  The effect of spatial correlations on the spread of infectious diseases was
investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on
complex networks. It was found that in addition to the reduction of the
effective transmission rate, through the screening of infectives, spatial
correlations may have another major effect through the enhancement of
stochastic fluctuations. As a consequence large populations will have to become
even larger to 'average out' significant differences from the solution of
deterministic models. Furthermore, time series of the (unforced) model provide
patterns of recurrent epidemics with slightly irregular periods and realistic
amplitudes, suggesting that stochastic models together with complex networks of
contacts may be sufficient to describe the long term dynamics of some diseases.
The spatial effects were analysed quantitatively by modelling measles and
pertussis, using a SEIR (Susceptible-Exposed-Infective-Recovered) model. Both
the period and the spatial coherence of the epidemic peaks of pertussis are
well described by the unforced model for realistic values of the parameters.
