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

Abstract

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.

Estimating the epidemiology of emerging Xylella fastidiosa outbreaks in olives

“…Our findings on key epidemiological parameters, such as the transmission rate at different stages of the disease, symptomless period, and time to death, help to achieve informed policy. These will be important for predicting the spread and control of this disease using spatially explicit landscape-scale models (White et al, 2017;Soubeyrand et al, 2018;Abboud et al, 2019; EFSA Panel on Plant Health, 2019a). Furthermore, these epidemiological parameters are difficult and costly to measure experimentally, but models fitted to monitoring data can provide estimates and uncertainty distributions, giving valuable knowledge on X. fastidiosa disease dynamics and, potentially, other plant diseases.…”

“…pauca in Puglian olive groves. Previous models of X. fastidiosa dynamics (White et al, 2017;Abboud et al, 2019;Daugherty and Almeida, 2019) have generally assumed simple tree to tree infection growth dynamics (e.g., logistic-or Gompertz-type growth models of the number or proportion of infected host plants), or used a simplified compartmental Susceptible-Infected (SI) model that omits critical features of the X. fastidiosa epidemiology, such as the symptomless period and host mortality rate (Soubeyrand et al, 2018). Our aim is to build a more realistic model that captures additional details of the infection process using a deterministic discrete-time modified compartmental model, adapted to the particular epidemiology of X. fastidiosa subsp.…”

Using Early Data to Estimate the Actual Infection Fatality Ratio from COVID-19 in France

“…The mechanistic-statistical formalism, which is becoming standard in ecology [9][10][11] allows the analyst to couple a mechanistic model that describes a latent variable, here an ordinary differential equation model (ODE) of the SIR type, and uncertain, non-exhaustive data. To bridge the gap between the mechanistic model and the data, the approach uses a probabilistic model describing the data collection process.…”

Spatiotemporal Prediction of COVID-19 Mortality and Risk Assessment

“…Let Λ = {Λ t,z , z ∈ D ⊂ R d , t ∈ R + , } be a spatiotemporal risk process on (Ω, A, P) such that (1) where T is a bounded Borel set in R + , and B denotes the Borel σ-algebra. Process Λ is assumed to satisfy E ln (Λ t (•)) 2 H < ∞, with Λ t (z) = Λ t,z , for every z ∈ D and t ∈ R + . Here,…”

“…Specifically, the stochastic SIR-like model fitting is performed, assuming that the counts are observed with error and the dynamical evolution of the SIR process is stochastic. Parameter uncertainty is also modelled under this Bayesian statistical framework (see also [2]).…”