Global Hopf bifurcation of an SIRS epidemic model with age-dependent recovery

In this paper, an age structured SIRS epidemic model with age of recovery is studied which allows the removed individuals to become susceptible again when they lose the protection property as the time goes. The age structured model is reformulated as an abstract non-densely defined Cauchy problem and the expression of the basic reproduction number, R0, is obtained. If R0<1, the model only has the disease-free steady state and it is global stability. If R0>1, besides the disease-free steady state the model also has an endemic steady state. By analyzing the associated characteristic equation, the existence of a local Hopf bifurcation is proved under certain conditions. Also, we considered the global continuation of the local Hopf bifurcation. Finally, some numerical simulations are carried out to illustrate the theoretical results.