Age-Structured Models

Pierre Magal; Shigui Ruan

doi:10.1007/978-3-030-01506-0_8

Age-Structured Models

Pierre Magal, Shigui Ruan

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English (US)
Title of host publication	Applied Mathematical Sciences (Switzerland)
Publisher	Springer
Pages	357-449
Number of pages	93
DOIs	https://doi.org/10.1007/978-3-030-01506-0_8
State	Published - Jan 1 2018

Publication series

Name	Applied Mathematical Sciences (Switzerland)
Volume	201
ISSN (Print)	0066-5452
ISSN (Electronic)	2196-968X

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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

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Access to Document

10.1007/978-3-030-01506-0_8