Analytical Bayesian approach for the design of surveillance and control programs to assess pest-eradication success

Large invasive species eradication programs are undertaken to protect native biodiversity and agriculture. Programs are typically followed by a series of surveys to assess the likelihood of eradication success and, when residual pests are detected, small-scale control or 'mop-ups' are implemented to eliminate these infestations. Further surveys follow to confirm absence with 'freedom' declared when a target probability of absence is reached. Such biosecurity programs comprise many interacting processes - stochastic biological processes including growth, and response and control interventions - and are an important component of post-border biosecurity. Statistical frameworks formulated to contribute to the design and efficiency of these surveillance and control programs are few and, those available, rely on the simulation of the component processes. In this paper we formulate an analytical Bayesian framework for a general biosecurity program with multiple components to assess pest-eradication success. Our model incorporates stochastic growth and detection processes, and several pest control mechanisms. Survey results and economic considerations are also taken into account to support a range of biosecurity management decisions. Using a case study we demonstrate that solutions match published simulation results and extend the available analysis. Principally, we show how analytical solutions can offer a powerful tool to support the design of effective and cost-efficient biosecurity systems, and we establish some general principles that guide and contribute to robust design.