IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v525y2019icp732-740.html
   My bibliography  Save this article

Pattern formation in a reaction–diffusion parasite–host model

Author

Listed:
  • Zhang, Baoxiang
  • Cai, Yongli
  • Wang, Bingxian
  • Wang, Weiming

Abstract

In this paper, we investigate the Turing pattern formation of a reaction–diffusion parasite–host model analytically and numerically. We give the stability of the constant positive steady-state which shows that the model exhibits stationary Turing pattern as a result of diffusion. Via numerical simulations, we present the pattern formation and find that the model dynamics exhibits a diffusion-controlled formation growth of “spots → spots-stripes → stripes → holes-stripes → holes” pattern replication. The results show that we must do our best to regulate the parameters in the special range to avoid disease outbreak.

Suggested Citation

  • Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:732-740
    DOI: 10.1016/j.physa.2019.03.088
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119303231
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.03.088?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. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    2. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    3. Cai, Yongli & Ding, Zuqin & Yang, Bin & Peng, Zhihang & Wang, Weiming, 2019. "Transmission dynamics of Zika virus with spatial structure—A case study in Rio de Janeiro, Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 729-740.
    4. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    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. Luo, Yantao & Zhang, Long & Zheng, Tingting & Teng, Zhidong, 2019. "Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Ye, Yong & Zhao, Yi & Zhou, Jiaying, 2022. "Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

    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. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    2. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    3. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    4. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    5. Jialin Chen & Xiaqing He & Fengde Chen, 2021. "The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    6. Liu, Qun & Jiang, Daqing, 2023. "Analysis of a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    7. Zainab Saeed Abbas & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on a Harvested Food Web System," Mathematics, MDPI, vol. 10(18), pages 1-37, September.
    8. Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Lívia Madeira Triaca & Felipe Garcia Ribeiro & César Augusto Oviedo Tejada, 2021. "Mosquitoes, birth rates and regional spillovers: Evidence from the Zika epidemic in Brazil," Papers in Regional Science, Wiley Blackwell, vol. 100(3), pages 795-813, June.
    10. Hiba Abdullah Ibrahim & Raid Kamel Naji, 2023. "The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey," Mathematics, MDPI, vol. 11(13), pages 1-28, June.
    11. 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.
    12. Balcı, Ercan, 2023. "Predation fear and its carry-over effect in a fractional order prey–predator model with prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    13. Sebastian Sund & Lars H. Sendstad & Jacco J. J. Thijssen, 2022. "Kalman filter approach to real options with active learning," Computational Management Science, Springer, vol. 19(3), pages 457-490, July.
    14. Liu, Qun & Jiang, Daqing, 2020. "Stationary distribution of a stochastic cholera model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    15. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    16. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    17. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    18. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    19. Das, Amartya & Samanta, G.P., 2020. "A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    20. Bao, Kangbo & Zhang, Qimin & Rong, Libin & Li, Xining, 2019. "Dynamics of an imprecise SIRS model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 489-506.

    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:phsmap:v:525:y:2019:i:c:p:732-740. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.