We develop a mathematical model of the wild mosquito dispersal with impulsive releases of the sterile mosquitoes and obtain a threshold condition that determines the eradication and uniform persistence of the wild mosquitoes using Floquet theory and impulsive comparison theorem. The effect of the dispersal rate on dynamics is investigated by means of numerical simulation. Additionally, we investigate a three-dimensional dispersal model of mosquitoes with impulsive state feedback control to effectively control the abundance of the wild mosquitoes below the acceptable level when the density of the wild mosquitoes reaches a certain threshold. Dynamics of such state-dependent control is also presented by applying numerical simulations since it is difficult to implement theoretical analysis. Finally, a brief discussion is given.

我们开发了野生蚊子散布的数学模型，并利用 Floquet 理论和脉冲比较定理获得了一个阈值条件，该阈值条件确定了野生蚊子的根除和一致持久性。通过数值模拟研究了扩散速率对动力学的影响。此外，我们研究了具有脉冲状态反馈控制的蚊子三维散布模型，以在野蚊密度达到一定阈值时有效地将野蚊丰度控制在可接受水平以下。由于难以实现理论分析，因此还通过应用数值模拟来呈现这种状态相关控制的动力学。最后，进行了简要的讨论。