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 the site is N = 6056. B1-B3 Predictions (same conventions as for panels A1-A3) based upon model M V , with the assumption that the value of v (the linear decay rate of b(t), cf. gray line in Figure 3D ,H) is known from the beginning. C1-C3, D1-D3 Predictions based upon model M DT a (DT = 1 month), with constant dispersal parameter a, and monthly rates of transmission (b t , e t ) (cf. Figure 3H ). C1-C3 Predicted and observed trajectories (same conventions as in A1-A3). D1-D3 The associated secondary infection rates b t , estimated from observed data, marked by orange circles (coinciding with the mode of the distributions; cf. Figure 3H ). Predictions are made under the assumption that the positions and values of the peaks in the time series for b t (blue circles in panels D1-D3, same as the peaks in Figure 3H ) are known in advance. A spline interpolator (dark red line in panels D1-D3) is used to impute missing values of b t . doi:10.1371/journal.pcbi.1003587.g006 constant-dispersal model M DT a with monthly-varying rates (DT = 1 month, cf. Figures 3F-I) . In Figures 6D1-D3 , the modes of the estimated monthly values of b t (orange circles) are shown for each observation window together with the peak values of b t (blue circles) that are known in advance (same values as in Figure 3H ). In order to impute the missing values of b t , a spline interpolator (dark red line) was built from all the known and estimated values of b t . The missing values of e t were assumed to be constant and equal to the average of e t over the observation window. Predictions based on the first three months ( Figure 6C1 , with corresponding estimates for b t in Figure 6D1 ) capture the future progress of disease, with a smaller credible interval than for scenarios A and B (cf. Figures 6A1, B1) . Increasing the observation window to six and nine snapshots does not have a significant effect on forecast ( Figures 6C2-C3) , as most of the additional true values of b t (orange circles starting from month 4 in Figures 6D2-D3 ) are already well imputed from the first three months (cf. corresponding times in Figure 6D1 , dark red line). We conclude that knowledge of the peak values of b t , supplemented by a few early stage observations, provide enough information to predict the future course of the epidemic. Among the different scenarios we investigated (including several not discussed here), we found scenario C to correspond to the minimal amount of extra information that could produce reliable predictions from the early stages.