Epidemic process

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A random process (cf. Stochastic process) that serves as a mathematical model of the spread of some epidemy. One of the simplest such models can be described as a continuous-time Markov process whose states at the moment are the number of sick persons and the number of exposed persons. If and , then at the time , , , the transition probability is determined as follows: with probability ; with probability . In this case the generating function

satisfies the differential equation



[a1] N.T.J. Bailey, "The mathematical theory of infections diseases and its applications" , Hafner (1975)
[a2] D. Ludwig, "Stochastic population theories" , Springer (1974)
How to Cite This Entry:
Epidemic process. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by B.A. Sevast'yanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article