The many faces of endemic disease spread. a. Depending on the maximum mitigation required, vastly different dynamics for the endemic incidence can emerge. a1. Classically (without any mitigation), seasonal outbreaks are expected. a2, a3. However, complex oscillatory dynamics can arise when mitigation and seasonality are comparable, featuring complex-periodic waves (e.g., 3 waves in 2 years), or chaos. b. The average number of infections observed for chaotic dynamics (a2.) is substantially lower than that for unmitigated seasonal waves (a1.) and is comparable to when mitigating too strongly (a3.). This implies that societies might have to trade off predictability for reductions in the average number of infections, and that above a certain point, over-mitigation does not pay off. Figure modified from.2