Fig 1.
Schematic diagrams illustrating the compartments in the model (and how individual plants move between them) and the rates at which infections occur.
A. Model transitions. For plants of either type (crop or sentinel), individual hosts begin in the Healthy compartment (HC or HS) before moving to the corresponding Undetectable compartment (UC or US) upon infection. Undetectable plants progress to the appropriate Detectable compartment (DC or DS) once visual symptoms develop. B. Force of infection. The rates at which different infectious hosts generate new infections. A Detectable crop plant can infect a Healthy crop or sentinel at rate βC whilst an Undetectable crop can infect a Healthy crop or sentinel at the scaled rate εCβC. Similarly, Detectable and Undetectable sentinels infect Healthy plants at rates βS and εSβS, respectively.
Table 1.
The epidemiological parameters of the model, their meanings, and their baseline values chosen to be consistent with X. fastidiosa infection in O. europaea (crop) and C. roseus (sentinel).
Other model parameter values are considered in S2 Text, S1–S2 Tables, and S2–S10 Figs.
Fig 2.
The baseline case–the model in the absence of sentinel plants.
A. Schematic illustrating how crop plants progress through the model compartments, and the rates at which transmissions occur. Individual hosts begin in the Healthy compartment (HC), move to the Undetectable compartment (UC) upon infection and progress to the Detectable compartment (DC) once visual symptoms develop. A Detectable crop infects Healthy crops at per capita rate βC whilst an Undetectable crop generates infections at the scaled per capita rate εCβC. B. Schematic illustrating the implementation of the monitoring programme. Monitoring begins at a random time δ relative to the time of primary infection, where δ is drawn from a U[0, Δ] distribution. Random samples of size N are subsequently selected from the population at regular time intervals Δ. Infection is detected at a given time if a Detectable plant is contained in the sample selected at that time. C. The baseline EDP, expressed as a percentage of the total crop population size, as the sample size (N = NC) and sample interval (Δ) vary.
Fig 3.
The optimal number of sentinel plants to include in the sample depends on the sample size, sample interval and the total number of sentinels in the population.
A. The effect of varying the number of sentinels included in the sample (NS) on the percentage change in EDP compared to the baseline level, in the case PS = 50, N = 50, Δ = 30 days. The number of sentinels in the sample for which the reduction in EDP is maximised () is indicated by the green circle. Black dashed line marks the baseline EDP. B. The optimal number of sentinels
to include in the sample when PS = 50, as the sample size (N) and sample interval (Δ) vary. Solid black line marks the maximum possible number of sentinels that could be sampled at any time (min(PS, N)). Grey shading marks the unfeasible region in which NS exceeds this maximum. Green circle marks the case considered in A (PS = 50, N = 50, Δ = 30 days). C. The analogous figure to B, but with PS = 100 sentinels added to the population. D. The analogous figure to B, but with PS = 200 sentinels added to the population.
Fig 4.
Optimal reductions in EDP compared to the baseline level.
A. The best achievable percentage changes in the EDP compared to the baseline level for each (N, Δ) pair when PS = 50, corresponding to the optimal strategies identified in Fig 3B. Green circle marks the case considered in Fig 3A (PS = 50, N = 50, Δ = 30 days). Note that the baseline level depends on N and Δ (Fig 2C, S12A Fig), so the relative changes in EDP shown here are not a measure of the resultant EDP. The resultant EDP decreases with sampling effort (S12B, S12C and S12D Fig). B. The analogous figure to A, but with PS = 100 sentinels added to the population and results corresponding to the strategies identified in Fig 3C. C. The analogous figure to A, but with PS = 200 sentinels added to the population and results corresponding to the strategies identified in Fig 3D. D. Combinations of the sample size N and sample interval Δ for which adding PS = 50 (dark green), PS = 100 (light green) or PS = 200 (blue) sentinels to the population led to the greatest reduction in the EDP compared to the baseline level (of the three values of PS considered).
Fig 5.
Optimising the number of sentinels to include in the population.
A. The optimal number of sentinel plants to include in the population, , for which the maximal reduction in the EDP compared to the baseline level is achieved (if NS is also chosen optimally). Region 1: When the sampling effort was small,
was low.
increased for larger sample sizes (moving to the right on the figure) and smaller sample intervals (moving downwards on the figure). Region 2:
dropped again when the sampling effort was very high. In that region, the baseline EDP was very low (Fig 2C), and the scope for reducing it insufficient to offset the increase in transmission rate caused by adding large numbers of sentinel plants into the population. Region 3: When the sample interval (Δ) was large, the optimal number of sentinel plants to include in the population was equal to the sample size (N) (contour lines are vertical). In that region, the sample interval was long enough to allow for repeated sampling of the same plants, eliminating the need for PS to exceed the sample size. Region 4: When the sample interval (Δ) was small, the optimal total number of sentinels in the population was substantially larger than the sample size. In that region, a large sentinel population was necessary to avoid frequent repeated sampling of the same plants. B. The percentage change in the EDP compared to the baseline value at the optimum, achieved when
and
. C. The resultant value of the EDP at the optimum, expressed as a percentage of the total crop population.