The technique of sterile mosquitoes plays an important role in the control of mosquito-borne diseases such as malaria, dengue, yellow fever, west Nile, and Zika. To explore the interactive dynamics between the wild and sterile mosquitoes, we formulate a delayed mosquito population suppression model with constant releases of sterile mosquitoes. Through the analysis of global dynamics of solutions of the model, we determine a threshold value of the release rate such that if the release threshold is exceeded, then the wild mosquito population will be eventually suppressed, whereas when the release rate is less than the threshold, the wild and sterile mosquitoes coexist and the model exhibits a complicated feature. We also obtain theoretical results including a sufficient and necessary condition for the global asymptotic stability of the zero solution. We provide numerical examples to demonstrate our results and give brief discussions about our findings.

中文翻译：

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带有无菌蚊子的蚊虫种群抑制的延迟微分方程模型

无菌蚊子技术在控制蚊媒疾病（例如疟疾，登革热，黄热病，西尼罗河和寨卡病）中起着重要作用。为了探索野生和无菌蚊子之间的相互作用动力学，我们制定了具有恒定释放无菌蚊子的延迟蚊子种群抑制模型。通过对模型解的全局动力学分析，我们确定了释放速率的阈值，使得如果超过释放阈值，则最终将抑制野生蚊子种群，而当释放速率小于阈值时，野生和无菌蚊子共存，并且模型展现出复杂的特征。我们还获得了理论结果，包括零解的全局渐近稳定性的充分必要条件。