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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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    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.

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