Quarantine and surveillance strategies for plant pathogen detection and control

Incursions of plant pests and diseases pose serious threats to food security, agricultural productivity and the natural environment. One of the challenges in confidently delimiting and eradicating incursions is how to choose from an arsenal of surveillance and quarantine approaches in order to best control multiple dispersal pathways. Anthropogenic spread (propagules carried on humans or transported on produce or equipment) can be controlled with quarantine measures, which in turn can vary in intensity. In contrast, environmental spread processes are more difficult to control, but often have a temporal signal (e.g. seasonality) which can introduce both challenges and opportunities for surveillance and control. This leads to complex decisions regarding when, where and how to search. Recent modelling investigations of surveillance performance have optimised the output of simulation models, and found that a risk-weighted randomised search can perform close to optimally. However, exactly how quarantine and surveillance strategies should change to reflect different dispersal modes remains largely unaddressed. Here we develop a spatial simulation model of a plant fungal-pathogen incursion into an agricultural region, and its subsequent surveillance and control. We include structural differences in dispersal via the interplay of biological, environmental and anthropogenic connectivity between host sites (farms). Our objective was to gain broad insights into the relative roles played by different spread modes in propagating an invasion, and how incorporating knowledge of these spread risks may improve approaches to quarantine restrictions and surveillance. We find that broad heuristic rules for quarantine restrictions fail to contain the pathogen due to residual connectivity between sites, but surveillance measures enable early detection and successfully lead to suppression of the pathogen in all farms. Alternative surveillance strategies attain similar levels of performance by incorporating environmental or anthropogenic dispersal risk in the prioritisation of sites. Our model provides the basis to develop essential insights into the effectiveness of different surveillance and quarantine decisions for fungal pathogen control. Parameterised for authentic settings it will aid our understanding of how the extent and resolution of interventions should suitably reflect the spatial structure of dispersal processes.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.