title: Recurrent epidemics in small world networks.
abstract: The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic susceptible-infective-recovered (SIR) 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 have another major effect through the enhancement of stochastic fluctuations, which may become considerably larger than in the homogeneously mixed stochastic model. As a consequence, in finite spatially structured populations significant differences from the solutions of deterministic models are to be expected, since sizes even larger than those found for homogeneously mixed stochastic models are required for the effects of fluctuations to be negligible. 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 susceptible-exposed-infective-recovered (SEIR) 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.
authors.affiliation: Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal.
authors.forename: J
authors.initials: J
authors.lastname: Verdasca
authors.forename: M M
authors.initials: MM
authors.lastname: Telo da Gama
authors.forename: A
authors.initials: A
authors.lastname: Nunes
authors.forename: N R
authors.initials: NR
authors.lastname: Bernardino
authors.forename: J M
authors.initials: JM
authors.lastname: Pacheco
authors.forename: M C
authors.initials: MC
authors.lastname: Gomes
mesh_terms: D004196:Disease Outbreaks; D004198:Disease Susceptibility; D018562:Disease Transmission, Infectious; D006801:Humans; D008457:Measles / Q000453:epidemiology; D008954:Models, Biological; D015233:Models, Statistical; D016571:Neural Networks, Computer; D012008:Recurrence; D014917:Whooping Cough / Q000453:epidemiology