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Increasing rates of global trade and travel, as well as changing climaticpatterns, have led to more frequent outbreaks of plant disease epidemicsworldwide. Mathematical modelling is a key tool in predicting where and howthese new threats will spread, as well as in assessing how damaging they mightbe. Models can also be used to inform disease management, providing a rationalmethodology for comparing the performance of possible control strategiesagainst one another. For emerging epidemics, in which new pathogens or pathogenstrains are actively spreading into new regions, the spatial component ofspread becomes particularly important, both to make predictions and to optimisedisease control. In this chapter we illustrate how the spatial spread ofemerging plant diseases can be modelled at the landscape scale via spatiallyexplicit compartmental models. Our particular focus is on the crucial role ofthe dispersal kernel-which parameterises the probability of pathogen spreadfrom an infected host to susceptible hosts at any given distance-in determiningoutcomes of epidemics. We add disease management to our model by testingperformance of a simple ''one off'' form of reactive disease control, in whichsites within a particular distance of locations detected to contain infectionare removed in a single round of disease management. We use this simplifiedmodel to show how ostensibly arcane decisions made by the modeller-most notablywhether or not the underpinning disease model allows for stochasticity (i.e.randomness)-can greatly impact on disease management recommendations. Ourchapter is accompanied by example code in the programming language R availablevia an online repository, allowing the reader to run the models we present forhim/herself.

Optimising reactive disease management using spatially explicit models at the landscape scale