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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 accumu-1

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.

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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.