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Pest management through continuous and impulsive control strategies.

Hong Zhang1, Jianjun Jiao, Lansun Chen

  • 1Department of Mathematics, Jiangsu University, ZhenJiang, JiangSu 212013, PR China. cnczzhanghong@163.com

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This study introduces mathematical models for continuous and impulsive pest control. Continuous control ensures long-term pest reduction, while impulsive control can eradicate pests if implemented above a critical threshold.

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Area of Science:

  • Mathematical modeling
  • Ecology
  • Pest management

Background:

  • Pest control strategies are crucial for agriculture and public health.
  • Mathematical models aid in understanding and optimizing pest management interventions.
  • Differentiating between continuous and impulsive control methods is essential for effective strategies.

Purpose of the Study:

  • To develop and analyze mathematical models for continuous and impulsive pest control strategies.
  • To determine conditions for stable pest population reduction using continuous control.
  • To investigate conditions for pest eradication or persistence using impulsive control.

Main Methods:

  • Formulation of two distinct mathematical models: one for continuous control and one for impulsive control.
  • Analysis of model equilibria and stability using asymptotic stability criteria.
  • Numerical simulations to explore periodic solutions and system dynamics under impulsive control.

Main Results:

  • Continuous control model demonstrates a globally asymptotically stable positive equilibrium, enabling long-term pest level maintenance.
  • Impulsive control model shows a globally asymptotically stable pest-eradication periodic solution when infective pest release exceeds a critical value.
  • Below the critical threshold for impulsive control, the system becomes permanent, indicating pest persistence.

Conclusions:

  • Continuous pest control offers a reliable method for maintaining low pest levels.
  • Impulsive pest control, specifically through periodic release of infective pests, can achieve eradication if applied above a critical threshold.
  • The study provides insights into the comparative efficiency of continuous versus impulsive pest control policies.