Abstract According to the official report, the first case of COVID-19 and the first death in the United States occurred on January 20 and February 29, 2020, respectively. On April 21, California reported that the first death in the state occurred on February 6, implying that community spreading of COVID-19 might have started earlier than previously thought. Exactly what is time ZERO, i.e., when did COVID-19 emerge and begin to spread in the US and other countries? We develop a comprehensive predictive modeling framework to address this question. Using available data of confirmed infections to obtain the optimal values of the key parameters, we validate the model and demonstrate its predictive power. We then carry out an inverse inference analysis to determine time ZERO for ten representative States in the US, plus New York city, UK, Italy, and Spain. The main finding is that, in both the US and Europe, COVID-19 started around the new year day.
In this paper, we propose a novel neighbor-preferential growth (NPG) network model. Theoretical analysis and numerical simulations indicate the new model can reproduce not only a scale-free degree distribution and its power exponent is related to the edge-adding number m, but also a small-world effect which has large clustering coefficient and small average path length. Interestingly, the clustering coefficient of the model is close to that of globally coupled network, and the average path length is close to that of star coupled network. Meanwhile, the synchronizability of the NPG model is much stronger than that of BA scale-free network, even stronger than that of synchronization-optimal growth network.
According to the official report, the first case of COVID-19 and the first death in the United States occurred on January 20 and February 29, 2020, respectively. On April 21, California reported that the first death in the state occurred on February 6, implying that community spreading of COVID-19 might have started earlier than previously thought. Exactly what is time zero, i.e., when did COVID-19 emerge and begin to spread in the U.S. and other countries? We develop a comprehensive predictive modeling framework to address this question. Using available data of confirmed infections to obtain the optimal values of the key parameters, we validate the model and demonstrate its predictive power. We then carry out an inverse inference analysis to determine time zero for 10 representative states in the U.S., plus New York City, United Kingdom, Italy, and Spain. The main finding is that, in both the U.S. and Europe, COVID-19 started around the new year day.2 MoreReceived 28 August 2020Accepted 28 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013155Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMedical physics & public healthViral diseasesTechniquesEpidemic spreadingSpreading modelsInterdisciplinary Physics
We uncover a phenomenon in coupled nonlinear networks with a symmetry: as a bifurcation parameter changes through a critical value, synchronization among a subset of nodes can deteriorate abruptly, and, simultaneously, perfect synchronization emerges suddenly among a different subset of nodes that are not directly connected. This is a synchronization metamorphosis leading to an explosive transition to remote synchronization. The finding demonstrates that an explosive onset of synchrony and remote synchronization, two phenomena that have been studied separately, can arise in the same system due to symmetry, providing another proof that the interplay between nonlinear dynamics and symmetry can lead to a surprising phenomenon in physical systems.
Abstract Due to the heterogeneity among the States in the US, predicting COVID-19 trends and quantitatively assessing the effects of government testing capability and control measures need to be done via a State-by-State approach. We develop a comprehensive model for COVID-19 incorporating time delays and population movements. With key parameter values determined by empirical data, the model enables the most likely epidemic scenarios to be predicted for each State, which are indicative of whether testing services and control measures are vigorous enough to contain the disease. We find that government control measures play a more important role than testing in suppressing the epidemic. The vast disparities in the epidemic trends among the States imply the need for long-term placement of control measures to fully contain COVID-19.
Symmetries, due to their fundamental importance to dynamical processes on networks, have attracted a great deal of current research. Finding all symmetric nodes in large complex networks typically relies on automorphism groups from algebraic-group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computationally extremely efficient approach to finding and characterizing all symmetric nodes by introducing a structural position vector (SPV) for each node in networks. We establish the mathematical result that symmetric nodes must have the same SPV value and demonstrate, using six representative complex networks from the real world, that all symmetric nodes in these networks can be found in linear time. Furthermore, the SPVs not only characterize the similarity of nodes but also quantify the nodal influences in propagation dynamics. A caveat is that the proved mathematical result relating the SPV values to nodal symmetries is not sufficient; i.e., nodes having the same SPV values may not be symmetric, which arises in regular networks or networks with a dominant regular component. We point out with an analysis that this caveat is, in fact, shared by the known existing approaches to finding symmetric nodes in the literature. We further argue, with the aid of a mathematical analysis, that our SPV method is generally effective for finding the symmetric nodes in real-world networks that typically do not have a dominant regular component. Our SPV-based framework, therefore, provides a physically intuitive and computationally efficient way to uncover, understand, and exploit symmetric structures in complex networks arising from real-world applications.
An urgent problem in controlling COVID-19 spreading is to understand the role of undocumented infection. We develop a five-state model for COVID-19, taking into account the unique features of the novel coronavirus, with key parameters determined by the government reports and mathematical optimization. Tests using data from China, South Korea, Italy, and Iran indicate that the model is capable of generating accurate prediction of the daily accumulated number of confirmed cases and is entirely suitable for real-time prediction. The drastically disparate testing and diagnostic standards/policies among different countries lead to large variations in the estimated parameter values such as the duration of the outbreak, but such uncertainties have little effect on the occurrence time of the inflection point as predicted by the model, indicating its reliability and robustness. Model prediction for Italy suggests that insufficient government action leading to a large fraction of undocumented infection plays an important role in the abnormally high mortality in that country. With the data currently available from United Kingdom, our model predicts catastrophic epidemic scenarios in the country if the government did not impose strict travel and social distancing restrictions. A key finding is that, if the percentage of undocumented infection exceeds a threshold, a non-negligible hidden population can exist even after the the epidemic has been deemed over, implying the likelihood of future outbreaks should the currently imposed strict government actions be relaxed. This could make COVID-19 evolving into a long-term epidemic or a community disease a real possibility, suggesting the necessity to conduct universal testing and monitoring to identify the hidden individuals.
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