Population Persistence and Extinction in a Discrete-time, Stage-structured Epidemic Model

2004/08/09 by Keith E. Emmert, Keith Emmert, Linda J.S. Allen +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Medicine · #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models #Viral Infections and Vectors

paper · doi:10.1080/10236190410001654151

openalex publication_date 2004/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• The Mathematics of Infectious Diseases

Cited by

• Extinction and quasi-stationarity for discrete-time, endemic SIS and SIR models
• Persistence in a discrete-time, stage-structured epidemic model

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