The Nilaparvata lugens is primary vector of rice diseases such as rice ragged stunt. A recent study reported the Wolbachia wStri can cause the cytoplasmic incompatibility of N.lugens, and inhibit the infection and transmission of rice ragged stunt virus in the laboratory. In this work, based on multi-strains infection mechanisms including incomplete cytoplasmic incompatibility and imperfect maternal transmission, we use differential equations to describe the spreading dynamics of Wolbachia wStri and wLug in N.lugens population. The system can exhibit one or two stable equilibria. The stability of equilibrium infected with wStri shows that wStri can invade wild populations when the cytoplasmic incompatibility intensity of wStri and the maternal inheritance leakage rate of wLug are higher than some certain thresholds. The stability conditions of the equilibria are related to the mutual fitness of the populations. If one population is more adaptable than the other, it will be in the ascendancy. An initial value region is found, from which the trajectory of system tends to the equilibrium infected with wStri. Studies on subsystem without wStri demonstrate there is a symbiotic relation between Wolbachia wLug and N.lugens population, and Wolbachia wLug can promote the reproduction of N.lugens. In addition, our numerical results are consistent with relevant literatures experimental results. Our results can guide the release of N.lugens infected with wStri in rice fields to control the growth of wild N.lugens population.

的稻褐飞虱是水稻病害的初级矢量如水稻参差不齐特技。最近的一项研究报道了Wolbachia wStri在实验室中可引起N.lugens的细胞质不相容性，并抑制水稻残株矮化病毒的感染和传播。在这项工作中，基于不完全细胞质不相容性和不完全母体传播等多株感染机制，我们使用微分方程来描述Wolbachia wStri和wLug在N.lugens种群中的传播动态。该系统可以表现出一两个稳定的平衡。感染wStri的平衡稳定性表明wStri可侵入野生种群时的胞质不相容强度wStri和的母系遗传泄漏率wLug比一些特定阈值更高。均衡的稳定条件与种群的相互适应度有关。如果一个种群的适应性强于另一个种群，它将处于优势地位。找到一个初始值区域，系统的轨迹从该区域趋于被wStri感染的平衡。对没有wStri 的子系统的研究表明Wolbachia wLug和N.lugens种群之间存在共生关系，Wolbachia wLug可以促进N.lugens的繁殖蓝藻。另外，我们的数值结果与相关文献的实验结果是一致的。我们的研究结果可以指导稻田中感染wStri的N.lugens的释放，以控制野生N.lugens种群的生长。