### Abstract

We present continuous-time models for age-structured populations and disease transmission. We show how to use the method of characteristic lines to analyze the model dynamics and to write an age-structured population model as an integral equation model. We then extend to an agestructured SIR epidemic model. As an example we describe an age-structured model for AIDS, derive a formula for the reproductive number of infection, and show how important a role pair-formation plays in the modeling process. In particular, we outline the semi-group method used in an age-structured AIDS model with non-random mixing. We also discuss models for populations and disease spread with discrete age structure.

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

Publisher | Springer Verlag |

Pages | 205-227 |

Number of pages | 23 |

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

*Mathematical Epidemiology*(pp. 205-227). (Lecture Notes in Mathematics; Vol. 1945). Springer Verlag. https://doi.org/10.1007/978-3-540-78911-6_9