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Mean-field-type equations for spread of epidemics: the ‘small world’ model

1999; Elsevier BV; Volume: 274; Issue: 1-2 Linguagem: Inglês

10.1016/s0378-4371(99)00393-3

1873-2119

A. Kleczkowski, Bryan T. Grenfell,

Opinion Dynamics and Social Influence

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.