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Pattern formation of an epidemic model with time delay

Author

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  • Li, Jing
  • Sun, Gui-Quan
  • Jin, Zhen

Abstract

One of the central issues in epidemiology is the study of the distribution of disease. And time delay widely exists in the process of disease spread. Thus, in this paper, we presented an epidemic model with spatial diffusion and time delay. By mathematical analysis, we find two different types of instability. One is the diffusion induced instability, and the other one is delay induced instability. Moreover, we derive the corresponding patterns by performing a series of numerical simulations. The obtained results show that the interaction of diffusion and time delay may give rise to rich dynamics in epidemic systems.

Suggested Citation

  • Li, Jing & Sun, Gui-Quan & Jin, Zhen, 2014. "Pattern formation of an epidemic model with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 100-109.
    • Handle: RePEc:eee:phsmap:v:403:y:2014:i:c:p:100-109
    DOI: 10.1016/j.physa.2014.02.025
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    References listed on IDEAS

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    1. Jessica A. Belser & Kortney M. Gustin & Melissa B. Pearce & Taronna R. Maines & Hui Zeng & Claudia Pappas & Xiangjie Sun & Paul J. Carney & Julie M. Villanueva & James Stevens & Jacqueline M. Katz & T, 2013. "Pathogenesis and transmission of avian influenza A (H7N9) virus in ferrets and mice," Nature, Nature, vol. 501(7468), pages 556-559, September.
    2. David A. Steinhauer, 2013. "Pathways to human adaptation," Nature, Nature, vol. 499(7459), pages 412-413, July.
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    Citations

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    Cited by:

    1. Kerr, Gilbert & González-Parra, Gilberto & Sherman, Michele, 2022. "A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. 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.
    3. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. 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.
    5. Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    6. Julio C. Miranda & Abraham J. Arenas & Gilberto González-Parra & Luis Miguel Villada, 2024. "Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay," Mathematics, MDPI, vol. 12(5), pages 1-36, February.
    7. Zheng, Qianqian & Shen, Jianwei & Pandey, Vikas & Guan, Linan & Guo, Yantao, 2023. "Turing instability in a network-organized epidemic model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    8. Liu, Pan-Ping, 2015. "Periodic solutions in an epidemic model with diffusion and delay," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 275-291.
    9. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.
    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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