  We investigate a time-delayed epidemic model for multi-strain diseases with
temporary immunity. In the absence of cross-immunity between strains, dynamics
of each individual strain exhibits emergence and anni- hilation of limit cycles
due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node
bifurcation of limit cycles depending on the time delay associated with
duration of temporary immunity. Effects of all-to-all and non-local coupling
topologies are systematically investigated by means of numerical simulations,
and they suggest that cross-immunity is able to induce a diverse range of
complex dynamical behaviors and synchro- nization patterns, including discrete
traveling waves, solitary states, and amplitude chimeras. Interestingly,
chimera states are observed for narrower cross-immunity kernels, which can have
profound implications for understanding the dynamics of multi-strain diseases.
