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Browsing by Author "Yu, Xiangnan"

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    Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19
    (Pergamon, 2020) Zhang, Yong; Yu, Xiangnan; Sun, HongGuang; Tick, Geoffrey R.; Wei, Wei; Jin, Bin; University of Alabama Tuscaloosa; Hohai University; Nanjing Normal University; Nanjing Medical University
    Fractional calculus provides a promising tool for modeling fractional dynamics in computational biology, and this study tests the applicability of fractional-derivative equations (FDEs) for modeling the dynamics and mitigation scenarios of the novel coronavirus for the first time. The coronavirus disease 2019 (COVID19) pandemic radically impacts our lives, while the evolution dynamics of COVID-19 remain obscure. A time-dependent Susceptible, Exposed, Infectious, and Recovered (SEIR) model was proposed and applied to fit and then predict the time series of COVID-19 evolution observed over the last three months (up to 3/22/2020) in China. The model results revealed that 1) the transmission, infection and recovery dynamics follow the integral-order SEIR model with significant spatiotemporal variations in the recovery rate, likely due to the continuous improvement of screening techniques and public hospital systems, as well as full city lockdowns in China, and 2) the evolution of number of deaths follows the time FDE, likely due to the time memory in the death toll. The validated SEIR model was then applied to predict COVID-19 evolution in the United States, Italy, Japan, and South Korea. In addition, a time FDE model based on the random walk particle tracking scheme, analogous to a mixing-limited bimolecular reaction model, was developed to evaluate non-pharmaceutical strategies to mitigate COVID-19 spread. Preliminary tests using the FDE model showed that self-quarantine may not be as efficient as strict social distancing in slowing COVID-19 spread. Therefore, caution is needed when applying FDEs to model the coronavirus outbreak, since specific COVID-19 kinetics may not exhibit nonlocal behavior. Particularly, the spread of COVID-19 may be affected by the rapid improvement of health care systems which may remove the memory impact in COVID-19 dynamics (resulting in a short-tailed recovery curve), while the death toll and mitigation of COVID-19 can be captured by the time FDEs due to the nonlocal, memory impact in fatality and human activities. (C) 2020 Elsevier Ltd. All rights reserved.
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    Modeling COVID-19 spreading dynamics and unemployment rate evolution in rural and urban counties of Alabama and New York using fractional derivative models
    (Elsevier, 2021) Yu, Xiangnan; Zhang, Yong; Sun, HongGuang; Hohai University; University of Alabama Tuscaloosa
    The COVID-19 pandemic has been affecting the United States (U.S.) since the outbreak documented on 2/29/2020, and understanding its dynamics is critical for pandemic mitigation and economic recovery. This study proposed and applied novel time fractional derivative models (FDMs) to quantify the spatiotemporal dynamics of the COVID-19 pandemic spreading in the states of Alabama and New York, U.S., two states with quite different population compositions, urbanization, and industry structures. Model applications revealed that the pandemic evolving in the two states exhibited an overall similar time-dependent trend with subtle differences in propagation rates. Alabama may have more inter-county communications in rural areas than urban areas, while the opposite may be true for the New York State. Further analysis using the space FDM showed that the COVID-19 pandemic spread in rural/urban areas of the two states by following the tempered stable density distributions with different indexes, while the number of the state's pandemic epicenters affected the pattern of the COVID-19 pandemic spreading in space. Finally, applications of a novel time FDM revealed that the evolution of the economy, represented by the weekly unemployment insurance claims in the two states, exhibited different spreading and recovery rates, most likely due to their different exposures and responses to the pandemic. Therefore, COVID-19 spreading dynamics exhibited strong and subtly different spatiotemporal memories in rural and urban areas in the Alabama and New York States, motivating the application of FDMs.