IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v140y2020ics0960077920305063.html
   My bibliography  Save this article

A stochastic nutrient-phytoplankton model with viral infection and Markov switching

Author

Listed:
  • Chen, Zhewen
  • Zhang, Ruimin
  • Li, Jiang
  • Zhang, Shuwen
  • Wei, Chunjin

Abstract

In this paper, we extend a nutrient-phytoplankton model with viral infection from a deterministic model to a stochastic model by introducing white noise and color noise. We analyze this model mainly from the perspectives of mathematics and biology. Mathematically, we get a critical value. In the case of low white noise intensity, if this critical value is less than one, the infected phytoplankton tend to die out exponentially. If this critical value is greater than one, the infected phytoplankton is persistent in mean and the solution of system is positive recurrent. From a biological standpoint, we show that white noise may have negative effect on population survival, while Markov chain can balance the different survival states of the population and increase its survival probability, which can provide effective measures to control the infected phytoplankton and ensure the stationary distribution of the population in reality.

Suggested Citation

  • Chen, Zhewen & Zhang, Ruimin & Li, Jiang & Zhang, Shuwen & Wei, Chunjin, 2020. "A stochastic nutrient-phytoplankton model with viral infection and Markov switching," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305063
    DOI: 10.1016/j.chaos.2020.110109
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920305063
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110109?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. Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    2. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
    4. Chunjin Wei & Yingjie Fu, 2020. "Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems," Complexity, Hindawi, vol. 2020, pages 1-15, January.
    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. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    2. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.

    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. Xiaomei Feng & Yuan Miao & Shulin Sun & Lei Wang, 2022. "Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    2. Xu, Junyan & Zhang, Tonghua & Song, Keying, 2020. "A stochastic model of bacterial infection associated with neutrophils," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. Lifan Chen & Xingwang Yu & Sanling Yuan, 2022. "Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    4. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Gökçe, Aytül, 2021. "A mathematical study for chaotic dynamics of dissolved oxygen- phytoplankton interactions under environmental driving factors and time lag," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    6. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    7. Liu, Zhi-bin & Liu, Shutang & Wang, Wen & Wang, Da, 2021. "Effect of herd-taxis on the self-organization of a plankton community," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Liu, Liya & Jiang, Daqing & Hayat, Tasawar, 2021. "Dynamics of an SIR epidemic model with varying population sizes and regime switching in a two patch setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    9. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    10. Tiancai Liao & Hengguo Yu & Chuanjun Dai & Min Zhao, 2019. "Impact of Cell Size Effect on Nutrient-Phytoplankton Dynamics," Complexity, Hindawi, vol. 2019, pages 1-23, November.
    11. Wang, Huazheng & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of stochastic NP ecological model under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    12. Zhao, Shengnan & Yuan, Sanling & Zhang, Tonghua, 2022. "The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    13. Guo, Wenjuan & Zhang, Qimin, 2021. "Explicit numerical approximation for an impulsive stochastic age-structured HIV infection model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 86-115.
    14. Kirkow, Velizar & Wang, Hao & Garcia, Pablo Venegas & Ahmed, Shohel & Heggerud, Christopher M., 2022. "Impacts of a changing environment on a stoichiometric producer-grazer system: a stochastic modelling approach," Ecological Modelling, Elsevier, vol. 469(C).
    15. Chen, Jianxin & Zhang, Tonghua & Zhou, Yong-wu, 2021. "Stochastic sensitivity and dynamical complexity of newsvendor models subject to trade credit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 471-486.
    16. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2022. "Stability of spatial patterns in a diffusive oxygen–plankton model with time lag effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 109-123.
    17. Lu, Minmin & Wang, Yan & Jiang, Daqing, 2021. "Stationary distribution and probability density function analysis of a stochastic HIV model with cell-to-cell infection," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    18. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(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:chsofr:v:140:y:2020:i:c:s0960077920305063. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.