Dynamical modeling and stability analysis of a pest-predator system with biopesticide intervention and a specific nonlinear functional response

In this paper, a new mathematical model of the interactions between pests, predators of pests and biopesticides (viruses) is proposed and analysed. The susceptible pests transform to infected pests due to the effect of pesticides by following a special type of functional responses depending on virus. The model admits three types of equilibria, namely, pest-free equilibrium, virus-free equilibrium and interior equilibrium. We theoretically investigate the local stability of the equilibria. The findings show that the virus-free equilibrium is conditionally stable, whereas the pest-free equilibrium is always unstable. The interior equilibrium is locally asymptotically stable under certain parameter conditions. Some numerical simulations are performed to explore crop dynamics and to obtain significant insights.