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 contrast with the dispersal parameter, estimates for the transmission rates (b, e) were not constant ( Figures 2E,F and Figures 3B-I) , with the secondary transmission rate b showing substantial month to month fluctuations ( Figures 3F-H) . This result bears two consequences: first, it can frustrate control efforts based on the assumption of a single, intrinsic transmission rate [56] . Second, prediction of future disease severity (upon which the decision to apply control is made) is difficult and prone to systematic error ( Figure 6 ). We suggested that both b and e were driven by environmental variables that affected the infectivity, and possibly the susceptibility, of the host. Accordingly, we found strong evidence of a time pattern similar among all the census sites for the transmission rate b (Figures 3-4 ; see also Figures S8, S9). Savill et al. [55] explored analogous problems for the infectiousness of infected premises in the 2001 UK foot and mouth epidemic, and identified missing and inaccurate data as a rate-limiting step in refining parameter estimates. For ACC, the principal environmental variables that are likely to influence the pathogen, Xac, and the disease are known to be wind-speed, rain and temperature [29, 30, 32] . Extreme weather events have indeed been identified, with robust statistical evidence [28] , as the main determinants of the pattern of b (Figures 3F-H) : major rainstorm events, acting as environmental pulses, were linked to peaks in the monthly series of transmission rates, and a drought was responsible for the strong quenching of the rates in the second half of the observation period. The existence of a common external driver is also supported (Figure 4 and Figure S9 ) by the close similarities in the temporal patterns of transmission rates across different sites. Nevertheless, extensive exploratory analysis using environmental data for temperature, wind and rain as covariates did not succeed in identifying a mechanistic environmentally-driven model for b.