Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate

An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing...

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Bibliographic Details
Published inScience China. Mathematics Vol. 60; no. 8; pp. 1371 - 1398
Main Authors Liu, ZhiHua, Yuan, Rong
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.08.2017
Springer Nature B.V
Subjects
Age
Applications of Mathematics
Cauchy problems
Epidemics
Externality
Hopf bifurcation
Hopf分岔
Hopf分支
Incidence
Mathematics
Mathematics and Statistics
Uniqueness
传染率
传染病模型
半线性方程
年龄结构
流行病模型
非线性
non-densely defined
92D30
zero-Hopf bifurcation
epidemic
34K18
35K90
37G10
infection-age structured
normal form
stability
35K55
37L10
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Summary:An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR（susceptible-infected-recovered）epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.
Bibliography:infection-age structured, epidemic, non-densely defined, stability, normal form, zero-Hopf bifurcation
11-5837/O1
An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR（susceptible-infected-recovered）epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-0371-8