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). This gave rise to concerns about a possible second wave of coronavirus disease 2019 (COVID-19). These restrictions were imposed in response to the presence of COVID-19 in populations, usually with the broad support of affected populations. However, the lifting of restrictions is also a population response to the accumulating socio-economic impacts of restrictions, and lifting of restrictions is expected to increase the number of COVID-19 cases, in turn. This suggests that the COVID-19 pandemic exemplifies a coupled behavior-disease system where disease dynamics and social dynamics are locked in a mutual feedback loop. 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 governing epidemiological and social conditions, on account of instabilities generated by behavior-disease interactions. The second wave tends to have a higher peak than the first wave when the efficacy of restrictions is greater than 40% and when the basic reproduction number R0 is less than 2.4. Surprisingly, we also found that a lower R0 value makes a second wave more likely, on account of behavioral feedback (although a lower R0 does not necessarily cause more infections, in total). We conclude that second waves of COVID-19 can be interpreted as the outcome of non-linear interactions between disease dynamics and social behavior. We also suggest that further development of mathematical models exploring behavior-disease interactions could help us better understand how social and epidemiological conditions together determine how pandemics unfold.