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.

We showed that, in retrospect, advance knowledge of major weather events would have been required in order to forecast future epidemic progress. Our methods, based on limitedinformation forecast scenarios, should be applicable more generally, e.g., to windborne diseases where transmission is mostly driven by strong weather changes. In our analysis ( Figure 6 ), predictions based upon initial estimates, ignoring large weatherrelated fluctuations in transmission rates ( Figures 3E-I) , showed progressively more deviation from the actual outcome as more epidemic snapshots were included in the estimation (scenario A, Figures 6A1-A3) . Post facto predictions were effective only when the assumption of complete ignorance of the future was waived (scenarios B and C, Figures 6B1-B3, 6C1-C6 ), and some extra information, corresponding to major environmental events, was known in advance (i.e., the drought period and the amplitude of the fluctuations in b in scenario B; the peaks of b in scenario C). At the same time, of course, meteorological predictability imposes drastic constraints on prior knowledge of that kind. For example, the evolution of position, intensity, and heavier rainfall areas of supercell thunderstorms (two of which were most likely responsible for the first two peaks in the time series for b) can currently not be predicted with more than 2 hours lead time [57] . We can then draw a more general conclusion from our results: that the spatial and temporal scales for prediction must be chosen carefully, not only to match the scales of disease spread [54] [55] [56] , but also with respect to the scales of the weather events that might affect the spread. The spatial and temporal scales considered here (a few km and ,1 y, respectively) proved to be ''too small'' for prediction: at those scales, the model output is extremely sensitive to the number and timing of isolated rare weather events (i.e., the effect of those events could not be averaged out). An important question that arises is whether or not our results could be up-scaled: that is, how prediction would perform over larger (e.g., state-wide) spatial scales and longer (e.g., decadal) temporal scales, using the parameter values calculated here and weather templates (cf. [58] ) to generate time series for transmission rates. This is the object of ongoing investigation.