A STOCHASTIC MODEL OF INCUBATION-PERIOD DISTRIBUTIONS: MATHEMATICAL DEVELOPMENT.
BOOZ-ALLEN APPLIED RESEARCH INC BETHESDA MD
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One of the least-understood processes in the course of infectious disease lies in the incubation period between the initial inoculation with a dose of organisms and the appearance of the first symptom of disease. In naturally occurring diseases, this lack of understanding arises from the fact that cases of infection rarely come under observation until the end of incubation. In laboratory experiments, observations have tended to concentrate on the period of frank disease between the end of incubation and recovery or death. The present work consists of a comprehensive mathematical investigation of a very simple stochastic model of the birth and death of microorganisms during an incubation period, in an attempt to explain the frequency distribution of the length of incubation and the variation of this distribution with size of initial dose. The model starts with the assumption that during incubation the microorganisms act entirely independently and that each individual microorganism has a constant probability of dying in each unit of time, and another constant probability of dividing into two organisms birth. With the passage of time, the microorganisms in an inoculum either disappear or grow to a very large number.
- Medicine and Medical Research