Times from Infection to Disease-Induced Death and their Influence on Final Population Sizes After Epidemic Outbreaks

Alex P. Farrell, James Collins, Amy L. Greer, Horst Thieme

Research output: Contribution to journalArticle

3 Scopus citations


For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. However, if the incidence function is also lower density-dependent, very infectious diseases can lead to a drastic decline of the host population. Further, the final population size after an epidemic outbreak can possibly be substantially affected by the infection-age distribution of the initial infectives if the life expectations of infected individuals are an unbounded function of infection age (time since infection). This is the case for lognormal distributions, which fit data from infection experiments involving tiger salamander larvae and ranavirus better than gamma distributions and Weibull distributions.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalBulletin of Mathematical Biology
StateAccepted/In press - May 21 2018



  • Functional equation
  • Host extinction
  • Incidence function
  • Infection age
  • Lognormal distribution
  • Tiger salamander

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

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