### Resumé

Originalsprog | Engelsk |
---|---|

Tidsskrift | Bulletin of Mathematical Biology |

Vol/bind | 73 |

Udgave nummer | 10 |

Sider (fra-til) | 2305-2321 |

Antal sider | 17 |

ISSN | 0092-8240 |

DOI | |

Status | Udgivet - 2011 |

### Citer dette

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*Bulletin of Mathematical Biology*, bind 73, nr. 10, s. 2305-2321. https://doi.org/10.1007/s11538-010-9623-3

**The final size of an epidemic and its relation to the basic reproduction number.** / Andreasen, Viggo.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - The final size of an epidemic and its relation to the basic reproduction number

AU - Andreasen, Viggo

PY - 2011

Y1 - 2011

N2 - We study the final size equation for an epidemic in a subdivided population with general mixing patterns among subgroups. The equation is determined by a matrix with the same spectrum as the next generation matrix and it exhibits a threshold controlled by the common dominant eigenvalue, the basic reproduction number R00: There is a unique positive solution giving the size of the epidemic if and only if R00 exceeds unity. When mixing heterogeneities arise only from variation in contact rates and proportionate mixing, the final size of the epidemic in a heterogeneously mixing population is always smaller than that in a homogeneously mixing population with the same basic reproduction number R00. For other mixing patterns, the relation may be reversed.

AB - We study the final size equation for an epidemic in a subdivided population with general mixing patterns among subgroups. The equation is determined by a matrix with the same spectrum as the next generation matrix and it exhibits a threshold controlled by the common dominant eigenvalue, the basic reproduction number R00: There is a unique positive solution giving the size of the epidemic if and only if R00 exceeds unity. When mixing heterogeneities arise only from variation in contact rates and proportionate mixing, the final size of the epidemic in a heterogeneously mixing population is always smaller than that in a homogeneously mixing population with the same basic reproduction number R00. For other mixing patterns, the relation may be reversed.

U2 - 10.1007/s11538-010-9623-3

DO - 10.1007/s11538-010-9623-3

M3 - Journal article

VL - 73

SP - 2305

EP - 2321

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 10

ER -