利用交配中断和诱捕控制害虫的数学模型
Mathematical model for pest-insect control using mating disruption and trapping
摘要：
控制害虫是保护作物生产的主要挑战。在综合害虫管理（IPM）计划的背景下，我们开发了一个通用模型来研究交配中断控制的影响，使用人工雌性信息素混淆男性和不利影响他们的交配机会。因此，繁殖率降低，导致总体规模下降。为了更有效的控制，诱捕被用来捕获被人工信息素吸引的雄性。该模型，来自生物和生态的假设，是由一个系统的常微分方程。首先对无控制模型进行了理论分析，建立了地方病平衡点的性质。然后，控制被添加，并且模型的理论分析使得能够识别信息素的门限值，这对于现场应用是实际感兴趣的。特别地，我们证明了存在一个阈值，超过该阈值，平凡平衡点的全局渐近稳定性得到保证，即种群灭绝。最后通过数值实验对理论结果进行了验证。
英文摘要：
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 to the artificial pheromone. The model, derived from biological and ecological assumptions, is governed by a 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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