Early detection surveillance for an emerging plant pathogen: a rule of thumb to predict prevalence at first discovery.

Emerging plant pathogens are a significant problem for conservation and food security. Surveillance is often instigated in an attempt to detect an invading epidemic before it gets out of control. Yet in practice many epidemics are not discovered until already at a high prevalence, partly due to a lack of quantitative understanding of how surveillance effort and the dynamics of an invading epidemic relate. We test a simple rule of thumb to determine, for a surveillance programme taking a fixed number of samples at regular intervals, the distribution of the prevalence an epidemic will have reached on first discovery (discovery-prevalence) and its expectation E(q*). We show that E(q*) = r/(N/Δ), i.e. simply the rate of epidemic growth divided by the rate of sampling; where r is the epidemic growth rate, N is the sample size and Δ is the time between sampling rounds. We demonstrate the robustness of this rule of thumb using spatio-temporal epidemic models as well as data from real epidemics. Our work supports the view that, for the purposes of early detection surveillance, simple models can provide useful insights in apparently complex systems. The insight can inform decisions on surveillance resource allocation in plant health and has potential applicability to invasive species generally.