Gastroenteritis, causing vomiting and diarrhoea, is very common all over the world. Viral causes, such as norovirus and rotavirus, are the most frequent, although some bacteria, parasites and fungi can also lead to gastroenteritis. Many countries operate surveillance systems of diseases, including gastroenteritis or specific gastroenteritis causing pathogens. Typically, statistical methods are used to analyse surveillance data and alert public health authorities of unexpectedly high levels of illness. These methods use historical data to predict the expected value of current data. In this thesis, we address some of the challenges that remain when analysing gastroenteritis surveillance data, with a particular focus on syndromic surveillance data. We work with both mechanistic and statistical modelling approaches in an attempt to bridge the gap between the statistical methods that are used in practice for syndromic surveillance and mechanistic models that are used to model infectious diseases. In particular, we address three challenges. In chapter 2 we present a flexible framework for deriving approximations of stochastic mechanistic models of epidemics for fast inference. In chapter 3 we investigate day of the week and public holiday effects in syndromic indicators of gastroenteritis from syndromic surveillance systems operated by Public Health England in order to improve existing surveillance methodologies. In chapter 4 we identify and analyse additional online datasets for gastroenteritis, and in particular norovirus, surveillance.