We consider an SIR (Susceptible-Infective-Recovered) epidemic on a static (configuration model) random network. We describe the final stages of the epidemic and analyse the time until extinction of the epidemic. Furthermore we consider the effect of control measures, such as vaccination on the duration of the epidemic. The analysis heavily relies on theory on branching processes.

We show that the epidemic is always exponentially declining in the final stages, even if the degree distribution of the network has infinite variance. Furthermore, we show that control measures, although decreasing the size of the epidemic, might well increase the duration of the epidemic, which might have serious public health and economic implications.