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 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.