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Using non-smooth models to determine thresholds for microbial pest management.

Aili Wang1, Yanni Xiao2, Robert Smith3

  • 1School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, 721013, People's Republic of China.

Journal of Mathematical Biology
|February 2, 2019
PubMed
Summary

Mathematical models for pest management using infectious agents and chemical pesticides show that appropriate threshold levels and control intensity can maintain pest populations below economic thresholds, improving control strategies.

Keywords:
Filippov systemGlobal dynamicsImpulsive differential equationsMicrobial pest managementThreshold policy

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Area of Science:

  • Mathematical Biology
  • Ecology
  • Pest Management

Background:

  • Pest outbreaks pose significant threats to agriculture and ecosystems.
  • Current pest control methods often rely on chemical pesticides, leading to environmental concerns.
  • Biological control using infectious pests offers a sustainable alternative for pest population regulation.

Purpose of the Study:

  • To develop and analyze mathematical models for microbial pest management using threshold policies.
  • To investigate the dynamics of non-smooth pest control systems.
  • To determine optimal control strategies for maintaining pest populations below economic thresholds.

Main Methods:

  • Development of two non-smooth mathematical models: an impulsive model with state-dependent control and a Filippov system model.
  • Analysis of model stability, including order-1 and order-k periodic solutions and chaotic phenomena using Poincaré maps.
  • Investigation of global stability for pseudo-equilibria and regular equilibria by examining sliding dynamics.

Main Results:

  • The impulsive model demonstrates the existence and stability of periodic solutions and potential for chaotic dynamics.
  • The Filippov model analysis provides insights into the global stability of equilibrium points.
  • Both models confirm that judicious selection of threshold levels and control intensity is crucial for effective pest population suppression.

Conclusions:

  • Mathematical modeling provides a robust framework for designing effective pest management strategies.
  • Threshold-based control, incorporating biological and chemical methods, can sustainably manage pest populations.
  • The study extends existing models by considering state-dependent and non-smooth control interventions for enhanced pest control outcomes.