A Stochastic Model for Distributions of Biological Response Times

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Abstract
Distributions of time to biological response are determined as functions of challenge dose for a birth-death model employing the following simple assumptions: the actual number of organisms in the challenge dose is Poisson-distributed; the probabilities, per unit time, of birth (division) and of death are each independent of time and population size during the period prior to response; response occurs when and if the number of organisms in the host grows to a fixed large number. Curves and tables are given of frequency of occurrence of various times to response, and of the moments of these distributions. The model is shown to give agreement with experimental data to useful accuracy.

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