Societal self-regulation induces complex infection dynamics and chaos

Abstract: Classically, endemic infectious diseases are expected to display relatively stable, predictable infection dynamics. Accordingly, basic disease models such as the susceptible-infected-recovered-susceptible model display stable endemic states or recurrent seasonal waves. However, if the human population reacts to high infection numbers by mitigating the spread of the disease, then this delayed behavioral feedback loop can generate infection waves itself, driven by periodic mitigation and subsequent relaxation. We show that such behavioral reactions, together with a seasonal effect of comparable impact, can cause complex and unpredictable infection dynamics, including Arnold tongues, coexisting attractors, and chaos. Importantly, these arise in epidemiologically relevant parameter regions where the costs associated to infections and mitigation are jointly minimized. By comparing our model to data, we find signs that COVID-19 was mitigated in a way that favored complex infection dynamics. Our results challenge the intuition that endemic disease dynamics necessarily implies predictability and seasonal waves and show the emergence of complex infection dynamics when humans optimize their reaction to increasing infection numbers.