Modeling the dynamics of Diamondback Moth infestations on cabbage biomass

The Diamondback Moth (Plutella xylostella) is a notorious agricultural pest that poses significant challenges to cabbage production. In this study, we formulated and analyzed the deterministic differential equations to capture the infestations dynamics of diamondback moth in a cabbages biomass, taking into account the use of environmentally friendly pesticides. To study its dynamics we computed the threshold number, ℛ∗, based on the pest-free equilibrium point. The results indicate that when ℛ∗≤1, the equilibrium point ξ1 is both locally and globally stable. Conversely, when ℛ∗>1, the coexistence point becomes globally asymptotically stable. The stability of the equilibrium points were both Locally and globally assessed using Ruth Hurwitz’s criteria for local stability and Lyapunov functions for global analysis. A comprehensive numerical analysis was conducted, confirming the substantial support for the analytical findings. Finally, this research suggests that in order to reduce the impact of the diamondback moth, it is necessary to decrease the threshold value smaller than a unity through the adoption of effective inter-cropping techniques and the use of environmentally friendly pesticides