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 | |
| 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
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 proceeding › Chapter
}
TY - CHAP
T1 - Age-Structured Models
AU - Magal, Pierre
AU - Ruan, Shigui
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85068116512&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85068116512&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-01506-0_8
DO - 10.1007/978-3-030-01506-0_8
M3 - Chapter
T3 - Applied Mathematical Sciences (Switzerland)
SP - 357
EP - 449
BT - Applied Mathematical Sciences (Switzerland)
PB - Springer
ER -