Mathematical model for pest–insect control using mating disruption and trapping Article - 2017

Roumen Anguelov, Claire Dufourd, Yves Dumont

Roumen Anguelov, Claire Dufourd, Yves Dumont, « Mathematical model for pest–insect control using mating disruption and trapping  », Applied Mathematical Modelling, 2017, pp. 437-457. ISSN 0307-904X

Abstract

Controlling pest insects is a challenge of main importance to preserve crop production. In the context of Integrated Pest Management (IPM) programs, we develop a generic model to study the impact of mating disruption control using an artificial female pheromone to confuse males and adversely affect their mating opportunities. Consequently the reproduction rate is diminished leading to a decline in the population size. For more efficient control, trapping is used to capture the males attracted by the artificial pheromone. The model, derived from biological and ecological assumptions, is governed by a piecewise smooth system of ODEs. A theoretical analysis of the model without control is first carried out to establish the properties of the endemic equilibrium. Then, control is added and the theoretical analysis of the model enables to identify threshold values of pheromone which are practically interesting for field applications. In particular, we show that there is a threshold above which the global asymptotic stability of the trivial equilibrium is ensured, i.e. the population goes to extinction. Finally, we illustrate the theoretical results via numerical experiments.

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