引用本文:罗育东, 张国洪.具有强Allee效应的野生蚊子和绝育蚊子相互作用模型[J].西南大学学报(自然科学版),2019,41(1):65~71
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具有强Allee效应的野生蚊子和绝育蚊子相互作用模型
罗育东, 张国洪
西南大学 数学与统计学院, 重庆 400715
摘要:
假设野生蚊子具有强Allee效应,建立了包括野生蚊子和绝育蚊子相互作用的连续时间动力学模型.通过研究系统的动力学性态,包括分析平衡点的存在性、稳定性,发现系统在一定条件下存在双稳定现象,并得到了不同野生蚊子释放策略条件下控制与消灭野生蚊子种群的阈值条件,同时借助数值模拟验证了相关的理论结果.
关键词:  绝育昆虫技术  释放策略  强Allee效应  稳定性
DOI:10.13718/j.cnki.xdzk.2019.01.010
分类号:O175
基金项目:国家自然科学基金项目(11701472).
A Model for the Interactive Dynamics of Sterile and Wild Mosquitoes with Strong Allee Effects
LUO Yu-dong, ZHANG Guo-hong
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Abstract:
The sterile insect technique is one of the effective ways to prevent and control mosquito-borne diseases such as malaria and dengue fever. This article assumes that wild mosquitoes have a strong Allee effect and formulates a continuous-time mathematical model for the interactive dynamics of the wild and the sterile mosquitoes. By studying the dynamic state of the system, including analyzing the existence and stability of the equilibria, we find that under certain conditions the system has bi-stability and the threshold conditions for controlling and eliminating wild mosquito populations under different strategies of wild mosquito release are obtained. At the same time, the relevant theoretical results are verified by numerical simulation.
Key words:  sterile insect technique  releasing strategy  strong Allee effect  stability
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