IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v270y2015icp808-829.html
   My bibliography  Save this article

A diffusive dengue disease model with nonlocal delayed transmission

Author

Listed:
  • Xu, Zhiting
  • Zhao, Yingying

Abstract

In this paper, we derive a nonlocal delayed and diffusive dengue transmission model with a spatial domain being bounded as well as unbounded. We first address the well-posedness to the initial-value problem for the model. In the case of a bounded spatial domain, we establish the threshold dynamics for the spatially heterogeneous system in terms of the basic reproduction number R0. Also, a set of sufficient conditions is further obtained for the global attractivity of the endemic steady state where all the parameters are spatially independent. In the case of an unbounded spatial domain, and when the coefficients are all constants, we show that there exist traveling wave solutions of the model. Numerical simulations are performed to illustrate our main analytic results.

Suggested Citation

  • Xu, Zhiting & Zhao, Yingying, 2015. "A diffusive dengue disease model with nonlocal delayed transmission," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 808-829.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:808-829
    DOI: 10.1016/j.amc.2015.08.079
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315011352
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.079?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. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    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. Chen, Zhenwu & Xu, Zhiting, 2019. "A delayed diffusive influenza model with two-strain and two vaccinations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 439-453.
    2. Wang, Wei & Ma, Wanbiao, 2018. "Hepatitis C virus infection is blocked by HMGB1: A new nonlocal and time-delayed reaction–diffusion model," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 633-653.

    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. Arenas, Abraham J. & González-Parra, Gilberto & Villanueva Micó, Rafael-J., 2010. "Modeling toxoplasmosis spread in cat populations under vaccination," Theoretical Population Biology, Elsevier, vol. 77(4), pages 227-237.
    2. Saha, Pritam & Sikdar, Gopal Chandra & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2023. "Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 16-43.
    3. Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Abidemi, A. & Abd Aziz, M.I. & Ahmad, R., 2020. "Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Ran, Xue & Hu, Lin & Nie, Lin-Fei & Teng, Zhidong, 2021. "Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate," Applied Mathematics and Computation, Elsevier, vol. 394(C).

    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:270:y:2015:i:c:p:808-829. 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.