IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v287-288y2016ip1-11.html
   My bibliography  Save this article

Multiple kinds of optimal impulse control strategies on plant–pest–predator model with eco-epidemiology

Author

Listed:
  • Liang, Xiyin
  • Pei, Yongzhen
  • Zhu, Meixia
  • Lv, Yunfei

Abstract

Yongzhen et al. (2010) describe a mathematical model of a scenario where a plant population is imported to a pest–predator system with an infected pest. Thus a plant–pest–predator eco-epidemiological model disturbed by an impulsive effect is proposed. First of all, the stability conditions of the susceptible pest-eradication periodic solution for eradicating the susceptible pest are investigated. Compared with the results in (Yongzhen et al., 2010), the presence of the plant population increases the cost of natural enemies as well as the demand for insecticide. In addition, we study the effect of the death rate of the infected pest on pest control in terms of evolution of virulence and the basic reproductive number. Results show that larger mortalities of the infected pest will lead to the frustrated invasion or the instability of susceptible pest-eradication periodic solutions. Next, we focus on the four kinds of optimal impulsive control strategies, biological control, chemical control, and integrated control with fixed period or variable period, to maximize the yields of plants at the terminal time with minimum efforts. All the optimal control problems are solved via a time scaling technique and a gradient-based optimization method. Our results show that two parameters, the amount of sprayed infective pest and the kill fraction of the susceptible pest, play a key role in improving the yield of the plants. In addition, for the four kinds of control strategies, our results also show that biological control is more effective than chemical control to achieve an optimal solution, and the last two strategies can produce higher yields than the first two control strategies.

Suggested Citation

  • Liang, Xiyin & Pei, Yongzhen & Zhu, Meixia & Lv, Yunfei, 2016. "Multiple kinds of optimal impulse control strategies on plant–pest–predator model with eco-epidemiology," Applied Mathematics and Computation, Elsevier, vol. 287, pages 1-11.
    • Handle: RePEc:eee:apmaco:v:287-288:y:2016:i::p:1-11
    DOI: 10.1016/j.amc.2016.04.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316302843
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.04.034?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. Y. Liu & K. L. Teo & L. S. Jennings & S. Wang, 1998. "On a Class of Optimal Control Problems with State Jumps," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 65-82, July.
    2. Wang, Fengyan & Pang, Guoping & Lu, Zhengyi, 2009. "Bifurcation and chaos of a pest-control food chain model with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1903-1914.
    3. Hui, Jing & Zhu, Deming, 2006. "Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 233-251.
    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. Zhang, Hongxia & Han, Ping & Guo, Qin, 2023. "Stability and jumping dynamics of a stochastic vegetation ecosystem induced by threshold policy control," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Huafei Chen & Jia Chen & Dan Qu & Kelin Li & Fei Luo, 2022. "An Uncertain Sandwich Impulsive Control System with Impulsive Time Windows," Mathematics, MDPI, vol. 10(24), pages 1-14, December.

    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. Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.
    2. Zhang, Tongqian & Ma, Wanbiao & Meng, Xinzhu & Zhang, Tonghua, 2015. "Periodic solution of a prey–predator model with nonlinear state feedback control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 95-107.
    3. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    4. Liu, Zhijun & Tan, Ronghua, 2007. "Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 454-464.
    5. Yu, Run & Leung, PingSun & Bienfang, Paul, 2009. "Modeling partial harvesting in intensive shrimp culture: A network-flow approach," European Journal of Operational Research, Elsevier, vol. 193(1), pages 262-271, February.
    6. Jiao, Jianjun & Chen, Lansun & Cai, Shaohong, 2009. "A delayed stage-structured Holling II predator–prey model with mutual interference and impulsive perturbations on predator," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1946-1955.
    7. Chen, Yiping & Liu, Zhijun, 2009. "Modelling and analysis of an impulsive SI model with Monod-Haldane functional response," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1698-1714.
    8. Sadana, Utsav & Reddy, Puduru Viswanadha & Zaccour, Georges, 2021. "Nash equilibria in nonzero-sum differential games with impulse control," European Journal of Operational Research, Elsevier, vol. 295(2), pages 792-805.

    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:287-288:y:2016:i::p:1-11. 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.