Recurrent epidemics in small world networks
  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. 
J. Verdasca (1), M. M. Telo da Gama (1 and 2), A. Nunes (1 and 2), N.   R. Bernardino (1), J. M. Pacheco (1 and 2) and M. C....