Table 1.
Description of parameters used in the model.
Fig 1.
Simulation model upon which the optimisation is based.
Plot A shows the distribution of citrus trees (which also represents the relative rate of introduction under the assumption of a ‘flat’ distribution of pathogen entry). Plot B shows the distribution of the relative risk of introduction according to the ‘travel census’ model (which is combined with the citrus density to estimate the relative distribution of introductions under the ‘variable’ model [that is, the ‘baseline’ model]). Plots C and D show the mean end prevalence if introductions are based only on citrus density (‘flat’ pathogen entry, C) or both citrus density and travel census risk (‘variable’ pathogen entry, D). Plots E and F show the 5th–95th percentiles of the disease progression curves under each of these assumptions, with greater intensity of colouration for percentiles approaching the median (shown as a solid line). The data used to create these plots can be found at https://doi.org/10.17866/rd.salford.12759929.v1 (files ‘spatialData_baselines.csv’, ‘dpcData.csv’, and ‘dpcSummary.csv’).
Fig 2.
Arrangement of sampling sites under different selection schemes.
These plots show the distribution of selected sites for 1 case of optimised selection and 2 alternative risk-based approaches based upon the mean end prevalence obtained from the simulation model. Plot A shows the sites selected to maximise the probability of detection when using simulated annealing. The progression of the detection probability over the first 15,000 iterations of the simulated annealing algorithm is shown in plot B, with the solid black line indicating the final detection probability after 100,000 iterations. Plot C shows the 20 sites with the highest mean end prevalence over all realisations, and plot D shows 1 arrangement of 20 sites selected with a probability proportional to the mean end prevalence. Clusters (defined as sites within 20 km of each other) are shown in distinct colours in plots A, C, and D. Estimates of the number of clusters and the probability of detection under the different sampling patterns are also shown. The data used to create these plots can be found at https://doi.org/10.17866/rd.salford.12759929.v1 (files ‘spatialData_baselines.csv’ and ‘ofProgressionExample.csv’).
Fig 3.
Impact of test sensitivity on optimal sampling pattern.
These plots show an example of the optimal distribution of sampling sites and clusters (points within 20 km of each other; shown in distinct colours) when the probability of correctly identifying any sampled infected tree (the diagnostic sensitivity) is low (0.01; plot A), medium (0.50; plot B), and high (1.00; plot C). The data used to create these plots can be found at https://doi.org/10.17866/rd.salford.12759929.v1 (file ‘spatialData_baselines.csv’).
Fig 4.
Impact of varying test sensitivity on detection probability and sampling site clustering.
These plots show the effect of different site-selection strategies on the detection probability or number of clusters. We consider 5 selection strategies: an optimised arrangement and weighted sampling according to 4 different ‘risk metrics’—the product of travel census probabilities and citrus density (‘Entry and spread’), citrus density, probability of entry according to the travel census model (‘Pathogen entry’), and random (that is, unweighted) selection. All selection strategies were repeated 100 times. Plots A and B show the detection probability for these different selection strategies, and plots C and D show the number of clusters (with a cluster being all points within 20 km of each other), all with fitted locally weighted regression curves. Plots A and C show the mean probability of detection or number of clusters, with the vertical dashed line representing the ‘baseline’ scenario of a diagnostic sensitivity of 0.5. Plots B and D show the variation in individual-level selection runs under this baseline scenario. The data used to create these plots can be found at https://doi.org/10.17866/rd.salford.12759929.v1 (file ‘optimisationOutputs_testSens.csv’).
Fig 5.
Impact of varying sample size on detection probability.
These plots show the effect of varying the number of sites—and therefore also the expected cost of surveillance—on the detection probability before the threshold prevalence is reached. Again, we consider a range of selection strategies: an optimised arrangement (based in this case on a single optimisation run for each number of sites) and 100 runs of a weighted sampling strategy based on 4 different ‘risk metrics’. These risk metrics are the product of travel census probabilities and citrus density (‘Entry and spread’), citrus density, probability of entry according to the travel census model (‘Pathogen entry’), and random (that is, unweighted) selection. Estimates of the probability of detection were made for all numbers of sites between 1 and 50 for all selection methods and additionally for all numbers of sites between 51 and 150 for the risk metric strategies, and estimates of the detection probability were interpolated using locally weighted regression. Plot A shows the mean probability of detection for a range of different numbers of sampling locations and demonstrates the variation in probability of detection for any given sample size, with the vertical dashed line representing the ‘baseline’ scenario of 20 sites. Plot B shows the mean expected annual surveillance costs required to achieve any given probability of detection between 0.50 and 0.95 for the different selection strategies. We assume that the total surveillance cost is the product of the number of sampling sites and the per-site cost of surveillance, as described in the text. The data used to create these plots can be found at https://doi.org/10.17866/rd.salford.12759929.v1 (files ‘optimisationOutputs_numSites.csv’ and ‘costEstimates.csv’).
Fig 6.
Impact of incorrect assumptions on performance of different site-selection methods.
These plots show the mean detection probability under different site-selection methods for different rates and patterns of pathogen entry. Plot A shows the detection probability when pathogen entry follows the travel census model, and plot B shows the same when entry is only affected by the citrus density. In all cases, sites were selected under the baseline model assumptions (that is, a maximal rate of pathogen entry equal to 0.05/year and a distribution of entry based upon the travel census model, as shown in the vertical dashed line). Each selection method was repeated 100 times, with each individual detection probability shown as a coloured point. The mean detection probability is shown as a black-bordered point, and a locally weighted regression curve is overlaid to better illustrate the trends. The risk metrics used for conventional targeted selection represent the product of travel census probabilities and citrus density (‘Entry and spread’), citrus density, the probability of entry according to the travel census model (‘Pathogen entry’), and random selection from the landscape. The data used to create these plots can be found at https://doi.org/10.17866/rd.salford.12759929.v1 (file ‘modelMisspecification.csv’).
Fig 7.
Maximising the probability to detect a pathogen is achieved not by selecting the highest-risk patches, but by spreading surveillance across all clusters of risk.
For ease of communication, we consider patch status as a dichotomous variable (which can be infected, shown in red, or uninfected, shown in green), rather than considering dynamic trends over time. We wish to sample the 2 patches that maximise the probability of detecting infection over all realisations (selected patches are shown with a blue dashed outline). The 2 ‘strategy’ diagrams on the top each show 3 possible realisations of patch infection status, with the status of the upper 2 host patches correlated due to their proximity. We consider 2 selection strategies: one in which patches are selected based on their mean risk (Strategy 1) and one in which only one high-risk patch is selected and the remaining resources placed in the low risk patch (Strategy 2). If our detection method is perfect, we demonstrate that Strategy 2 outperforms Strategy 1 (being able to detect infection in each of the 3 realisations). The plot on the bottom shows how this is affected by the ability to detect infection in the patch (that is, the diagnostic sensitivity), with the detection probability under Strategy 1 shown in orange and that under Strategy 2 shown in red, for all sensitivity estimates between 0 and 1. In this particular example, the mean probability to detect under Strategy 1 is calculated as 2 * (1 − (1 − sensitivity)2)/3, whereas for Strategy 2 it is equal to the sensitivity. When the sensitivity is low, selection of a single high-risk patch is insufficient to reliably detect infection, and since infection is more common in the uppermost sites, the optimal strategy is therefore to place all the resources amongst these sites (that is, Strategy 1). However, this strategy will never detect the infection in Realisation 3. This limitation becomes more apparent as the diagnostic sensitivity is increased, and beyond a sensitivity of 0.5, Strategy 2 outperforms Strategy 1, with the difference in performance increasing as the sensitivity is increased.