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Contact tracing is a crucial tool in infection prevention and control (IPC), which aims to identify outbreaks and prevent onward transmission. What constitutes a contact is typically based on strict binary criteria (i.e., being at a location at the same time). Missing data, indirect contacts and background sources can however substantially alter contact-tracing investigations. Here, we present StEP, a Spatial-temporal Epidemiological Proximity model that accounts for imperfect data by introducing a network-based notion of contact based on spatial-temporal proximity derived from background flows of patient movement. We showcase StEP by analysing outbreaks of multidrug-resistant bacteria and COVID-19 within a large hospital Trust in London (UK).StEP utilises spatial-temporal patient trajectories and the background hospital movement flows to recover enhanced contact networks. Firstly, we study a well-characterised outbreak of carbapenemase-producing Enterobacteriaceae (CPE) involving 116 hospitalised patients where genetic sequencing is used to learn model parameters. Secondly, our trained model is deployed in an unsupervised manner on three unseen outbreaks involving 867 patients of related CPE-types. Thirdly, we test application to an altogether novel pathogen by analysing a hospital outbreak of COVID-19 among 90 hospital patients, and demonstrate the power of StEP when characterising newly emerging diseases, even when there is a lack of sequencing data. In addition to recovering core contact structures, StEP identifies missing contacts that link seemingly unconnected infection clusters, revealing a larger extent of transmission than conventional methods. Via genomic analyses we confirm that the additional contacts detected through StEP lead to improved alignment to the plasmid phylogeny (the major outbreak driving force). Hence the StEP contact network is most aligned to the transmission structure. By considering spatial-temporal information in a continuous manner, StEP tackles several challenges associated with traditional contact-tracing. StEP allows both direct and indirect contacts as possible routes of disease transmission and is tuneable to a pathogen's epidemiological characteristics. Such flexible use of heterogeneous data in uncertain situations can significantly enhance IPC. [ABSTRACT FROM AUTHOR]