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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1371-1398
• 页数: 28页
• 语种: 英文
• DOI: 10.1007/s11425-016-0371-8

摘要

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.