基于农业意识的作物病虫害防治最佳干预措施
Farming awareness based optimum interventions for crop pest control
摘要：
我们开发了一个数学模型，系统的常微分方程的基础上，在作物害虫管理的农业警觉性的结果，铭记植物生物量，害虫，和控制水平。主要定性分析所提出的数学模型，类似于两个害虫的自由和共存平衡点和稳定性分析，调查。我们证明了该模型的所有解都是正的，且在初始条件下在某个有效集上有界。使用Routh-Hurwitz准则证明了无害虫和共存平衡点的局部稳定性。证明了当门限值小于1时，无虫平衡点是局部渐近稳定的。为了得到对作物害虫的最佳干预措施，即减少作物田间害虫的数量，我们应用最优控制理论，找到了相应的最优控制。我们建立了最优控制的存在性，并使用庞特里亚金的最小值原理来刻画它们。最后，我们利用数值模拟来说明所提出的模型的理论分析，有和没有控制措施。
英文摘要：
We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.
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