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| 1 | 害虫治理SI模型的最优脉冲控制策略显示文摘考虑到农药的副作用,释放有病害虫作为一种有价值的非化学工具在害虫治理的过程中变得越来越重要.受到Xiang(2009)和Bhattacharyya等人(2006)工作的启发,该文研究了一类害虫管理SI传染病模型.虽然该模型具有多种动力学行为但易感害虫不能灭绝.为此,在该模型中引入多次脉冲干预措施,得到了易感害虫灭绝周期解全局渐近稳定的充分条件.然而,从生态和经济方面来说,让易感害虫灭绝的策略是不可取的,这是因为田间适当数量的害虫对于保护天敌,以及维持农作物的经济补偿是有益的.因此,用最小的成本最小化害虫在终端时刻的数量,基于不同的控制策略,三种最优害虫控制问题被详细研究.通过时间缩放和时间平移变换的方法,计算了目标函数关于脉冲时间间隔,农药致死率和病虫释放量的梯度,这对获得最优害虫控制策略是至关重要的.最后,数值模拟的结果显示,与其他两种策略相比,非固定时刻的交替综合控制策略是最有效的.另外,通过对比发现,该文提出的策略比害虫灭绝策略更可取. | 陈苗苗 裴永珍 梁西银 吕云飞 | 2019 | 数学物理学报(A辑)2019，39，3： | 0 |
| 2 | Analysis and optimal control of a Huanglongbing mathematical model with resistant vector显示文摘Huanglongbing(HLB)is an incurable disease that affects citrus trees.To better understand the transmission of HLB,the mathematical model is developed to investigate the transmission dynamics of the disease between Asian citrus psyllid(ACP)and citrus trees.Through rigorous mathematical derivations,we derive the expression of the basic reproduction number(R_(0))of HLB.The findings show that the disease-free equilibrium is locally asymptotically stable if R_(0)<1,and if R_(0)>1 the system is uniformly persistent.By applying the global sensitivity analysis of R_(0),we can obtain some parameters that have the greatest influence on the HLB transmission dynamics.Additionally,the optimal control theory is used to explore the corresponding optimal control problem of the HLB model.Numerical simulations are conducted to reinforce the analytical results.These theoretical and numerical results provide useful insights for understanding the transmission dynamics of HLB and may help policy makers to develop intervention strategies for the disease. | Youquan Luo Fumin Zhang Yujiang Liu Shujing Gao | 2021 | Infectious Disease Modelling2021，6，1： | 0 |
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