# Epidemic process

From Encyclopedia of Mathematics

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

#### Comments

#### References

[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: http://encyclopediaofmath.org/index.php?title=Epidemic_process&oldid=14259

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