Declaring Sydney free from red imported fire ants Solenopsis invicta buren – a view from the branches of the scenario tree

Abstract

Tramps ants are a constant biosecurity threat to Australia. Red Imported Fire Ant Solenopsis invicta was detected in Sydney, New South Wales in 2014, and a successful eradication program was undertaken. Stratified surveillance was conducted as part the program, and allowed for scenario tree analysis to statistically support the claim of freedom. Our analysis demonstrated a mean probability of freedom was 93.1%, 99.5% and > 99.9% after one, two or three surveys for two nests within 2 km of the detection. We demonstrated > 99.9% probability of freedom after three surveys if for a threshold value of five nests were present. Our analysis was the basis of declaring Sydney free from S. invicta. Sydney was declared free 18 months after the first detection of S. invicta.

Appendices

Appendix: Model calculations

Adjusted risk

The relative risk values are normalised to take account of differing population proportions to produce an adjusted risk (AR) value, as:

$${AR}_{i}={RR}_{i}/\sum {(RR}_{i}\times {PPr}_{i})$$

where PPr_i is the population proportion for risk group i.

Effective probability of infestation

The effective probability of infestation (EPI) is the design prevalence, adjusted for risk, for each risk group, and is calculated as design prevalence multiplied by the adjusted risk. Further, the effective probability of infestation for residential properties was further adjusted to account for multiple residential blocks per nest area unit by dividing the value by the estimated number of blocks per unit (about 12).

Component sensitivity

For each survey component (RP, MRIP, HRIP), a component sensitivity (CSe) was calculated using a binomial approximation to the hypergeometric distribution as:

$$CSe= 1-{(1-USe \times \frac{n}{N})}^{(EPI \times N)}$$

where USe is the mean unit sensitivity across all units surveyed, n is the number of units surveyed and N is the number of units in the population. For RP in surveys 2 and 3 and HRIP and MRIP in all surveys, n = N.

For passive surveillance, USe was calculated as the product of P(owner notices a nest), and P(Confirmed).

Surveillance sensitivity

Surveillance sensitivity (SSe) is the combined sensitivity of all three components and was calculated as:

$$SSe=1-\Pi \left(1-{CSe}_{i}\right)$$

Probability of freedom

The probability of freedom (PFree) is calculated using Bayes’ Theorem as:

$$PFree=Prior/(1-SSe \times \left(1-Prior\right))$$

where prior is the prior level of confidence of freedom before the survey was undertaken. For the first survey this was assumed to be 0.5, representing no knowledge (or infestation and freedom are equally likely) while for subsequent surveys it was the posterior PFree estimate from the previous survey.