To reduce the global burden of mosquito-borne diseases, e.g. dengue, malaria, the need to develop new control methods is to be highlighted. The sterile insect technique (SIT) and various genetic modification strategies, have a potential to contribute to a reversal of the current alarming disease trends. In our previous work, the ordinary differential equation (ODE) models with different releasing sterile mosquito strategies are investigated. However, in reality, implementing SIT and the releasing processes of sterile mosquitos are very complex. In particular, the delay phenomena always occur. To achieve suppression of wild mosquito populations, in this paper, we reassess the effect of the delayed releasing of sterile mosquitos on the suppression of interactive mosquito populations. We extend the previous ODE models to the delayed releasing models in two different ways of releasing sterile mosquitos, where both constant and exponentially distributed delays are considered, respectively. By applying the theory and methods of delay differential equations, the effect of time delays on the stability of equilibria in the system is rigorously analyzed. Some sustained oscillation phenomena via Hopf bifurcations in the system are observed. Numerical examples demonstrate rich dynamical features of the proposed models. Based on the obtained results, we also suggest some new releasing strategies for sterile mosquito populations.

中文翻译：

---

野生和不育蚊子种群模型的动态延迟释放

为减轻登革热、疟疾等蚊媒疾病的全球负担，需要强调开发新的控制方法。昆虫不育技术 (SIT) 和各种基因改造策略有可能有助于扭转当前令人担忧的疾病趋势。在我们之前的工作中，研究了具有不同释放不育蚊子策略的常微分方程 (ODE) 模型。然而，在现实中，实施 SIT 和不育蚊子的释放过程非常复杂。特别是延迟现象总是会发生。为了实现对野生蚊子种群的抑制，在本文中，我们重新评估了延迟释放不育蚊子对抑制交互蚊子种群的影响。我们将先前的 ODE 模型扩展到延迟释放模型，以两种不同的方式释放不育蚊子，其中分别考虑了恒定和指数分布的延迟。运用时滞微分方程的理论和方法，严格分析了时滞对系统平衡稳定性的影响。观察到系统中通过 Hopf 分岔的一些持续振荡现象。数值示例展示了所提出模型的丰富动态特征。根据获得的结果，我们还提出了一些针对不育蚊子种群的新释放策略。严格分析了时间延迟对系统平衡稳定性的影响。观察到系统中通过 Hopf 分岔的一些持续振荡现象。数值示例展示了所提出模型的丰富动态特征。根据获得的结果，我们还提出了一些针对不育蚊子种群的新释放策略。严格分析了时间延迟对系统平衡稳定性的影响。观察到系统中通过 Hopf 分岔的一些持续振荡现象。数值示例展示了所提出模型的丰富动态特征。根据获得的结果，我们还提出了一些针对不育蚊子种群的新释放策略。