Aphids, the sap-sucking insects, often feeding in clusters on new plant growth, have resulted in large amounts of resources and efforts being spent attempting to control their activities. Taking cotton aphids as an example, this paper presents optimal control problems governed by stochastic models with impulsive interferences. Differing from the moment closure equation methods which are computationally intractable when the model contains excessive species, a new computational approach is employed to solve this problem. The key of the approach is to establish a functional relationship between the control variables involving the releasing rates of sterile insects and the spraying rates of pesticide and corresponding states on aphids and sterile aphids. Then the log-linear regression model is proposed to link the control variables with the moments (including the mean and variance) of states. Using training sample simulated from Gillespie algorithm, the regression coefficients for constraints and the objective function are estimated by least squares method. Simulation shows the error of the prediction of this model is relatively low and control results based on regression model are superior to the method based on the moment closure equations in terms of the control cost. Finally, the relative impacts of the prices and area of the field on optimal tactics are explored.

中文翻译：

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使用回归分析的具有脉冲控制的随机过程模型的最优害虫调控策略——以棉蚜为例

蚜虫是一种吸食汁液的昆虫，通常会成群地以新植物的生长为食，因此需要花费大量资源和努力来控制它们的活动。以棉蚜为例，提出了由具有脉冲干扰的随机模型控制的最优控制问题。与模型包含过多物种时难以计算的矩闭合方程方法不同，采用一种新的计算方法来解决这个问题。该方法的关键是建立涉及昆虫不育释放率和农药喷洒率的控制变量之间的函数关系以及蚜虫和不育蚜虫的相应状态。然后提出了对数线性回归模型，将控制变量与状态的矩（包括均值和方差）联系起来。使用Gillespie算法模拟的训练样本，通过最小二乘法估计约束和目标函数的回归系数。仿真表明，该模型的预测误差较小，基于回归模型的控制结果在控制成本方面优于基于矩闭合方程的方法。最后，探讨了价格和场地面积对最佳策略的相对影响。仿真表明，该模型的预测误差较小，基于回归模型的控制结果在控制成本方面优于基于矩闭合方程的方法。最后，探讨了价格和场地面积对最佳策略的相对影响。仿真表明，该模型的预测误差较小，基于回归模型的控制结果在控制成本方面优于基于矩闭合方程的方法。最后，探讨了价格和场地面积对最佳策略的相对影响。