Bayesian inference for an emerging arboreal epidemic in the presence of control

Abstract

The spread of Huanglongbing through citrus groves is used as a case study for modeling an emerging epidemic in the presence of a control. Specifically, the spread of the disease is modeled as a susceptible-exposed-infectious-detected-removed epidemic, where the exposure and infectious times are not observed, detection times are censored, removal times are known, and the disease is spreading through a heterogeneous host population with trees of different age and susceptibility. We show that it is possible to characterize the disease transmission process under these conditions. Two innovations in our work are (i) accounting for control measures via time dependence of the infectious process and (ii) including seasonal and host age effects in the model of the latent period. By estimating parameters in different subregions of a large commercially cultivated orchard, we establish a temporal pattern of invasion, host age dependence of the dispersal parameters, and a close to linear relationship between primary and secondary infectious rates. The model can be used to simulate Huanglongbing epidemics to assess economic costs and potential benefits of putative control scenarios.

Keywords: dispersal kernel; spatiotemporal model; stochastic model.

Fig. 1.

Layout of the Southern Gardens dataset with subregions used to estimate epidemic parameters. Green indicates blocks planted after 1998; blue indicates blocks planted before 1998; red indicates a subregion of mixed age; subregions in which the model could not be fit reliably are gray.

Fig. 2.

Estimated epidemic start time by subregion in years from the start of 2005. The large number in each subregion is the mean posterior value for and the smaller numbers give the 95% credible interval. The transparency of the pink shading is linearly proportional to the mean value of .

Fig. 3.

Length scale of the dispersal kernel, α, by average age of subregion at estimated epidemic start time. The line in black is the linear model fitted to the mean length scale in terms of the mean age.

Fig. 4.

A log-log plot of primary rate of infection, ε, vs. secondary rate of infection, β; 1,000 draws from the posteriors for 12 subregions are shown. Subregions less (more) than 8 y old are shown in green (blue). Mean parameter values for each subregion are labeled by subregion number. The clustering about the 45° line shown in red shows is roughly constant across subregions.