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Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19

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  • Zhang, Yong
  • Yu, Xiangnan
  • Sun, HongGuang
  • Tick, Geoffrey R.
  • Wei, Wei
  • Jin, Bin

Abstract

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 (COVID-19) 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.

Suggested Citation

  • Zhang, Yong & Yu, Xiangnan & Sun, HongGuang & Tick, Geoffrey R. & Wei, Wei & Jin, Bin, 2020. "Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303581
    DOI: 10.1016/j.chaos.2020.109959
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    References listed on IDEAS

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    Cited by:

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    2. Fernando Alcántara-López & Carlos Fuentes & Carlos Chávez & Fernando Brambila-Paz & Antonio Quevedo, 2021. "Fractional Growth Model Applied to COVID-19 Data," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    3. Maria Cieśla & Sandra Kuśnierz & Oliwia Modrzik & Sonia Niedośpiał & Patrycja Sosna, 2021. "Scenarios for the Development of Polish Passenger Transport Services in Pandemic Conditions," Sustainability, MDPI, vol. 13(18), pages 1-16, September.
    4. Zhou, Jiaying & Ye, Yong & Arenas, Alex & Gómez, Sergio & Zhao, Yi, 2023. "Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Aldila, Dipo, 2020. "Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Nie, Shiqian & Lei, Xiaochun, 2023. "A time-dependent model of the transmission of COVID-19 variants dynamics using Hausdorff fractal derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    7. Haiyue Chen & Benedikt Haus & Paolo Mercorelli, 2021. "Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability," Mathematics, MDPI, vol. 9(17), pages 1-25, August.
    8. Khajji, Bouchaib & Kouidere, Abdelfatah & Elhia, Mohamed & Balatif, Omar & Rachik, Mostafa, 2021. "Fractional optimal control problem for an age-structured model of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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