On the duration of a Maki-Thompson epidemic.
In a Maki-Thompson model for the spread of a rumor, it is assumed that a person tells a rumor to anyone he meets until he encounters another person who has already heard it. If the population is large, it has been proved that, in the end, approximately 80% of the population will know the rumor. In this paper we will derive the (asymptotic) mean of the time it takes until the rumor dies away. It is shown that this time grows rather slowly with population size. In fact, if the population consists of W persons, and if a person meets in the mean mu persons per time unit, then the asymptotic mean duration is approximately [2.68 ln(W) + 1.34]/mu time units.
Stockholm University, Department of Statistics, Sweden.
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Svensson
D003141:Communicable Diseases / Q000453:epidemiology*; D004812:Epidemiologic Methods; D006801:Humans; D007398:Interpersonal Relations; D008433:Mathematics; D015233:Models, Statistical; D013269:Stochastic Processes; D013997:Time Factors