Bulletin of Mathematical Biology

, Volume 80, Issue 7, pp 1937–1961 | Cite as

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

  • Alex P. Farrell
  • James P. Collins
  • Amy L. Greer
  • Horst R. Thieme
Original Article


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.


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



The authors thank Andrea Pugliese and two anonymous referees for careful reading and useful comments.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  • Alex P. Farrell
    • 1
    • 4
  • James P. Collins
    • 2
  • Amy L. Greer
    • 3
  • Horst R. Thieme
    • 1
  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA
  2. 2.School of Life SciencesArizona State UniversityTempeUSA
  3. 3.Department of Population MedicineOntario Veterinary College University of GuelphGuelphCanada
  4. 4.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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