Interacting With COVID-19: How Population Behavior, Feedback and Memory Shaped Recurrent Waves of the Epidemic

Until the approval of vaccines at the end of 2020, societies relied on non-pharmaceutical interventions (NPIs) in order to control the COVID-19 pandemic. Spontaneous changes in individual behavior might have contributed to or counteracted epidemic control due to NPIs. For example, the population compliance to NPIs may have varied over time as people developed "epidemic fatigue" or altered their perception of the risk and severity of COVID-19. Whereas official measures are well documented, the behavioral response of the citizens is harder to capture. We propose a mathematical model of the societal response, taking into account three main effects: the citizen response dynamics, the authorities' NPIs, and the occurrence of unpreventable events that significantly alter the virus transmission rate. A key assumption is that a society has a waning memory of the epidemic effects, which reflects on both the severity of the authorities' NPIs and on the citizens' compliance to the prescribed rules. This, in turn, feeds back onto the transmission rate of the disease, such that a higher number of hospitalizations decreases the probability of transmission. We show that the model is able to reproduce the COVID-19 dynamics in terms of hospital admissions for several European countries during 2020 over surprisingly long time scales. Also, it is capable of capturing the effects of disturbances (for example the emergence of new virus variants) and can be exploited for implementing control actions to limit such effects. A possible application, illustrated in this letter, consists of exploiting the estimations based on the data of one country, to predict and control the evolution in another country, where the virus spreading is still in an earlier phase.