Brown planthopper Nilaparvata lugens is a serious rice damaging pest and can transmit rice ragged stunt virus. A new biological control method for Nilaparvata lugens by using Wolbachia wStri has been successful in the laboratory. No matter using the strategy of population replacement or the strategy of population suppression to release Nilaparvata lugens infected with wStri, theoretical analysis shows that Nilaparvata lugens infected with wStri may eventually disappear after interacting with the wild Nilaparvata lugens, so the Nilaparvata lugens infected with wStri should be released several times. The question is when and how much to release. In this paper, we propose a population replacement model and a population suppression model with state-dependent impulse release. The existence and stability conditions of the corresponding periodic solutions for these two systems are obtained by applying the theory of semi-continuous dynamical system. We found that the defined evaluation index of wStri release time determines the property of the solutions of the systems. The growth period of Nilaparvata lugens infected with wStri is divided into several stages according to the evaluation index of wStri release time, and the release measures for different stages are put forward, especially the release strategy to make the wild Nilaparvata lugens extinct is discussed. Based on the concept of control degree, a more realistic control goal is also discussed, which is to keep the wild Nilaparvata lugens under a lower level within a finite time. Numerical simulation shows that the effective control has good robustness to the biological parameters of insect, and both strategies can effectively control the wild Nilaparvata lugens.

褐飞虱Nilaparvata lugens是一种严重的水稻危害害虫，可以传播水稻衣衫褴褛的特技病毒。一种利用Wolbachia wStri生物防治褐飞虱的新方法已在实验室取得成功。无论是采用种群替代策略还是种群抑制策略释放感染wStri的褐飞虱，理论分析表明感染wStri的褐飞虱最终可能在与野生褐飞虱相互作用后消失，因此感染wStri的褐飞虱可能最终消失。应该多次释放。问题是何时以及释放多少。在本文中，我们提出了种群替换模型和具有状态相关脉冲释放的种群抑制模型。应用半连续动力系统理论，得到了这两个系统相应周期解的存在性和稳定性条件。我们发现定义的wStri发布时间评价指标决定了系统解的性质。wStri感染褐飞虱的生长期根据wStri的评价指标分为几个阶段提出了放流时间，提出了不同阶段的放流措施，重点讨论了使野生褐飞虱灭绝的放流策略。基于控制度的概念，还讨论了一个更现实的控制目标，即在有限时间内将野生褐飞虱控制在较低水平。数值模拟表明，该有效控制对昆虫生物学参数具有较好的鲁棒性，两种策略均能有效控制野生褐飞虱。