  Networks have become an important tool for infectious disease epidemiology.
Most previous theoretical studies of transmission network models have either
considered simple Markovian dynamics at the individual level, or have focused
on the invasion threshold and final outcome of the epidemic. Here, we provide a
general theory for early real-time behaviour of epidemics on large
configuration model networks (i.e. static and locally unclustered), in
particular focusing on the computation of the Malthusian parameter that
describes the early exponential epidemic growth. Analytical, numerical and
Monte-Carlo methods under a wide variety of Markovian and non-Markovian
assumptions about the infectivity profile are presented. Numerous examples
provide explicit quantification of the impact of the network structure on the
temporal dynamics of the spread of infection and provide a benchmark for
validating results of large scale simulations.
