  We present a modelling framework for the spreading of epidemics on temporal
networks from which both the individual-based and pair-based models can be
recovered. The proposed temporal pair-based model that is systematically
derived from this framework offers an improvement over existing pair-based
models by moving away from edge-centric descriptions while keeping the
description concise and relatively simple. For the contagion process, we
consider the Susceptible-Infected-Recovered (SIR) model, which is realized on a
network with time-varying edges. We show that the shift in perspective from
individual-based to pair-based quantities enables exact modelling of Markovian
epidemic processes on temporal tree networks. On arbitrary networks, the
proposed pair-based model provides a substantial increase in accuracy at a low
computational and conceptual cost compared to the individual-based model. From
the pair-based model, we analytically find the condition necessary for an
epidemic to occur, otherwise known as the epidemic threshold. Due to the fact
that the SIR model has only one stable fixed point, which is the global
non-infected state, we identify an epidemic by looking at the initial stability
of the model.
