  A feature often observed in epidemiological networks is significant
heterogeneity in degree. A popular modelling approach to this has been to
consider large populations with highly heterogeneous discrete contact rates.
This paper defines an individual-level non-Markovian stochastic process that
converges on standard ODE models of such populations in the appropriate
asymptotic limit. A generalised Sellke construction is derived for this model,
and this is then used to consider final outcomes in the case where
heterogeneity follows a truncated Zipf distribution.
