Conditions for a second wave of COVID-19 due to interactions between disease dynamics and social processes

In May 2020, many jurisdictions around the world began lifting physical distancing restrictions against the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), giving rise to concerns about a possible second wave of coronavirus disease 2019 (COVID-19). These restrictions were imposed as a collective population response to the presence of COVID-19 in communities. However, lifting restrictions is also a population response to their socio-economic impacts, and is expected to increase COVID-19 cases, in turn. This suggests that the COVID-19 pandemic exemplifies a coupled behaviour-disease system. Here we develop a minimal mathematical model of the interaction between social support for school and workplace closure and the transmission dynamics of SARS-CoV-2. We find that a second wave of COVID-19 occurs across a broad range of plausible model input parameters, on account of instabilities generated by behaviour-disease interactions. We conclude that second waves of COVID-19–should they materialize–can be interpreted as the outcomes of nonlinear interactions between disease dynamics and population behaviour.