Bayesian Analysis for Inference of an Emerging Epidemic: Citrus Canker in Urban Landscapes

Neri, Franco M.; Cook, Alex R.; Gibson, Gavin J.; Gottwald, Tim R.; Gilligan, Christopher A.

Successful control of disease depends upon matching the scale of control with the inherent spatial and temporal scales of the epidemic [54] [55] [56] . For our dataset, we have identified a short initial transient period at all four sites for which a and b are not well estimated, with comparatively wider posterior distributions than for later assessments. Clearly, relying upon data for the first three 30-d intervals leads to great uncertainty in estimates of the dispersal scale, and hence decisions about the scale of control ( Figure 2 ). The use of sliding windows shows that fewer but later snapshots could be as precise in estimating dispersal parameters (measured by posterior distributions) as cumulative windows with more snapshots (Figures 2A,D) . Estimates for the dispersal parameter changed very little over time ( Figure 2D ): this motivated consideration of a new, simpler model where dispersal was constant throughout the epidemic (M DT a , Table 1 ). The robustness of the results for the dispersal scale was confirmed by goodness of fit tests, in which the posterior predictive distribution of several test statistics showed close concordance with the observed statistics ( Figure 5 and Figures S2,S3,S4 ). The evidence that the dispersal parameter (almost identical for three out of four census sites, Figure 3A ) did not change significantly over time, and the fact that this parameter was estimated with substantial precision with few snapshots, are encouraging results in view of control decisions where the scale of control depends on the scale of dispersal [54] [55] [56] .