A Mathematical Model to Study the Combined Uses of Infected Pests and Nutrients in Crop Pest Control: Stability Changes and Optimal Control

This study presents a comprehensive analysis of farming-awareness campaigns aimed at enhancing crop pest management through the strategic deployment of infected pests as a biological control mechanism. Additionally, the role of nutrient supplementation is examined within these campaigns to facilitate crop recovery and improve overall agricultural yield. A mathematical model is developed and rigorously analyzed to assess the efficacy of these integrated pest control strategies. The model is investigated with a focus on equilibrium states, stability analysis, and the conditions leading to Hopf bifurcation. Furthermore, optimal control theory is employed to optimize the release of infected pests, ensuring maximum crop yield while maintaining ecological balance. Our study not only underscores the critical influence of nutrient supplementation in augmenting crop productivity but also highlights the risk of excessive nutrient application, which may destabilize the system. These results emphasize the necessity of maintaining an optimal nutrient threshold. By integrating farming-awareness campaigns with precise biological control measures and nutrient management, our study establishes a robust framework for sustainable pest mitigation and agricultural productivity enhancement. The findings suggest that the synergistic application of infected pests and nutrient enrichment not only suppresses pest populations but also enhances crop resilience and productivity.