Universal Behavior in a Generalized Model of Contagion
Monday, November 17, 2003 - 11:00am - 11:50am
Models of contagion arise broadly both in the biological and social sciences, with applications ranging from the transmission of infectious disease (1, 2) to the diffusion of innovations (3, 4) and the spread of cultural fads (5-7). We present 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 as special limiting cases, and interpolates between them. We study in detail a simple version of the model, finding that under general conditions only three classes of collective dynamics exist, two of which correspond to familiar epidemic threshold (8) and critical mass (9) dynamics, while the third is a distinct intermediate case. Furthermore, we find that for a given length of memory, the class into which a particular system falls is determined entirely by the values of two variables, each of which ought to be measurable empirically. 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.