Gaussian process approximations for fast inference from infectious disease data

•We compare Gaussian process approximations to stochastic epidemic models.•We give a framework to quantify the accuracy of these approximations.•Gaussian process approximations are used for fast inference from outbreak data. We present a flexible framework for deriving and quantifying the accuracy of Gaussian process approximations to non-linear stochastic individual-based models of epidemics. We develop this for the SIR and SEIR models, and we show how it can be used to perform quick maximum likelihood inference for the underlying parameters given population estimates of the number of infecteds or cases at given time points. We also show how the unobserved processes can be inferred at the same time as the underlying parameters.