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.

Time-lagged spatial statistic. When t 0 w0, the spatial autocorrelation function between all infected trees at time T is inevitably offset by the spatial configuration of trees already infected at time t 0 , especially in later stages of the epidemic. It is then useful to introduce a statistic that measures the spatial association between ''mother foci'' (henceforth, M), i.e., trees infected at t 0 , and ''daughter foci'' (henceforth, D), i.e., trees becoming infected after t 0 . We define n MS (d; t 0 ) as the number of pairs at time t 0 that comprise an infected tree (mother focus) and a susceptible tree a distance d apart. At time Twt 0 , a number n MD (d; T) of those initial infected-susceptible pairs have turned into infected-infected (mother-daughter) pairs. If spatial dependence is ignored, the probability for any M-S pair at time t 0 to become an M-D pair by time T coincides with the probability for an initially susceptible host to be infected between t 0 and T: If there is spatial dependence, the probability of observing an M-D pair is affected by d, and the observed number n MD (d; T) can differ significantly from the expected value. Such difference is measured by the time-lagged statistic R T t0 (d):