  Classically, endemic diseases are expected to display relatively stable,
predictable infection dynamics. Indeed, diseases like influenza show yearly
recurring infection waves that can be anticipated accurately enough to develop
and distribute new vaccines. In contrast, newly-emerging diseases may cause
more complex, unpredictable dynamics, like COVID-19 has demonstrated. Here we
show that complex infection dynamics can also occur in the endemic state of
seasonal diseases when including human behaviour. We implement human behaviour
as a feedback between incidence and disease mitigation and study the system as
an epidemiological oscillator driven by seasonality. When behaviour and
seasonality have a comparable impact, we find a rich structure in parameter and
state space with Arnold tongues, co-existing attractors, and chaos. Moreover,
we demonstrate that if a disease requires active mitigation, balancing costs of
mitigation and infections can lead societies right into this complex regime. We
observe indications of this when comparing past COVID-19 and influenza data to
model simulations. Our results challenge the intuition that endemicity implies
predictability and seasonal waves, and show that complex dynamics can dominate
even in the endemic phase.
