A multi-seasonal mathematical framework for evaluating integrated pest management strategies against the African maize stalk borer Busseola fusca

The maize stalk borer (\textit{Busseola fusca}) threatens maize production and food security across sub-Saharan Africa, causing substantial yield losses for smallholder farmers. Although integrated pest management (IPM) offers a sustainable approach, a unified quantitative framework capturing interactions among complementary control strategies and seasonal pest dynamics has remained lacking. To address this gap, we develop a multi-seasonal mathematical model integrating five interventions: chemical control (ovicides, larvicides, adulticides), biological control, host-plant resistance, cultural practices, and their interactions within a seasonal framework capturing within-season proliferation and between-season carryover. Using Floquet theory, we derive the seasonal control reproduction number, \(R_{c}^{\text{seasonal}}\), serving as a threshold for pest persistence or extinction. We establish positivity and boundedness of solutions, characterize the periodic pest-free equilibrium, and prove its stability when \(R_{c}^{\text{seasonal}} < 1\). Local sensitivity analysis reveals that ovicide efficacy (\(\delta_E\), elasticity \(-0.3023\)) and off-season ovicide application (\(u_E^{\text{off}}\), \(-0.2133\)) exert the strongest negative influence on \(R_{c}^{\text{seasonal}}\), indicating that egg-targeted control particularly during the off-season produces the greatest reduction in seasonal pest persistence. Global sensitivity analysis identifies egg control intensity (\(u_E\), \(S_T = 0.7786\)) as the primary driver of the reproduction number, while larval abundance exhibits total-order indices approaching unity (\(S_T \approx 1.0\)). Comparative analysis of over 60 strategies shows biological control alone achieves \(R_{c}^{\text{seasonal}} = 0.8675 < 1\), whereas individual chemical controls (larvicide: \(R_{c}^{\text{seasonal}} = 1.0347\); adulticide: \(R_{c}^{\text{seasonal}} = 1.0302\)). Comprehensive IPM packages achieve the lowest values (IPM-High: \(R_{c}^{\text{seasonal}} = 0.5315\); all controls with resistance: \(R_{c}^{\text{seasonal}} = 0.5618\)), demonstrating strong synergies. These findings provide quantitative guidance for designing season-specific integrated pest management programmes that maximize long-term suppression of \textit{B. fusca} while reducing reliance on chemical insecticides.