Farming awareness based optimum interventions for crop pest control

Area of Science:

• Mathematical Biology
• Agricultural Science
• Ecology

Background:

• Crop pests pose a significant threat to agricultural productivity and food security.
• Effective pest management strategies are crucial for sustainable agriculture.

Purpose of the Study:

• To develop and analyze a mathematical model for crop pest management.
• To investigate the impact of farming alertness on pest dynamics.
• To determine optimal control strategies for pest reduction.

Main Methods:

• Development of a system of ordinary differential equations to model plant biomass, pest population, and control levels.
• Qualitative analysis of equilibrium points (pest-free and coexistence) and their stability using the Routh-Hurwitz criterion.
• Application of optimal control theory and Pontryagin's minimum principle to find control strategies.
• Numerical simulations to validate theoretical findings.

Main Results:

• The model demonstrates that solutions are positive and bounded under specific initial conditions.
• The pest-free equilibrium is locally asymptotically stable when a threshold value is less than one.
• Optimal control strategies were derived to minimize pest numbers in crop fields.
• Numerical simulations confirmed the model's predictions with and without control measures.

Conclusions:

• The developed mathematical model provides insights into crop pest dynamics and management.
• Optimal control theory offers effective strategies for reducing pest populations.
• Farming alertness, modeled mathematically, can inform better pest control interventions for increased crop yields.