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Non-smooth plant disease models with economic thresholds
Tingting Zhao1, Yanni Xiao, Robert J Smith
1Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
Mathematical Biosciences
|October 9, 2012
Summary
This study introduces a Filippov plant disease model with a cultural control strategy to manage infections. It analyzes global dynamics and sliding behavior, offering insights for integrated disease management.
Area of Science:
- Mathematical Biology
- Control Theory
- Ecology
Background:
- Plant diseases pose significant economic threats, necessitating effective management strategies.
- Threshold policies are crucial for maintaining disease levels below economic damage thresholds.
- Filippov systems offer a framework for modeling discontinuous dynamics in biological systems.
Purpose of the Study:
- To investigate the global dynamic behavior of a Lotka-Volterra Filippov plant disease model.
- To analyze the sliding dynamics and equilibria of the model under a cultural control strategy.
- To provide a mathematical foundation for integrated plant disease management.
Main Methods:
- Utilizing Filippov systems to model plant disease dynamics with discontinuous control.
- Analyzing five types of equilibria for the Lotka-Volterra Filippov model.
- Employing iterative equations and Lyapunov functions to study global dynamics and attractors.
Main Results:
- Global dynamic behavior, including sliding dynamics, was investigated for the plant disease model.
- Five types of equilibria were identified and analyzed.
- Bounded global attractors were determined for four types of equilibria using Lyapunov functions.
Conclusions:
- The study provides a robust mathematical framework for understanding plant disease dynamics under cultural control.
- The findings support the development of effective control regimens within integrated disease management programs.
- This research contributes to the application of Filippov systems in ecological modeling and disease control.
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