Is testing the bee-all and end-all of varroa eradication?

Varroa destructor is a significant European honeybee pest, impacting agricultural industries globally. Since arriving in 2022, Australia faces the possibility that varroa will become established in European honeybee colonies nationally. Australia initially pursued a strategy of testing and subsequently eliminating hives infested with varroa. These management efforts raise interesting questions about the interplay between hive testing and elimination, and the spread of varroa between hives. This study uses mathematical modelling to investigate how combined hive testing and elimination strategies impact the spread of varroa through a network of European honeybee hives. We develop a model of both within-hive reproduction of varroa and hive testing, and between-hive movement of varroa on a network of hives. This model is used to assess the impact of various testing and hive elimination strategies on the total number of hives eliminated on the network of hives. Each model simulation starts with a single infested hive, and from this we observed one of two dynamics: either the infestation is caught before spreading, or varroa spreads extensively through the network before being caught by testing. Within our model we implement two common hive testing methods - sugar shake and alcohol testing. A shared limitation of these testing methods is that they can only detect mites in a specific stage of their lifecycle. As such, testing is not only dependent on how many varroa mites are in a hive, but what lifecycle stage the mites are in at the time of testing. By varying testing and movement parameters, we see that this testing limitation greatly impacts the number of hives eliminated in various scenarios. We find that there are largely two invasion possibilities: either there is only a small incursion, or that varroa achieves complete spread on the network. Furthermore, testing earlier, or testing more frequently, does not guarantee a smaller invasion. Our model results suggest irregular testing schedules, e.g. testing multiple times in close succession rather than just once in a given timeframe, may help overcome the limitations of common hive testing strategies.