Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
ON EXPECTED DURATIONS OF BIRTH-DEATH PROCESSES, WITH APPLICATIONS TO BRANCHING PROCESSES AND SIS EPIDEMICS
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-9228-7357
Number of Authors: 32016 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 1, p. 203-215Article in journal (Refereed) Published
Abstract [en]

We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q] = 1, and where the birth rate if the population is currently in state (has size) n is alpha(n). We focus on two important examples, namely alpha(n) = lambda n being a branching process, and alpha(n) = lambda n(N-n)/N which corresponds to an SIS (susceptible -> infective -> susceptible) epidemic model in a homogeneously mixing community of fixed size N. The processes are assumed to start with a single individual, i. e. in state 1. Let T, A(n), C, and S denote the (random) time to extinction, the total time spent in state n, the total number of individuals ever alive, and the sum of the lifetimes of all individuals in the birth-death process, respectively. We give expressions for the expectation of all these quantities and show that these expectations are insensitive to the distribution of Q. We also derive an asymptotic expression for the expected time to extinction of the SIS epidemic, but now starting at the endemic state, which is not independent of the distribution of Q. The results are also applied to the household SIS epidemic, showing that, in contrast to the household SIR (susceptible -> infective -> recovered) epidemic, its threshold parameter R-* is insensitive to the distribution of Q.

Place, publisher, year, edition, pages
2016. Vol. 53, no 1, p. 203-215
Keywords [en]
Birth-death process, branching processes, SIS epidemics, insensitivity results
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-175568DOI: 10.1017/jpr.2015.19ISI: 000374172100016OAI: oai:DiVA.org:su-175568DiVA, id: diva2:1368266
Available from: 2019-11-06 Created: 2019-11-06 Last updated: 2019-12-17Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Britton, TomNeal, Peter
By organisation
Department of Mathematics
In the same journal
Journal of Applied Probability
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf