Abstract

In simple SI epidemic and endemic models, three classes of incidence functions are identified for their potential to be associated with host extinction: weakly upper density-dependent incidences are never associated with host extinction. Power incidences that depend on the number of susceptibles and infectives by powers strictly between 0 and 1 are associated with initial-constellation-dependent host extinction for all parameter values. Homogeneous incidences, of which frequency-dependent incidence is a very particular case, and power incidences are associated with global host extinction for certain parameter constellations and with host survival for others. Laboratory infection experiments with salamander larvae are equally well fitted by power incidences and certain upper density-dependent incidences such as the negative binomial incidence and do not rule out homogeneous incidences such as an asymmetric frequency-dependent incidence either.

Original languageEnglish (US)
Pages (from-to)1-62
Number of pages62
JournalJournal of Mathematical Biology
DOIs
StateAccepted/In press - May 21 2018

Fingerprint

Infectious Diseases
infectious diseases
Communicable Diseases
Incidence
incidence
Experiments
Extinction
extinction
Dependent
Laboratory Infection
Urodela
Negative Binomial
salamanders and newts
Larva
Infection
Strictly

Keywords

  • Host decline
  • Host extinction
  • Host persistence
  • Incidence function
  • Tiger salamanders

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

Do fatal infectious diseases eradicate host species? / Farrell, Alex P.; Collins, James; Greer, Amy L.; Thieme, Horst.

In: Journal of Mathematical Biology, 21.05.2018, p. 1-62.

Research output: Contribution to journalArticle

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