The modern world features a plethora of social, technological and biological epidemic phenomena. These epidemics now spread at unprecedented rates thanks to advances in industrialisation, transport and telecommunications. Effective real-time decision making and management of modern epidemic outbreaks depends on the two factors: the ability to determine epidemic parameters as the epidemic unfolds, and the ability to characterise rigorously the uncertainties inherent in these parameters. This paper presents a generic maximum-likelihoodbased methodology for online epidemic fitting of SIR models from a single trace which yields confidence intervals on parameter values. The method is fully automated and avoids the laborious manual efforts traditionally deployed in the modelling of biological epidemics. We present case studies based on both synthetic and real data.