基于植物疾病控制的非光滑动力学模型的研究

项目名称： 基于植物疾病控制的非光滑动力学模型的研究

项目编号： No.11501446

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 赵婷婷

作者单位： 西北大学

项目金额： 18万元

中文摘要： 植物疾病严重影响农作物生产。经典的植物疾病模型通常利用常微分方程刻画疾病的发展与控制，忽略了人为控制的周期性、持续性和状态依赖性。本项目引入经济阈值，考虑种植和化学等综合策略，提出非光滑模型进行理论和应用研究。基于资源的有限性建立具有非线性种植策略的脉冲微分模型，将线性脉冲推广至非线性脉冲，寻求根除疾病的阈值，揭示影响疾病发展的关键因素。根据疾病的传播机理建立具有综合控制的病毒动力学与种群动力学的复合模型，以实施策略的费用为目标函数，探求费用最少的最优控制周期和经济阈值，探寻最佳防治方案。以染病植物和易感植物的数量为准则，建立具有双切换面的Filippov模型，探究该分段光滑系统的复杂动力学，寻求有效的防治策略使得染病植物数量最终不超过经济阈值。根据我国甘薯病毒病等疾病的统计数据估计模型参数，预测疾病发展趋势，探讨防治方案的有效性，为农业部门实施的防治措施提供定量评估和优化建议。

中文关键词： 综合疾病管理；经济阈值；非光滑模型；Lyapunov函数；参数估计

英文摘要： Plant disease is a key constraint in yield and quality of cultivated crops. Classical plant disase mathematical models with ordinary differential equations are proposed to describe the development and control of plant diseases, however, periodicity, non-instantaneousness and state-dependency of the control behavior are usually ignored. On the basis of the economic threshold, and the integrated strategies including cultural and chemical tactics and so on, we establish non-smooth plant disease models to do theoretical and applied research. Firstly, the impulsive model with nonlinear cultural control strategy is proposed due to the availability of resource. We extend the linear impulse to the nonlinear impulse, then explore the threshold concerning disease eradication and the key factor that can affect the development of diseases. Secondly, according to transmission approaches of plant diseases, the hybrid model with viral dynamics and population dynamics is established. By setting the cost for the implementation of various strategies as the target function, the optimal control period and economic threshold with the least expensive are investigated. Meanwhile, the optimal integrated control scheme will be obtained. Thirdly, the numbers of infected plants and susceptible plants can be controlled as the criterion, then the Filippov model with double swithching surfaces is proposed. We analyze the complex dynamic behavior of the piecewise smooth system to seek the effective control strategies that can be used to maintain the number of infected plants below the economic threshold. According to the statistical data of plant diseases in our country, such as sweet potato virus disease and so on, we estimate the parameters, forecast the development trend of disease and study the effectiveness of prevention and control measures. The results obtained are potential to provide the assessment and optimal suggestion on the control methods for the agricultural sector.

英文关键词： Integrated disease management;Economic threshold;Non-smooth model;Lyapunov function;Parameter estimation