脉冲释放沃尔巴克氏体感染雄蚊模型动力学分析

Dynamic Analysis of the Wolbachia-Infected Male Mosquitoes Model by Pulsed Release

摘要: 本文以昆虫不相容技术为背景研究了具有阶段和性别结构的野生与不育蚊子相互作用脉冲模型。其目的是研究采用周期释放不育蚊子的方法控制野生蚊子数量的可行性。首先通过动力学分析得到了系统平凡周期解的存在性，并分别利用Floquet理论和Lyapunov稳定性定理给出了相应的局部稳定性条件和全局稳定性条件，从而验证了脉冲释放不育蚊子可以使野生蚊子灭绝。其次得到了系统非平凡周期解的存在性，并在具体参数下讨论了其局部稳定性，发现系统在一定阈值条件下出现平凡周期解和非平凡周期解共存的双稳现象，这表明脉冲控制也可以在不消灭野生蚊子的情况下控制它们的数量。最后利用数值模拟验证了相关理论结果。

Abstract: In this paper, we study a wild and sterile mosquito interaction impulsive model with stage-structure and sex-structure based on insect incompatibility technology. The aim is to study the feasibility of controlling the number of wild mosquitoes by releasing sterile mosquitoes periodically. Firstly, the existence of trivial periodic solutions is obtained by dynamic analysis, and the corresponding local stability and global stability conditions are proved by Floquet theory and Lyapunov stability theorem respectively. The results show that the pulsed release of sterile mosquitoes could make the wild mosquitoes extinct. Then, the existence of nontrivial periodic solutions is obtained, and its local stability is discussed under specific parameter values. It is found that the system has the bistable phenomenon in which trivial periodic solution and non-trivial periodic solution coexist under certain threshold conditions. This shows that the population of mosquitoes can be controlled by pulse control without eliminating them. Finally, numerical simulation verifies the theoretical results.