Despite centuries of continuous efforts, mosquito-borne diseases (MBDs) remain enormous health threat of human life worldwide. Lately, the USA government has approved an innovative technology of releasing Wolbachia-infected male mosquitoes to suppress the wild mosquito population. In this paper we first introduce a stage-structured model for natural mosquitos, then we establish a new model considering the releasing of Wolbachia-infected male mosquitoes and the mating competition between the natural male mosquitoes and infected males on the suppression of natural mosquitoes. Dynamical analysis of the two models, including the existence and local stability of the equilibria and bifurcation analysis, reveals the existence of a forward bifurcation or a backward bifurcation with multiple attractors. Moreover, globally dynamical properties are further explored by using Lyapunov function and theory of monotone operators, respectively. Our findings suggest that infected male augmentation itself cannot always guarantee the success of population eradication, but leads to three possible levels of population suppression, so we define the corresponding suppression rate and estimate the minimum release ratio for population eradication. Furthermore, we study how the release ratio of infected males and natural ones, mating competition, the rate of cytoplasmic incompatibility and the basic offspring number affect the suppression rate of natural mosquitoes. Our results show that the successful eradication relies on assessing the reproductive capacity of natural mosquitoes, a selection of suitable Wolbachia strains and an appropriate release amount of infected males. This study will be helpful for public health authorities in designing proper strategies to control vector mosquitoes and prevent the epidemics of MBDs.

尽管经过几个世纪的不懈努力，蚊媒疾病（MBD）仍然是全世界人类生命的巨大健康威胁。最近，美国政府批准了一种创新技术，该技术可以释放感染了沃尔巴克氏菌的雄性蚊子，以抑制野生蚊子的数量。在本文中，我们首先介绍了自然蚊子的阶段结构模型，然后考虑了沃尔巴克菌的释放建立了一个新模型。感染的雄性蚊子以及天然雄性蚊子和被感染的雄性蚊之间的交配竞争对天然蚊子的抑制作用。两种模型的动力学分析，包括平衡的存在性和局部稳定性以及分叉分析，揭示了存在多个吸引子的前向分支或后向分支。此外，分别使用李雅普诺夫函数和单调算子理论进一步探索了全局动力学性质。我们的研究结果表明，感染的男性增强本身并不能总能确保根除人群的成功，但是会导致三种可能的人口抑制水平，因此我们定义了相应的抑制率并估计了根除人群的最小释放率。此外，我们研究了感染的雄性和天然雄性的释放率，交配竞争，细胞质不相容率和基本后代数量如何影响天然蚊子的抑制率。我们的结果表明，成功根除蚊子取决于评估天然蚊子的繁殖能力，并选择合适的蚊子。Wolbachia菌株和适当释放量的受感染雄性。这项研究将有助于公共卫生当局设计适当的策略来控制媒介蚊子和预防MBD的流行。