Abstract Surveillance of health outcomes in space and time gives insight into the underlying mech- anisms driving those outcomes, for example with respect to exposures, risk factors and - in the case of infectious diseases - transmission. There are unique challenges for the analysis and interpretation of such data in the case of a rare and/or declining disease and of a rapidly growing novel epidemic. Policy objectives are also often similar - to target interventions to regions most at risk, both in the present and the near-future, for most efficient and effective use of available resources. This thesis uses the examples of visceral leishmaniasis elimination in north-eastern India and the emergence of the novel SARS- CoV-2 virus in England to explore these ideas, from the perspective of decision-making around policies for disease control. Spatial variability driven not by transmission of the disease itself but of its observation influences decisions on further intervention - in the case of VL feeding back into surveillance policies to create a cycle of increasing bias - but is rarely quantified. Patterns in observed incidence of both diseases suggest that the impact of these surveillance systems is likely not consistent over space. The potential pattern of this spatially-varying bias is characterised for visceral leishmaniasis with respect to delays to diagnosis - an important indicator not only of the strength of the surveillance system but also of the likelihood of breaking transmission in low incidence areas. An understanding of the mechanism of surveillance is crucial for appropriate interpretation of the resulting data, and hence for appropriate distribution of intervention efforts. However, in particular in resource-constrained settings of emergence and elimination, the process can be stochastic and difficult to define. This motivates the routine collection of data describing the surveillance process itself, to provide important context to the result- ing observations. Ways in which such information could be incorporated going forward are discussed, suggesting directions of future research to more accurately infer the true spatial distribution of disease burden in such settings.