Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China
TL;DR: A parsimonious model is introduced that captures both, quarantine of symptomatic infected individuals as well as population wide isolation in response to mitigation policies or behavioral changes, and implies that the observed scaling law in confirmed cases is a direct signature of effective contaiment strategies and/or systematic behavioral changes that affect a substantial fraction of the susceptible population.
Abstract: The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase of confirmed cases during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law $t^{\mu}$ is surprisingly universal, with a range of exponents $\mu=2.1\pm0.3$. The universality of this behavior indicates that despite social, regional, demographical, geographical, and socio-economical heterogeneities of affected Chinese provinces, this outbreak is dominated by fundamental mechanisms that are not captured by standard epidemiological models. We show that the observed scaling law is a direct consequence of containment policies that effectively deplete the susceptible population. To this end we introduce a parsimonious model that captures both, quarantine of symptomatic infected individuals as well as population wide isolation in response to mitigation policies or behavioral changes. For a wide range of parameters, the model reproduces the observed scaling law in confirmed cases and explains the observed exponents. Quantitative fits to empirical data permit the identification of peak times in the number of asymptomatic or oligo-symptomatic, unidentified infected individuals, as well as estimates of local variations in the basic reproduction number. The model implies that the observed scaling law in confirmed cases is a direct signature of effective contaiment strategies and/or systematic behavioral changes that affect a substantial fraction of the susceptible population. These insights may aid the implementation of containment strategies in potential export induced COVID-19 secondary outbreaks elsewhere or similar future outbreaks of other emergent infectious diseases.
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TL;DR: It is estimated that across these six countries, interventions prevented or delayed on the order of 62 million confirmed cases, corresponding to averting roughly 530 million total infections, and anti-contagion policies have significantly and substantially slowed this growth.
Abstract: Governments around the world are responding to the novel coronavirus (COVID-19) pandemic1 with unprecedented policies designed to slow the growth rate of infections. Many actions, such as closing schools and restricting populations to their homes, impose large and visible costs on society, but their benefits cannot be directly observed and are currently understood only through process-based simulations2–4. Here, we compile new data on 1,717 local, regional, and national non-pharmaceutical interventions deployed in the ongoing pandemic across localities in China, South Korea, Italy, Iran, France, and the United States (US). We then apply reduced-form econometric methods, commonly used to measure the effect of policies on economic growth5,6, to empirically evaluate the effect that these anti-contagion policies have had on the growth rate of infections. In the absence of policy actions, we estimate that early infections of COVID-19 exhibit exponential growth rates of roughly 38% per day. We find that anti-contagion policies have significantly and substantially slowed this growth. Some policies have different impacts on different populations, but we obtain consistent evidence that the policy packages now deployed are achieving large, beneficial, and measurable health outcomes. We estimate that across these six countries, interventions prevented or delayed on the order of 62 million confirmed cases, corresponding to averting roughly 530 million total infections. These findings may help inform whether or when these policies should be deployed, intensified, or lifted, and they can support decision-making in the other 180+ countries where COVID-19 has been reported7.
1,095 citations
TL;DR: Modeling and Bayesian inference reveal the time dependence of SARS-CoV-2 interventions on the number of new infections using the example of Germany and the impact of these measures on the disease spread using change point analysis.
Abstract: As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A major challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well with the times of publicly announced interventions. Thereby, we can quantify the effect of interventions, and we can incorporate the corresponding change points into forecasts of future scenarios and case numbers. Our code is freely available and can be readily adapted to any country or region.
704 citations
University of Oxford1, Australian National University2, Harvard University3, University of Bristol4, University of Manchester5, University of London6, London School of Economics and Political Science7, University of Cambridge8, Tufts University9, Medical Research Council10, Imperial College London11
TL;DR: The results indicate that, by using effective interventions, some countries could control the epidemic while avoiding stay-at-home orders, and this model accounts for uncertainty in key epidemiological parameters, such as the average delay from infection to death.
Abstract: Governments are attempting to control the COVID-19 pandemic with nonpharmaceutical interventions (NPIs). However, the effectiveness of different NPIs at reducing transmission is poorly understood. We gathered chronological data on the implementation of NPIs for several European, and other, countries between January and the end of May 2020. We estimate the effectiveness of NPIs, ranging from limiting gathering sizes, business closures, and closure of educational institutions to stay-at-home orders. To do so, we used a Bayesian hierarchical model that links NPI implementation dates to national case and death counts and supported the results with extensive empirical validation. Closing all educational institutions, limiting gatherings to 10 people or less, and closing face-to-face businesses each reduced transmission considerably. The additional effect of stay-at-home orders was comparatively small.
674 citations
TL;DR: Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.
Abstract: We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.
486 citations
TL;DR: A review of the literature written on the subject of non-pharmaceutical interventions during the COVID-19 pandemic can be found in this paper, where the authors classified the sample into seven main categories: epidemic models, surveys, comments/perspectives, papers aiming to quantify the effects of NPIs, reviews, articles using data proxies to measure NPIs and publicly available datasets describing NPIs.
257 citations
References
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TL;DR: Characteristics of patients who died were in line with the MuLBSTA score, an early warning model for predicting mortality in viral pneumonia, and further investigation is needed to explore the applicability of the Mu LBSTA scores in predicting the risk of mortality in 2019-nCoV infection.
16,282 citations
"Effective containment explains sub-..." refers background in this paper
...[5] Nanshan Chen, Min Zhou, Xuan Dong, Jieming Qu, Fengyun Gong, Yang Han, Yang Qiu, Jingli Wang, Ying Liu, Yuan Wei, Jia’an Xia, Ting Yu, Xinxin Zhang, and Li Zhang....
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...The current outbreak of the new coronavirus in Mainland China (COVID-19, previously named 2019-nCoV) is closely monitored by governments, researchers, and the public alike [1–7]....
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TL;DR: There is evidence that human-to-human transmission has occurred among close contacts since the middle of December 2019 and considerable efforts to reduce transmission will be required to control outbreaks if similar dynamics apply elsewhere.
Abstract: Background The initial cases of novel coronavirus (2019-nCoV)–infected pneumonia (NCIP) occurred in Wuhan, Hubei Province, China, in December 2019 and January 2020. We analyzed data on the...
13,101 citations
"Effective containment explains sub-..." refers background in this paper
...[9] Qun Li, Xuhua Guan, Peng Wu, Xiaoye Wang, Lei Zhou, Yeqing Tong, Ruiqi Ren, Kathy S....
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...Although in Hubei the number of cases was observed to grow exponentially in early January [9], the...
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Book•
28 Oct 2007TL;DR: Mathematical modeling of infectious dis-eases has progressed dramatically over the past 3 decades and continues to be a valuable tool at the nexus of mathematics, epidemiol-ogy, and infectious diseases research.
Abstract: By Matthew James Keelingand Pejman RohaniPrinceton, NJ: Princeton University Press,2008.408 pp., Illustrated. $65.00 (hardcover).Mathematical modeling of infectious dis-eases has progressed dramatically over thepast 3 decades and continues to flourishat the nexus of mathematics, epidemiol-ogy, and infectious diseases research. Nowrecognized as a valuable tool, mathemat-ical models are being integrated into thepublic health decision-making processmore than ever before. However, despiterapid advancements in this area, a formaltraining program for mathematical mod-eling is lacking, and there are very fewbooks suitable for a broad readership. Tosupport this bridging science, a commonlanguage that is understood in all con-tributing disciplines is required.
3,467 citations
"Effective containment explains sub-..." refers background in this paper
...On a very basic level, an outbreak as the one in Hubei is captured by SIR dynamics [17]....
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...[17] Matthew James Keeling and Pejman Rohani....
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TL;DR: The early outbreak data largely follows the exponential growth and indicates the potential of 2019-nCoV to cause outbreaks, as well as the impact of the variations in disease reporting rate, modelled through theonential growth.
1,561 citations
"Effective containment explains sub-..." refers background or result in this paper
...The current outbreak of the new coronavirus in Mainland China (COVID-19, previously named 2019-nCoV) is closely monitored by governments, researchers, and the public alike [1–7]....
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...[6] Shi Zhao, Qianyin Lin, Jinjun Ran, Salihu S....
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...3 for the discussed provinces, consistent with estimates found in previous early assessment studies [6, 7, 18, 19]....
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TL;DR: Using a transmission model, a basic reproductive number is estimated for Wuhan coronavirus (2019-nCoV) and it is estimated that 58-76% of transmissions must be prevented to stop increasing.
Abstract: Since first identified, the epidemic scale of the recently emerged novel coronavirus (2019-nCoV) in Wuhan, China, has increased rapidly, with cases arising across China and other countries and regions. using a transmission model, we estimate a basic reproductive number of 3.11 (95%CI, 2.39-4.13); 58-76% of transmissions must be prevented to stop increasing; Wuhan case ascertainment of 5.0% (3.6-7.4); 21022 (11090-33490) total infections in Wuhan 1 to 22 January.
855 citations