A Memory-Based Model for Evaluating Trap and Removal Strategies Against the Red Palm Weevil

The red palm weevil (Rhynchophorus ferrugineus, RPW) is one of the most destructive pests of date palms worldwide. Its larvae feed inside the stem, so damage is often irreversible before any symptoms are visible. Early detection and rapid removal of infested palms are therefore essential. We develop a five-compartment fractional-order mathematical model that tracks healthy palms, infested palms, larvae, adult weevils, and pheromone traps. The model uses fractional-order (Caputo) derivatives, which allow past infestation history to influence current dynamics. We use this memory as a phenomenological representation of delayed and cumulative effects, such as the 2–4 month larval development cycle, and we test it against integer-order, Erlang-distributed, and fixed-delay alternatives. We provide mathematical proofs that the model is well posed and identify a threshold, the basic reproduction number R0, that separates eradication from persistent infestation. The model is calibrated to two UAE datasets: the 1994/95 Al Ain survey of about 1.1×106 palms (R0 > 1) and the 2025 national program outcomes (R0 < 1), using the reported first and last counts of each series and a reconstructed monthly trajectory between them. This drop in R0 corresponds to three control improvements: sensor-based early detection, endotherapy (localized insecticide injection into the stem), and preventive stem injection. Model comparison supports a fractional order of about 0.95 only for the 1994/95 epoch, whereas the 2025 data are described equally well without memory. Sensitivity analysis shows that faster removal of infested palms, lower RPW-to-palm contact rates, and reduced larval production are among the most effective control tactics. Model simulations of suspended and restored control suggest, as a hypothesis-generating scenario derived from hypothesized data, that a lapse in control can allow a transient resurgence, which supports continued monitoring. These results give quantitative guidance for planning pest management programs.