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Phys Rev Lett. 2004 May 28;92(21):218701. Epub 2004 May 24.

Universal behavior in a generalized model of contagion.

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Institute for Social and Economic Research and Policy, Columbia University, 420 West 118th Street, New York, New York 10027, USA.


Models of contagion arise broadly in both the biological and the social sciences, with applications ranging from the transmission of infectious diseases to the spread of cultural fads. In this Letter, we introduce a general model of contagion which, by explicitly incorporating memory of past exposures to, for example, an infectious agent, rumor, or new product, includes the main features of existing contagion models and interpolates between them. We obtain exact solutions for a simple version of the model, finding that under general conditions only three classes of collective dynamics exist. Furthermore, we find that, for a given length of memory, the class into which a particular system falls is determined by only two parameters. Our model suggests novel measures for assessing the susceptibility of a population to large contagion events, and also a possible strategy for inhibiting or facilitating them.

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