title: Calculating the time to extinction of a reactivating virus, in particular bovine herpes virus.
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.
authors.affiliation: Animal Sciences Group, WUR P.O. Box 65, 8200 AB Lelystad, The Netherlands. aline.dekoeijer@wur.nl
authors.forename: A A
authors.initials: AA
authors.lastname: de Koeijer
authors.forename: O
authors.initials: O
authors.lastname: Diekmann
authors.forename: M C M
authors.initials: MC
authors.lastname: de Jong
mesh_terms: D000818:Animals; D002417:Cattle; D002418:Cattle Diseases / Q000453:epidemiology / Q000821:virology*; D004196:Disease Outbreaks / Q000662:veterinary*; D006566:Herpesviridae Infections / Q000453:epidemiology / Q000662:veterinary* / Q000821:virology; D007242:Herpesvirus 1, Bovine / Q000502:physiology*; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D014775:Virus Activation; D017735:Virus Latency