A mathematical representation of the push and pull technique via spatially-explicit physiologically-based models

The push and pull is an insect pest control strategy which combines attractants and repellents to manipulate the spatial distribution of the populations. Recent studies have proven its efficacy and have identified this technique as an auspicious alternative to traditional agrochemicals. Although being promising, its implementation still faces significant challenges as, for instance, the spatial and temporal deployment of control agents. Mathematical modelling could play a pivotal role in such sense, as it might reproduce different trap/repellent configurations in silico . This study aims to apply a generalised spatially-explicit model based on ordinary differential equations to simulate the effect of traps and repellents on insect pest populations. The theoretical framework, as well as the model behaviour, has been introduced with reference to the case study of the olive fruit fly Bactrocera oleae . Eight spatial arrangements of traps and repellents were compared to further assess the model behaviour and their impact in reducing the adult population. Simulations indicate that increasing the density of control agents enhances effectiveness up to a threshold, and that the spatial configuration of push and pull components plays a critical role on control success. The model hereby introduced lays the groundwork for further formulations of optimal control problems aimed to optimise the push and pull strategy within pest management programmes, which so far are still driven by empirical methods.