  An epidemic model with distributed time delay is derived to describe the
dynamics of infectious diseases with varying immunity. It is shown that
solutions are always positive, and the model has at most two steady states:
disease-free and endemic. It is proved that the disease-free equilibrium is
locally and globally asymptotically stable. When an endemic equilibrium exists,
it is possible to analytically prove its local and global stability using
Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and
traceDDE to investigate different dynamical regimes in the model using
numerical continuation for different values of system parameters and different
integral kernels.
