Intervention fatigue is the primary cause of strong secondary waves in the COVID-19 pandemic

Abstract

As of November 2020, the number of COVID-19 cases is increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this study, we first reconstruct the time evolution of the effective reproduction numbers ${\cal R}(t)$ for each country by integrating the equations of the classic SIR model. We cluster countries based on the estimated ${\cal R}(t)$ through a suitable time series dissimilarity. The result suggests that simple dynamical mechanisms determine how countries respond to changes in COVID-19 case counts. Inspired by these results, we extend the SIR model to include a social response to explain the number $X(t)$ of new confirmed daily cases. As a first-order model, we assume that the social response is on the form $d_t{\cal R}=-\nu (X-X^*)$, where $X^*$ is a threshold for response. The response rate $\nu$ depends on whether $X^*$ is below or above this threshold, on three parameters $\nu_1,\;\nu_2,\,\nu_3,$, and on $t$. When $X X^*$, $\nu=\nu_2\exp{(-\nu_3t)}$, models the impact of interventions when incidence rate is high. The parameter $\nu_3$ represents the fatigue, i.e., the reduced effect of intervention as time passes. The proposed model reproduces typical evolving patterns of COVID-19 epidemic waves observed in many countries. Estimating the parameters $\nu_1,\,\nu_2,\,\nu_3$ and initial conditions, such as ${\cal R}_0$, for different countries helps to identify important dynamics in their social responses. One conclusion is that the leading cause of the strong second wave in Europe in the fall of 2020 was not the relaxation of interventions during the summer, but rather the general fatigue to interventions developing in the fall.