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.

The authors have declared no competing interest.

All authors received support from the Max-Planck-Society. SC, JW, SB and VP acknowledge funding from BMBF, RESPINOW (Project 031L0298) and infoXpand (Project 031L0300A) consortia.

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All code to reproduce the analysis and figures shown in the manuscript as well as in the supplementary information will be available online on GitHub https://github.com/Priesemann-Group/chaosproject