  This paper presents a compact pairwise model that describes the spread of
multi-stage epidemics on networks. The multi-stage model corresponds to a
gamma-distributed infectious period which interpolates between the classical
Markovian models with exponentially distributed infectious period and epidemics
with a constant infectious period. We show how the compact approach leads to a
system of equations whose size is independent of the range of node degrees,
thus significantly reducing the complexity of the model. Network clustering is
incorporated into the model to provide a more accurate representation of
realistic contact networks, and the accuracy of proposed closures is analysed
for different levels of clustering and number of infection stages. Our results
support recent findings that standard closure techniques are likely to perform
better when the infectious period is constant.
