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 exhibit emergence and annihilation 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 synchronization 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.
One of the most fascinating phenomena that has intrigued researchers in the area of nonlinear dynamics for the last fifteen years is a very peculiar pattern of behavior known as chimera states, which is characterized by the simultaneous coexistence of regions of coherent and incoherent dynamics. This pattern was found when identical oscillators were connected with a non-local coupling of high symmetry. In the following years, chimera states have attracted a lot of interest and have been studied theoretically and experimentally in a variety of different contexts. This paper investigates how chimera states can appear in epidemic models, and it also explores wider dynamics of multi-strain diseases with time delay and non-local coupling.