连续和状态脉冲投放不育蚊子的模型与分析

Modeling and Analysis of Continuous and State Impulsive Releases of Sterile Mosquitoes

考虑了不育蚊子对疾病传播的影响,建立了两种不同投放方式的数学模型。首先,建立了一个连续投放不育蚊子的数学模型,利用连续动力系统的相关理论证明了该系统的各个平衡点的稳定性。其次,为了考虑更严格且符合实际的情况,我们通过监测野生蚊子的密度来确定投放量,利用半连续动力系统几何理论和后继函数建立了状态脉冲投放不育蚊子的模型,并证明了此模型的阶-1周期解的存在性和轨道渐近稳定性。结论表明,结合野生蚊子和不育蚊子的总数量按比例投放一定量的不育蚊子可有效控制疾病的传播。

Considering the impact of sterile mosquitoes on disease transmission,we established two mathematical models of different releasing methods.Firstly,a mathematical model for continuously releasing sterile mosquitoes was established,and the stability of each equilibrium of the system were proved by the theory of continuous dynamic system.Secondly,in order to consider more rigorous and realistic situations,a model with state impulsive releasing sterile mosquitoes was presented by using the geometric theory and successor functions of semicontinuous dynamical systems.In the meantime,the existences of order one periodic solution of the model and its orbital asymptotic stability are investigated.The results showed that the spread of the disease can be effectively controlled by releasing a certain amount of sterile mosquitoes in proportion to the total number of wild mosquitoes and sterile mosquitoes.