## Abstract

After some historical remarks about the development of mathematical theory for infectious disease dynamics, we introduce a basic mathematical model for the spread of an infection with immunity. The concepts of the model are explained and the model equations are derived from first principles. Using this simple framework, we derive central concepts of infectious disease modeling such as the basic reproduction number, the endemic steady state, and the critical vaccination coverage. We explain how the basic model can be extended in various directions to accommodate specific modeling questions and needs. Finally, we give some recent examples of the use of infectious disease modeling for public health policy making.

Original language | English |
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Title of host publication | International Encyclopedia of Public Health |

Publisher | Elsevier |

Pages | 579-585 |

Number of pages | 7 |

Edition | 2 |

ISBN (Electronic) | 9780128037089 |

ISBN (Print) | 9780128036785 |

DOIs | |

Publication status | Published - 2017 |

## Keywords

- Age structure
- Basic reproduction number
- Compartmental models
- Contingency planning
- Cost-effectiveness analysis
- Critical vaccination coverage
- Elimination
- Endemic steady state
- Extinction of infection
- Final epidemic size
- Force of infection
- Heterogeneity
- Minor and major outbreaks
- Network models
- Population mixing
- Scale-free networks
- SIR model
- Stochastic models