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As of November 2020, the number of COVID-19 cases is increasing rapidly inmany countries. In Europe, the virus spread slowed considerably in the latespring due to strict lockdown, but a second wave of the pandemic grewthroughout the fall. In this study, we first reconstruct the time evolution ofthe effective reproduction numbers ${\cal R}(t)$ for each country byintegrating the equations of the classic SIR model. We cluster countries basedon the estimated ${\cal R}(t)$ through a suitable time series dissimilarity.The result suggests that simple dynamical mechanisms determine how countriesrespond to changes in COVID-19 case counts. Inspired by these results, weextend 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 socialresponse is on the form $d_t{\cal R}=-\nu (X-X^*)$, where $X^*$ is a thresholdfor response. The response rate $\nu$ depends on whether $X^*$ is below orabove this threshold, on three parameters $\nu_1,\;\nu_2,\,\nu_3,$, and on $t$.When $X<X^*$, $\nu= \nu_1$, describes the effect of relaxed intervention whenthe incidence rate is low. When $X>X^*$, $\nu=\nu_2\exp{(-\nu_3t)}$, models theimpact of interventions when incidence rate is high. The parameter $\nu_3$represents the fatigue, i.e., the reduced effect of intervention as timepasses. The proposed model reproduces typical evolving patterns of COVID-19epidemic waves observed in many countries. Estimating the parameters$\nu_1,\,\nu_2,\,\nu_3$ and initial conditions, such as ${\cal R}_0$, fordifferent countries helps to identify important dynamics in their socialresponses. One conclusion is that the leading cause of the strong second wavein Europe in the fall of 2020 was not the relaxation of interventions duringthe summer, but rather the general fatigue to interventions developing in thefall.

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