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Characterization of the Killing-Rate for a Pest Control Model: The Cumulative Lethal Rate Based on Pesticide
1College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421008, Hunan, China.
Bulletin of Mathematical Biology
|May 21, 2026
Summary
Repeated pesticide use has a cumulative lethal effect on pests. This study introduces a model showing that below a critical spraying period, pests are eradicated, while above it, a stable pest population persists.
Area of Science:
- Pest Management
- Mathematical Biology
- Toxicology
Background:
- Pesticide resistance and cumulative effects pose challenges in pest control.
- Understanding dose-response relationships is crucial for effective pesticide application.
Purpose of the Study:
- To precisely formulate the cumulative lethal rate of pesticides.
- To analyze a pest population model incorporating cumulative pesticide effects.
- To determine optimal pesticide application strategies.
Main Methods:
- Formulation of a cumulative lethal rate using a dose-response function.
- Derivation of a spray-period integral for the cumulative lethal rate.
- Analysis of a logistic growth model with cumulative lethal effects.
- Investigation of model dynamics, including periodic solutions.
Main Results:
- A threshold dynamics based on the spraying period was identified.
- Below a critical spraying period, pest extinction is globally stable.
- Above the critical period, a unique, stable, positive periodic pest population emerges.
Conclusions:
- The spraying period is a critical factor in pest population dynamics.
- Optimal pesticide strategies balance dosage, control time, and population persistence.
- Mathematical modeling provides insights into effective pest management.
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