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

Keith E. Emmert; Linda J.S. Allen

doi:10.1080/10236190410001654151

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

Keith E. Emmert, Linda J.S. Allen

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1177-1199
Number of pages	23
Journal	Journal of Difference Equations and Applications
Volume	10
Issue number	13-15
DOIs	https://doi.org/10.1080/10236190410001654151
State	Published - Nov 2004

Keywords

Bifurcation diagram
Populations
SIR epidemic model
Structured population

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10.1080/10236190410001654151

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