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.

Finally, while the lack of predictability is disappointing, it bears an important broader warning, namely that if a component of an epidemic-pathogen, vector or host-is affected by weather, or climate, but that relationship is poorly understood and there are insufficient long-term data, prediction of the future evolution of the epidemic can be both challenging and prone to systematic error. Our system was mainly driven by stochastic weather events occurring on very short time scales. At longer scales, we can consider influenza and mosquito-borne diseases as further contrasting illustrations. Following recent evidence [59] that absolute humidity is a strong driver of the rates of transmission and survival of the influenza virus, a framework to predict seasonal outbreaks of influenza was recently proposed [60] . With daily climatological data and real-time population disease status as inputs, retrospective forecasts could predict historical peaks of influenza outbreak with good accuracy seven weeks in advance [60] . While this case concerns short-term seasonal changes in weather, longer-term changes are also known to influence the risk and spread of disease. The importance of climate on the spread of mosquito-borne diseases is broadly accepted [61] [62] [63] though very complex and not fully understood [64] [65] [66] . Large scale weather anomalies, such as unusually long rain [67] or drought periods [68, 69] , can lead to unpredictable vector densities, which in turn frustrates public health planning [70] . Global climate change is expected to increase the frequency and intensity of unpredictable extreme weather events, with a far-reaching projected impact on many infectious diseases [70] . In the face of such future challenges, it will be increasingly important for epidemiologists to explore and identify the external factors limiting the predictive capability of their models. Figure S1 Mapping infectious pressure from primary and secondary sources. A Snapshot of census site D2 at 150 days. The density of susceptible hosts is in gray scale; overlapped red circles are infected hosts. The infectious pressure on susceptible hosts comes from two contributions: secondary sources (red circles) and external sources. B, C Infectious pressure from secondary sources only. Maps of the infectious pressure integrated over 30 days (equal to the expected density of new infections), estimated for the E model (panel B) and for the C model (panel C). Differences between the two models are evident in the top region of the system, far away from the secondary sources. D, E Infectious pressure from primary and secondary sources. Maps of the integrated infectious pressure, estimated for the E model (panel D) and for the C model (panel E). The differences between the two models disappear when primary infection is taken into account. See Text S1 for a description of the methods used to build the maps and a detailed discussion. (TIF) (3, 9) months, at two (A, D), four (B, E), and six months (C, F) from the beginning of the interval. Discrepancies between experimental (red lines) and simulated (grey shaded area) spatial statistics, explained by a lag of the experimental statistics, are solved by artificially shifting forward by two months the experimental autocorrelation function (J, H) and the experimental time-lagged statistics (I, J). See Text S1 for a detailed explanation. (TIF) Figure S7 Posterior predictive distributions from a model with negligible backgrou