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.
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U2 - 10.1007/978-3-030-01506-0_8
DO - 10.1007/978-3-030-01506-0_8
M3 - Chapter
AN - SCOPUS:85068116512
T3 - Applied Mathematical Sciences (Switzerland)
SP - 357
EP - 449
BT - Applied Mathematical Sciences (Switzerland)
PB - Springer
ER -