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Dynamic analysis of a delayed COVID-19 epidemic with home quarantine in temporal-spatial heterogeneous via global exponential attractor method

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  • Zhu, Cheng-Cheng
  • Zhu, Jiang

Abstract

As the COVID-19 epidemic has entered the normalization stage, the task of prevention and control remains very arduous. This paper constructs a time delay reaction-diffusion model that is closer to the actual spread of the COVID-19 epidemic, including relapse, time delay, home quarantine and temporal-spatial heterogeneous environment that affect the spread of COVID-19. These factors increase the number of equations and the coupling between equations in the system, making it difficult to apply the methods commonly used to discuss global dynamics, such as the Lyapunov function method. Therefore, we use the global exponential attractor theory in the infinite-dimensional dynamic system to study the spreading trend of the COVID-9 epidemic with relapse, time delay, home quarantine in a temporal-spatial heterogeneous environment. Using our latest results of global exponential attractor theory, the global asymptotic stability and the persistence of the COVID-19 epidemic are discussed. We find that due to the influence of relapse in the in temporal-spatial heterogeneity environment, the principal eigenvalue λ* can describe the spread of the epidemic more accurately than the usual basic reproduction number R0. That is, the non-constant disease-free equilibrium is globally asymptotically stable when λ*<0 and the COVID-19 epidemic is persisting uniformly when λ*>0. Combine with the latest official data of the COVID-19 and the prevention and control strategies of different countries, some numerical simulations on the stability and global exponential attractiveness of the spread of the COVID-19 epidemic in China and the USA are given. The simulation results fully reflect the impact of the temporal-spatial heterogeneous environment, relapse, time delay and home quarantine strategies on the spread of the epidemic, revealing the significant differences in epidemic prevention strategies and control effects between the East and the West. The results of this study provide a theoretical basis for the current epidemic prevention and control.

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  • Zhu, Cheng-Cheng & Zhu, Jiang, 2021. "Dynamic analysis of a delayed COVID-19 epidemic with home quarantine in temporal-spatial heterogeneous via global exponential attractor method," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309371
    DOI: 10.1016/j.chaos.2020.110546
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    References listed on IDEAS

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    1. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    6. Nabi, Khondoker Nazmoon, 2020. "Forecasting COVID-19 pandemic: A data-driven analysis," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Altan, Aytaç & Karasu, Seçkin, 2020. "Recognition of COVID-19 disease from X-ray images by hybrid model consisting of 2D curvelet transform, chaotic salp swarm algorithm and deep learning technique," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    2. Xin Ai & Xinyu Liu & Yuting Ding & Han Li, 2022. "Dynamic Analysis of a COVID-19 Vaccination Model with a Positive Feedback Mechanism and Time-Delay," Mathematics, MDPI, vol. 10(9), pages 1-24, May.
    3. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.
    4. Li, Tingting & Guo, Youming, 2022. "Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    5. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    6. Cheng-Cheng Zhu & Jiang Zhu & Jie Shao, 2023. "Epidemiological Investigation: Important Measures for the Prevention and Control of COVID-19 Epidemic in China," Mathematics, MDPI, vol. 11(13), pages 1-23, July.
    7. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    8. Jung-Hoon Kim & Joo-Young Kim, 2022. "How Should the Structure of Smart Cities Change to Predict and Overcome a Pandemic?," Sustainability, MDPI, vol. 14(5), pages 1-17, March.
    9. Xu, Yuan-Hao & Wang, Hao-Jie & Lu, Zhong-Wen & Hu, Mao-Bin, 2023. "Impact of awareness dissemination on epidemic reaction–diffusion in multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    10. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.

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