Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate - Liu, ZhiHua; Yuan, Rong (Science China. Mathematics, 2017)
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.