A model for an SI disease in an age - Structured population

Fred Brauer

doi:10.3934/dcdsb.2002.2.257

A model for an SI disease in an age - Structured population

Fred Brauer

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We formulate and analyze a model for an infectious disease which does not cause death but for which infectives remain infective for life. We derive the basic reproductive number R₀ and show that there is a unique globally asymptotically stable equilibrium, namely the disease - free equilibrium if R₀ < 1 and the endemic equilibrium if R ₀ > 1. However, the relation between the basic reproductive number, the mean age at infection, and the mean life span depends on the distribution of life spans and may be quite different from that for exponentially distributed life spans or very short infective periods.

Original language	English (US)
Pages (from-to)	257-264
Number of pages	8
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	2
Issue number	2
DOIs	https://doi.org/10.3934/dcdsb.2002.2.257
State	Published - May 2002
Externally published	Yes

Keywords

Age - structured populations
Epidemic models

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2002.2.257

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abstract = "We formulate and analyze a model for an infectious disease which does not cause death but for which infectives remain infective for life. We derive the basic reproductive number R0 and show that there is a unique globally asymptotically stable equilibrium, namely the disease - free equilibrium if R0 < 1 and the endemic equilibrium if R 0 > 1. However, the relation between the basic reproductive number, the mean age at infection, and the mean life span depends on the distribution of life spans and may be quite different from that for exponentially distributed life spans or very short infective periods.",

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AB - We formulate and analyze a model for an infectious disease which does not cause death but for which infectives remain infective for life. We derive the basic reproductive number R0 and show that there is a unique globally asymptotically stable equilibrium, namely the disease - free equilibrium if R0 < 1 and the endemic equilibrium if R 0 > 1. However, the relation between the basic reproductive number, the mean age at infection, and the mean life span depends on the distribution of life spans and may be quite different from that for exponentially distributed life spans or very short infective periods.

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A model for an SI disease in an age - Structured population

Abstract

Keywords

ASJC Scopus subject areas

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