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.

nd infection. Predictive distributions for site D1 are calculated from estimates for model M DT a , DT = 6 months (same census site and intervals as in Figure 5 ), with Cauchy kernel (cf. Text S1, Equation S5b) and background infection e kept at a very small constant value. Predictive distributions for disease progress (A, C, F, I; the total number of hosts being N = 6056), spatial autocorrelation function C t1 (B, D, G, J), and time-lagged statistic R t1 t0 (E, H, K) are shown, for intervals (0, 6) months (A, B), (3, 9) months (C, D, E), (6, 12) months (F, G, H), (9, 15) months (I, J, K). Symbols and conventions are the same as for Figure 5 . For the last three periods (C-K), the progress of the epidemic is well reproduced (C,F,I), but simulated spatial statistics (D,G,J and E,H,K) clearly and consistently overestimate experimental spatial statistics (compare with Figure 5 , same panels, for the exponential kernel with external infection). See Text S1 for more details. (TIF) Figure S8 Temporal pattern of secondary rates in sites D1 and D2: Effect of shift. Joint posterior distributions for the transmission rate, b t (model M DT a , DT = 1 month) for sites D1 and D2 (cf. Figure 4B ), plotted with no artificial shift in time (A) and with a 1-month shift in the rates for site D2 (B, same as Figure 4B and reproduced here for comparison). While the joint densities in A lack a clear correlation pattern, consistency for the two sites emerges in B upon introducing a 1-month lag for the parameters of D2. (TIF) Figure S9 Consistency of longer-term secondary rates amongst sites: 6-month resolution. Joint posterior distributions for the transmission rate, b t (model M DT a , DT = 6 months; cf. Figure 4 and Figure S8 for DT = 1 month) for sites B1 and B2 (A), sites D1 and D2 plotted with no artificial shift in time (B), and sites D1 and D2 with a 1-month shift in the rates for site D2 (C). Here, using a lower time resolution for rates, the consistency in the pattern of b t among census sites emerges with more regularity, although the qualitative behaviour is the same as in Figure 4 and Figure S8 . Figure 1A) . For each polygon (small sub-areas delimited by gray lines), the human population density and number of households is known from census data. The estimated density of residential citrus trees (colour-coded) was found using an empirical relationship between the number of citrus trees per household and human population density (W. Luo and T. Gottwald, private communication). The estimate shows that the host population was distributed with high spatial heterogeneity around every census site. Moreover, new infections were found in the area, and outside census sites, during all the epidemic (see Methods), which motivates the use of a primary infection rate e in the model (Equation (2b)). (TIF) Table 1 ). Pairwise differences between DIC values for E and C models (columns with header E-C) show that the two models are essentially equivalent, with a trend for E to perform better than C as the frequency of rate change increases. Only for census site D1 is model E clearly favoured. See Text S1 for more details. (PDF)