  Increasing rates of global trade and travel, as well as changing climatic
patterns, have led to more frequent outbreaks of plant disease epidemics
worldwide. Mathematical modelling is a key tool in predicting where and how
these new threats will spread, as well as in assessing how damaging they might
be. Models can also be used to inform disease management, providing a rational
methodology for comparing the performance of possible control strategies
against one another. For emerging epidemics, in which new pathogens or pathogen
strains are actively spreading into new regions, the spatial component of
spread becomes particularly important, both to make predictions and to optimise
disease control. In this chapter we illustrate how the spatial spread of
emerging plant diseases can be modelled at the landscape scale via spatially
explicit compartmental models. Our particular focus is on the crucial role of
the dispersal kernel-which parameterises the probability of pathogen spread
from an infected host to susceptible hosts at any given distance-in determining
outcomes of epidemics. We add disease management to our model by testing
performance of a simple ''one off'' form of reactive disease control, in which
sites within a particular distance of locations detected to contain infection
are removed in a single round of disease management. We use this simplified
model to show how ostensibly arcane decisions made by the modeller-most notably
whether or not the underpinning disease model allows for stochasticity (i.e.
randomness)-can greatly impact on disease management recommendations. Our
chapter is accompanied by example code in the programming language R available
via an online repository, allowing the reader to run the models we present for
him/herself.
