<p>This paper presents the formulation and analysis of a mathematical model for pest control with the aim of controlling its natural pests using awareness-based interventions such as the use of biopesticides with nutrients applications. Biopesticides are used to control biologically. In addition, a balanced application of nutrients is critical to increase crop growth and high yield. In the model, a time delay due to the time it takes the farmer to respond to the awareness campaign is considered. Nonnegativity and boundedness are shown to verify the plausibility of the delay model. The dynamics of the system has been analyzed with and without delay by finding the equilibrium points and their stability nature. The incidence of Hopf bifurcation is studies for both delayed and nondelayed systems. This study shows that the nutrient that is required for plant growth leads to higher yield of crops. An excess amount of nutrients causes instability in the system which is not favorable for crop growth and ultimately the yield is reduced. However, the rate of application of biopesticides stabilizes the system. Hopf bifurcation is also seen when the delay parameter crosses its critical value, indicating that people should respond to awareness campaigns with tolerable time delay.</p>

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Effects of biopesticides and nutrient in the dynamics of a delay model for awareness-based crop pest control

  • Fahad Al Basir,
  • Juan J. Nieto,
  • Tarak Nath Halder,
  • Aeshah A. Raezah

摘要

This paper presents the formulation and analysis of a mathematical model for pest control with the aim of controlling its natural pests using awareness-based interventions such as the use of biopesticides with nutrients applications. Biopesticides are used to control biologically. In addition, a balanced application of nutrients is critical to increase crop growth and high yield. In the model, a time delay due to the time it takes the farmer to respond to the awareness campaign is considered. Nonnegativity and boundedness are shown to verify the plausibility of the delay model. The dynamics of the system has been analyzed with and without delay by finding the equilibrium points and their stability nature. The incidence of Hopf bifurcation is studies for both delayed and nondelayed systems. This study shows that the nutrient that is required for plant growth leads to higher yield of crops. An excess amount of nutrients causes instability in the system which is not favorable for crop growth and ultimately the yield is reduced. However, the rate of application of biopesticides stabilizes the system. Hopf bifurcation is also seen when the delay parameter crosses its critical value, indicating that people should respond to awareness campaigns with tolerable time delay.