Abstract
The first wave of the COVID-19 pandemic was characterized by an initial rapid rise in new cases followed by a peak and a more erratic behaviour that varies between regions. This is not easy to reproduce with traditional SIR models, which predict a more symmetric epidemic. Here, we argue that superspreaders and population heterogeneity would predict such behaviour even in the absence of restrictions on social life. We present an agent-based lattice model of a disease spreading in a heterogeneous population. We predict that an epidemic driven by superspreaders will spread rapidly in cities, but not in the countryside where the sparse population limits the maximal number of secondary infections. This suggests that mitigation strategies should include restrictions on venues where people meet a large number of strangers. Furthermore, mitigating the epidemic in cities and in the countryside may require different levels of restrictions.