IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v265y2015icp275-291.html
   My bibliography  Save this article

Periodic solutions in an epidemic model with diffusion and delay

Author

Listed:
  • Liu, Pan-Ping

Abstract

A spatial diffusion SI model with delay and Neumann boundary conditions are investigated. We derive the conditions of the existence of Hopf bifurcation in one dimension space. Moreover, we analyze the properties of bifurcating period solutions by using the normal form theory and the center manifold theorem of partial functional differential (PFDs) equations. By numerical simulations, we found that spatiotemporal periodic solutions can occur in the epidemic model with spatial diffusion, which verifies our theoretical results. The obtained results show that interaction of delay and diffusion may induce outbreak of infectious diseases.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:275-291
    DOI: 10.1016/j.amc.2015.05.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315006451
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2015.05.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Omran, A.K. & Zaky, M.A. & Hendy, A.S. & Pimenov, V.G., 2022. "An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 218-239.
    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. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    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. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A. & Nistal, R., 2019. "On an SEIADR epidemic model with vaccination, treatment and dead-infectious corpses removal controls," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 47-79.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    4. 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.
    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. 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.
    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. 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).
    9. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:275-291. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.