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 |
ASJC Scopus subject areas
- Applied Mathematics
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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