Mean-field-type equations for spread of epidemics: The `small world' model

Adam Kleczkowski, Bryan T. Grenfell

Research output: Contribution to journalConference articlepeer-review

67 Scopus citations


In the paper we study a cellular automata (CA) model of epidemic dynamics. The effects of local spatial correlations on a temporal (aggregated) spread of single epidemics are studied, as a function of increasing proportion of global contacts (`small world' model). We conjecture that even in the presence of high local correlations, the aggregated (mean-field-type) models can be quite successful, if the contact rate is treated as a free parameter. The dependence of the (estimated) contact rate on the mixing parameter can be understood in terms of a simple probabilistic model. The contact rate reflects not only a microscopic and epidemiological situation, but also a complicated social pattern, including short- and long-range contacts as well as a possibly hierarchical structure of human society.

Original languageEnglish (US)
Pages (from-to)355-360
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - Dec 1 1999
Externally publishedYes
EventProceedings of the 1999 NATO Advanced Research Workshop 'Applications of Statistical Physics' - Budapest, Hung
Duration: May 19 1999May 22 1999

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics


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