Multi-seasonal modelling of the African maize stalk borer with assessment of crop residue management

•Two original multiseasonal models for a maize pest are developed.•Crop residues are burnt in one model (Slash-and-Burn Model), and buried in the soil in the other (Burying Model).•Stability analysis and R0 computation of semi-discrete models with 2D switchings.•Identification of thresholds of larvae destruction to reduce pest infestation.•Residue management strategies are discussed.