### Abstract

We use a stochastic branching process to describe the beginning of a disease outbreak. Unlike compartmental models, if the basic reproduction number is greater than one there may be a minor outbreak or a major epidemic with a probability depending on the nature of the contact network. We use a network approach to determine the distribution of outbreak and epidemic sizes.

Original language | English (US) |
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Title of host publication | Mathematical Epidemiology |

Publisher | Springer Verlag |

Pages | 133-146 |

Number of pages | 14 |

ISBN (Print) | 9783540789109 |

DOIs | |

State | Published - Jan 1 2008 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 1945 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Brauer, F. (2008). An introduction to networks in epidemic modeling. In

*Mathematical Epidemiology*(pp. 133-146). (Lecture Notes in Mathematics; Vol. 1945). Springer Verlag. https://doi.org/10.1007/978-3-540-78911-6_4