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.

In Figure 5 , we show the results of goodness-of-fit tests for the constant-dispersal model M DT a , DT = 6 months (cf. Table 1 ), for one of the Dade sites (D1; analogous results for the other sites are shown in Figures S2, S3, S4) . Intervals (t 0 ,t 1 ) shown are for t 0~0 , 6, 9, 12 months, with t 1~t0 z 6 months. Simulated disease progress curves are able to reproduce on average the observed epidemic progress (Figures 5A,C,F,I) . The spatial autocorrelation function calculated at the end of each interval, C t1 (d) (Equation 5) is shown in Figures 5B,D ,G,J. Predictive distributions of C t1 (d) (gray shaded areas) agree well with the autocorrelation estimated from experimental data (thick red lines). Some deviations emerge for the intervals [6, 12] and [9, 15] months ( Figures 5G,J) , where the experimental function appears to decay faster than the simulated function between 100 m and 250 m ( Figure 5G ) and 200 m and 600 m ( Figure 5J ), respectively. The spatial structure of the hosts infected at the beginning of the window (time t 0 ) can significantly bias the values of C t1 (d): such an effect emerges at short distances in Figure 5J , as the value 0 lies out of the 95% significance interval for C t1 (d) (dashed cyan lines). A statistic free from this bias is the time-lagged function R t1 t0 (d) (Equation 6, Figures 5E,H,K) , which measures the excess of newly infected trees at time t 1 at distance d from the trees already infected at t 0 . Significance intervals (dashed cyan lines) are always distributed around 0. Predictive distributions of R t1 t0 (d) (gray shaded areas) are in very good agreement with R t1 t0 (d) from observational data (thick solid red lines), except again for the interval [9,15] months ( Figure 5K ; for a possible origin of the disagreement see Text S1 and Figure S5 ). Overall, the spatial pattern of the epidemic is broadly well reproduced by the model estimates. We remark (cf. the beginning of this section) that very similar results were found for a model with Cauchy kernel (not shown here). Deviations appear when using different dispersal kernels (considered at the preliminary stage, see Methods), and extreme discrepancies with the data arise when testing models without primary infection (an example is given in Figure S7 ).