A fractional model for insect management in agricultural fields utilizing biological control

Bio-insecticides, such as baculoviruses, are the most well-known and environment friendly alternative to chemical insecticides in agriculture. In this research work, our main goal is to develop a sustainable and effective approach to control insect population by using the potential of baculoviruses. To achieve this, we formulate a novel fractional-order model utilizing the Caputo fractional operator to meticulously analyze the effects of baculovirus as a biological insecticide on insect population and consequently on crop yield. Since the virus density depletes rapidly due to ultraviolet (UV) radiation, enzymatic attacks, temperature variations and other factors in the crop field, a one-time spray of bio-insecticide may not be effective in controlling insects within a sufficient time frame. Therefore, we posit that the spraying of baculovirus is proportional to the density of the susceptible insects. The dynamic behavior of the baculovirus model underscores the critical influence of the fractional-order derivative in shaping the system’s behavior and stability. Additionally, the model analysis brings to light the intricate interplay between virus replication rate and virus infection rate in regulating insect density. To further enhance the model’s applicability, we also propose a fractional optimal control strategy to effectively reduce the insect density and associated costs, taking into account the time-dependent spraying rate of the virus. Numerical results obtained using the Adams–Bashforth–Moulton method, corroborate our analytical insights and underscore the importance of fractional-order derivative in this context.