IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v258y2015icp342-349.html
   My bibliography  Save this article

Patch invasion in a spatial epidemic model

Author

Listed:
  • Li, Li

Abstract

Understanding of patterns in disease spreading is an issue of significant current interest in epidemiology. In this paper, an epidemic model with spatial diffusion is considered. It was found that this model has stationary patterns including spotted and stripe patterns. Moreover, patch invasion was obtained in this reaction–diffusion epidemic model. It was well known that the spreading of disease takes place via irregular movement of separated patches due to environmental stochasticity. However, we show that pattern transition from stationary pattern to patch invasion appears to be possible in a fully deterministic parasite-host model, which may provide new insights to control the disease.

Suggested Citation

  • Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
  • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:342-349
    DOI: 10.1016/j.amc.2015.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315001587
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2015.02.006?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. Arenas, Abraham J. & González-Parra, Gilberto & Jódar, Lucas, 2010. "Randomness in a mathematical model for the transmission of respiratory syncytial virus (RSV)," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 971-981.
    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. Bettencourt, Luís M.A. & Cintrón-Arias, Ariel & Kaiser, David I. & Castillo-Chávez, Carlos, 2006. "The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 513-536.
    4. Varughese, M.M. & Fatti, L.P., 2008. "Incorporating environmental stochasticity within a biological population model," Theoretical Population Biology, Elsevier, vol. 74(1), pages 115-129.
    5. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
    Full references (including those not matched with items on IDEAS)

    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. Li, Shuang & Xiong, Jie, 2024. "SIR epidemic model with non-Lipschitz stochastic perturbations," Statistics & Probability Letters, Elsevier, vol. 210(C).
    2. De Martino, Giuseppe & Spina, Serena, 2015. "Exploiting the time-dynamics of news diffusion on the Internet through a generalized Susceptible–Infected model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 634-644.
    3. Wang, Haiying & Moore, Jack Murdoch & Wang, Jun & Small, Michael, 2021. "The distinct roles of initial transmission and retransmission in the persistence of knowledge in complex networks," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.
    5. William Brock & Anastasios Xepapadeas, 2020. "The Economy, Climate Change and Infectious Diseases: Links and Policy Implications," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 811-824, August.
    6. Zhiming Li & Zhidong Teng, 2019. "Analysis of uncertain SIS epidemic model with nonlinear incidence and demography," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 475-491, December.
    7. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    8. Sidemar Cezario & Thiago Marques & Rafael Pinto & Juciano Lacerda & Lyrene Silva & Thaisa Santos Lima & Orivaldo Santana & Anna Giselle Ribeiro & Agnaldo Cruz & Ana Claudia Araújo & Angélica Espinosa , 2022. "Similarity Analysis in Understanding Online News in Response to Public Health Crisis," IJERPH, MDPI, vol. 19(24), pages 1-14, December.
    9. Mann Manyombe, M.L. & Tsanou, B. & Mbang, J. & Bowong, S., 2017. "A metapopulation model for the population dynamics of anopheles mosquito," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 71-91.
    10. Nwaibeh, E.A. & Chikwendu, C.R., 2023. "A deterministic model of the spread of scam rumor and its numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 111-129.
    11. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    12. Lambiotte, R. & Panzarasa, P., 2009. "Communities, knowledge creation, and information diffusion," Journal of Informetrics, Elsevier, vol. 3(3), pages 180-190.
    13. González-Parra, Gilberto & Villanueva-Oller, Javier & Navarro-González, F.J. & Ceberio, Josu & Luebben, Giulia, 2024. "A network-based model to assess vaccination strategies for the COVID-19 pandemic by using Bayesian optimization," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    14. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    15. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    16. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    17. Guo, Yingjia, 2017. "Stochastic regime switching SIR model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 1-11.
    18. Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.
    19. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
    20. Wang, Haiying & Wang, Jun & Small, Michael & Moore, Jack Murdoch, 2019. "Review mechanism promotes knowledge transmission in complex networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 113-125.

    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:258:y:2015:i:c:p:342-349. 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.