Calculating the time to extinction of a reactivating virus, in particular bovine herpes virus

A.A. de Koeijer, O. Diekmann, M.C.M. de Jong

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)111-131
JournalMathematical Biosciences
Issue number2
Publication statusPublished - 2008


  • vaccine
  • cattle
  • field
  • model

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