Multi-seasonal modelling of Carica papaya and Paracoccus marginatus interactions under climate change

The papaya mealybug, Paracoccus marginatus, has emerged as a formidable threat to global tropical agriculture, capable of inducing devastating yield losses through its invasive sap-sucking behavior. While conventional models often overlook environmental complexities, in this study, we introduced a sophisticated multi-seasonal mathematical framework designed to unravel the intricate interplay between mealybug population dynamics, fluctuating climatic conditions, and the persistence of off-season natural reservoirs. Sensitivity analysis highlighted how parameter influences shift across seasons, while our qualitative analysis revealed a dual-threshold mechanism, governed by the local offspring number $ \mathcal{N}_0 $ and the global stability threshold $ \mathcal{N}_g $, as the definitive driver of the system's long-term evolution. While $ \mathcal{N}_0 < 1 $ analytically ensures local asymptotic stability, our theoretical discussion suggested the existence of a conjectured regime of bistability within the threshold range $ \mathcal{N}_g < \mathcal{N}_0 < 1 $. This finding highlighted a critical regime where the success of eradication efforts is strictly contingent upon the initial infestation levels. Furthermore, by employing uniform persistence theory, we proved that the pest inevitably establishes a permanent foothold whenever $ \mathcal{N}_0 > 1 $. To mitigate these agricultural losses, we evaluated the efficacy of two distinct intervention frameworks: (ⅰ) Pulsed biological control via impulsive parasitoid releases and (ⅱ) a synergistic integrated pest management (IPM) strategy combining biopesticides with natural enemies. Our simulations demonstrated that while impulsive parasitoid releases alone achieved substantial suppression, reducing immature and mature female populations by 89.35% and 93.04%, respectively, and recovering 75.92% of papaya production, the integrated approach proved transformative. By synchronizing biopesticide applications with parasitoid pulses, mealybug populations were nearly decimated, with reduction rates reaching 99.70% for immatures and an exhaustive 99.90% for adults. Although this intensive suppression yielded a 44.92% increase in net productivity, its primary value lies in providing a robust, non-linear pathway toward total pest eradication, effectively breaking the cycle of reinfestation.