### Abstract

The expected time to extinction of a herpes virus is calculated from a rather simple population-dynamical model that incorporates transmission, reactivation and fade-out of the infectious agent. We also derive the second and higher moments of the distribution of the time to extinction. These quantities help to assess the possibilities to eradicate a reactivating infection. The key assumption underlying our calculations is that epidemic outbreaks are fast relative to the time scale of demographic turnover.
Four parameters influence the expected time to extinction: the reproduction ratio, the reactivation rate, the population size, and the demographic turn-over in the host population.
We find that the expected time till extinction is very long when the reactivation rate is high (reactivation is expected more than once in a life time). Furthermore, the infectious agent will go extinct much more quickly in small populations.
This method is applied to bovine herpes virus (BHV) in a cattle herd. The results indicate that without vaccination, BHV will persist in large herds. The use of a good vaccine can induce eradication of the infection from a herd within a few decades. Additional measures are needed to eradicate the virus from a whole region within a similar time-span.

Original language | English |
---|---|

Pages (from-to) | 111-131 |

Journal | Mathematical Biosciences |

Volume | 212 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 |

### Keywords

- vaccine
- cattle
- field
- model

## Fingerprint Dive into the research topics of 'Calculating the time to extinction of a reactivating virus, in particular bovine herpes virus'. Together they form a unique fingerprint.

## Cite this

de Koeijer, A. A., Diekmann, O., & de Jong, M. C. M. (2008). Calculating the time to extinction of a reactivating virus, in particular bovine herpes virus.

*Mathematical Biosciences*,*212*(2), 111-131. https://doi.org/10.1016/j.mbs.2007.04.002