  The epidemic threshold is probably the most studied quantity in the modelling
of epidemics on networks. For a large class of networks and dynamics the
epidemic threshold is well studied and understood. However, it is less so for
clustered networks where theoretical results are mostly limited to idealised
networks. In this paper we focus on a class of models known as pairwise models
where, to our knowledge, no analytical result for the epidemic threshold
exists. We show that by exploiting the presence of fast variables and using
some standard techniques from perturbation theory we are able to obtain the
epidemic threshold analytically. We validate this new threshold by comparing it
to the numerical solution of the full system. The agreement is found to be
excellent over a wide range of values of the clustering coefficient,
transmission rate and average degree of the network. Interestingly, we find
that the analytical form of $R_0$ depends on the choice of closure,
highlighting the importance of model choice when dealing with real-world
epidemics. Nevertheless, we ex- pect that our method will extend to other
systems in which fast variables are present.
