Parasitoid-led control in seasonal multitrophic systems: Impulsive strategies under hyperparasitoid disruption

Hyperparasitoids, which parasitize primary parasitoids, undermine classical biological control and pose a major challenge to integrated pest management (IPM). This study proposes a novel four-species model comprising a pest (host), a parasitoid, a hyperparasitoid, and a hypothetical predator of the hyperparasitoid. The model captures essential trophic interactions in agroecosystems, with parameters informed by cabbage pest systems, and reveals how predator introduction can reinforce pest suppression when parasitoid-based control is disrupted by hyperparasitoids. Through analytical investigation, we establish model feasibility and stability, and identify bifurcation thresholds that highlight limitations of classical control under hyperparasitoid pressure. An optimal impulsive control framework is then developed using the state-dependent Riccati equation (SDRE), incorporating seasonal fluctuations in pest growth. Two control strategies are evaluated: direct suppression via parasitoid release and indirect suppression through predator release targeting hyperparasitoids, with particular attention given to the effects of varying impulsive control intervals. Simulations reveal that combining both strategies achieves effective pest suppression while highlighting a trade-off between control intensity and outcome, shaped by intervention timing and seasonal dynamics. While daily control yields stronger suppression, it demands greater operational effort. In contrast, weekly control aligned with pest seasonality maintains pest levels below the economic threshold with much lower intervention frequency. These findings underscore the importance of accounting for ecological seasonality to avoid underestimating or overestimating control requirements, and to design pest management strategies with efficient timing and resilient intervention levels.