Conditions for a Second Wave of COVID-19 Due to Interactions Between Disease Dynamics and Social Processes

Abstract

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 behaviour-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 behaviour-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 R_0 is less than 2.4. Surprisingly, we also found that a lower R_0 value makes a second wave more likely, on account of behavioural feedback (although a lower R_0 does not necessarily cause more infections, in total). We conclude that second waves of COVID-19 can be interpreted as the outcome of nonlinear interactions between disease dynamics and social behaviour. We also suggest that further development of mathematical models exploring behaviour-disease interactions could help us better understand how social and epidemiological conditions together determine how pandemics unfold.