Age-Structured Models

Pierre Magal, Shigui Ruan

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter we apply the results obtained in the previous chapters to age-structured models. In Section 8.1, a Hopf bifurcation theorem is established for the general age-structured systems. Section 8.2 deals with a susceptible-infectious epidemic model with age of infection, uniform persistence of the model is established, local and global stability of the disease-free equilibrium is studied by spectral analysis, and global stability of the unique endemic equilibrium is discussed by constructing a Liapunov functional. Section 8.3 focuses on a scalar age-structured model, detailed results on the existence of integrated solutions, local stability of equilibria, Hopf bifurcation, and normal forms are presented.

Original languageEnglish (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages357-449
Number of pages93
DOIs
StatePublished - Jan 1 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume201
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Fingerprint

Age-structured Model
Local Stability
Global Stability
Hopf Bifurcation
Liapunov Functional
Uniform Persistence
Endemic Equilibrium
Hopf bifurcation
Stability of Equilibria
Epidemic Model
Spectral Analysis
Normal Form
Infection
Scalar
Theorem
Spectrum analysis
Model

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Magal, P., & Ruan, S. (2018). Age-Structured Models. In Applied Mathematical Sciences (Switzerland) (pp. 357-449). (Applied Mathematical Sciences (Switzerland); Vol. 201). Springer. https://doi.org/10.1007/978-3-030-01506-0_8

Age-Structured Models. / Magal, Pierre; Ruan, Shigui.

Applied Mathematical Sciences (Switzerland). Springer, 2018. p. 357-449 (Applied Mathematical Sciences (Switzerland); Vol. 201).

Research output: Chapter in Book/Report/Conference proceedingChapter

Magal, P & Ruan, S 2018, Age-Structured Models. in Applied Mathematical Sciences (Switzerland). Applied Mathematical Sciences (Switzerland), vol. 201, Springer, pp. 357-449. https://doi.org/10.1007/978-3-030-01506-0_8
Magal P, Ruan S. Age-Structured Models. In Applied Mathematical Sciences (Switzerland). Springer. 2018. p. 357-449. (Applied Mathematical Sciences (Switzerland)). https://doi.org/10.1007/978-3-030-01506-0_8
Magal, Pierre ; Ruan, Shigui. / Age-Structured Models. Applied Mathematical Sciences (Switzerland). Springer, 2018. pp. 357-449 (Applied Mathematical Sciences (Switzerland)).
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