2020/11/24 by Kristoffer Rypdal, Rypdal, Kristoffer, Filippo Maria Bianchi +3
Mathematics · Medicine · #COVID-19 epidemiological studies #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Quantitative Methods (q-bio.QM)
paper · pdf · doi:10.48550/arxiv.2011.12053
openalex publication_date 2020/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As of November 2020, the number of COVID-19 cases is increasing rapidly in\nmany countries. In Europe, the virus spread slowed considerably in the late\nspring due to strict lockdown, but a second wave of the pandemic grew\nthroughout the fall. In this study, we first reconstruct the time evolution of\nthe effective reproduction numbers cal R(t) for each country by\nintegrating the equations of the classic SIR model. We cluster countries based\non the estimated cal R(t) through a suitable time series dissimilarity.\nThe result suggests that simple dynamical mechanisms determine how countries\nrespond to changes in COVID-19 case counts. Inspired by these results, we\nextend the SIR model to include a social response to explain the number X(t)\nof new confirmed daily cases. As a first-order model, we assume that the social\nresponse is on the form dt cal R=-\ν (X-X^*), where X^* is a threshold\nfor response. The response rate \ν depends on whether X^* is below or\nabove this threshold, on three parameters \ν1, ;\ν2, ,\ν3,, and on t.\nWhen X<X^*, \ν= \ν1, describes the effect of relaxed intervention when\nthe incidence rate is low. When X>X^*, \ν=\ν2\exp(-\ν3t), models the\nimpact of interventions when incidence rate is high. The parameter \ν3\nrepresents the fatigue, i.e., the reduced effect of intervention as time\npasses. The proposed model reproduces typical evolving patterns of COVID-19\nepidemic waves observed in many countries. Estimating the parameters\n\ν1, ,\ν2, ,\ν3 and initial conditions, such as cal R0, for\ndifferent countries helps to identify important dynamics in their social\nresponses. One conclusion is that the leading cause of the strong second wave\nin Europe in the fall of 2020 was not the relaxation of interventions during\nthe summer, but rather the general fatigue to interventions developing in the\nfall.\n