  This paper investigates the dynamics of infectious diseases with a
non-exponentially distributed infectious period. This is achieved by
considering a multi-stage infection model on networks. Using pairwise
approximation with a standard closure, a number of important characteristics of
disease dynamics are derived analytically, including the final size of an
epidemic and a threshold for epidemic outbreaks, and it is shown how these
quantities depend on disease characteristics, as well as the number of disease
stages. Stochastic simulations of dynamics on networks are performed and
compared to the results of pairwise models for several realistic examples of
infectious diseases to illustrate the role played by the number of stages in
the disease dynamics. These results show that a higher number of disease stages
results in faster epidemic outbreaks with a higher peak prevalence and a larger
final size of the epidemic. The agreement between the pairwise and simulation
methods is excellent in the cases we consider.
