  Recent years have seen a large amount of interest in epidemics on networks as
a way of representing the complex structure of contacts capable of spreading
infections through the modern human population. The configuration model is a
popular choice in theoretical studies since it combines the ability to specify
the distribution of the number of contacts (degree) with analytical
tractability. Here we consider the early real-time behaviour of the Markovian
SIR epidemic model on a configuration model network using a multi-type
branching process. We find closed-form analytic expressions for the mean and
variance of the number of infectious individuals as a function of time and the
degree of the initially infected individual(s), and write down a system of
differential equations for the probability of extinction that are numerically
fast compared to Monte Carlo simulation. We show that these quantities are all
sensitive to the degree distribution - in particular we confirm that the mean
prevalence of infection depends on the first two moments of the degree
distribution and the variance in prevalence depends on the first three moments
of the degree distribution. In contrast to most existing analytic approaches,
the accuracy of these results does not depend on having a large number of
infectious individuals, meaning that in the large population limit they would
be asymptotically exact even for one initial infectious individual.
