SIS epidemic attractors in periodic environments

The demographic dynamics are known to drive the disease dynamics in constant environments. In periodic environments, we prove that the demographic dynamics do not always drive the disease dynamics. We exhibit a chaotic attractor in an SIS epidemic model, where the demograhic dynamics are asymptotically cyclic. Periodically forced SIS epidemic models are known to exhibit multiple attractors. We prove that the basins of attraction of these coexisting attractors have infinitely many components.