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A theoretical method based on the concept of “system‐sized expansion” is applied to a generalization of Bartholomew's model of diffusion of information in a population of size N. The model considers a combination of mass‐mediated and interactively mediated messages, with the provision that the spreaders of information may not remain active for an indefinite period of time; it also takes into account the possibility that the parameters governing the process be time‐dependent. Explicit expressions for the time evolution of the diffusion process (including the probability distribution of the relevant variable, its mean value and variance) are derived in the asymptotic regime N ≫ 1. The nonlinear character of the model enables us to exploit our asymptotic expressions for studying finite‐size effects as well; the resulting expressions turn out to be reliable for N as low as 10.
Notes
Work supported in part by the Natural Sciences and Engineering Research Council of Canada.
Requests for reprints should be addressed to the second author c/o Department of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.
