Infectious diseases impose a critical challenge to human, animal, and plant health. Emerging and reemerging pathogens-such as SARS, inﬂuenza, and hemorrhagic fever among humans, or foot-and-mouth disease and classical swine fever among animals-hit the news coverage with regular certainty. Zoonoses and host-transmitted diseases underline how signiﬁcant the connection is between human and animal diseases. While plant epidemics receive less immediate attention, they can severely impact crop yield or wipe out entire species. Unifying for the above epidemics is that they all represent realization of temporal processes. Why does the spatial dimension then matter for the modelling of epidemics? It depends very much on the aims of the analysis: many relevant questions can be adequately answered by models considering the population as homogeneous. However, in other situations, heterogeneity is important, for example, induced by age or spatial structure of the population. Spatially varying demographic and environmental factors could inﬂuence the disease transmission. Furthermore, having a spatial resolution allows the model to express spatial heterogeneity in the manifestation of the disease over time. This becomes particularly important when investigating the probability of fade-out or short-term prediction of
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T&F Cat #K23899 — K23899 C026 — page 478 — 2/19/2016 — 20:30
the location of new cases. This kind of analysis represents an important mathematical contribution aimed at understanding the dynamics of disease transmission and predicting the course of epidemics in order to, for example, assess control measures or determine the source of an epidemic. This chapter is about the spatiotemporal analysis of epidemic processes.