Dom and 0 elsewhere. For the initial conditions:
For instance, when T˜ “ 4°C ‚ The disease is introduced at time τ0 ‚ x ˜0 “ p˜ x0 , y ˜0 q is the central point of the disease introduction ‚ The probability of infection at τ0 in x satisfies: ¸ ˜ kx ´ x ˜ 0 k2 u0 pxq “ p0 exp ´ 2σ 2 where σ 2 “
r02 q 2
Numerical Simulation
t = −335
t = −320
t = −200
t=0
t = 30
and q is the 0.95-
quantile of the χ distribution with 2 degrees of freedom. Then, at τ0 , 95% of the infected plants are located around the central point till a distance r0 . We denote by p0 , the infection probability at τ0 in x ˜0 .
t = −150
Visualization of the numerical solution when D = 0.25 × 104 , θ = 0.03, b = 1, α = 1, x ˜0 = (11911369, 6076691), r0 = 5000, p0 = 0.1, τ0 = −335. Candy ABBOUD
1/1
Expected Results – Estimation of the date and the location of the introduction point
– Estimation of the threshold of temperature
Forthcoming Research
References
– Incorporate into the model the possibility of multiple introductions of Xf
1. Soubeyrand and Roques (2014, Population Ecology)
– Enlarge the study domain to entire Corsica
2. Cornuet et al. (2012, Scandinavian J. of Statistics)
Acknowledgements This research is supported by an INRA-Region PACA PhD funding (socio-economic partner: AFIDOL), the HORIZON 2020 XF-ACTORS Project SFS-09-2016 and the INRADGAL project 21000679
