Population persistence and extinction in a discrete-time, stage-structured epidemic model

Keith E. Emmert, Linda J.S. Allen

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

A discrete-time model is formulated for the spread of disease in a structured host population. The host population is subdivided into three developmental stages, larva, juvenile and adult, and each stage can be infected by the pathogen. We investigate conditions on the parameters where either the host population does not survive or the host population survives and is free from the disease. Several different submodels of the full structured epidemic model are studied and conditions are derived for global stability of the extinction equilibrium and local stability of the disease-free equilibrium. Some numerical examples are presented to illustrate the dynamics of the model when the disease-free equilibrium is not stable. The motivation for our model is the spread of a fungal pathogen in amphibian populations.

Original languageEnglish
Pages (from-to)1177-1199
Number of pages23
JournalJournal of Difference Equations and Applications
Volume10
Issue number13-15
DOIs
StatePublished - Nov 2004

Keywords

  • Bifurcation diagram
  • Populations
  • SIR epidemic model
  • Structured population

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