异质集合种群上疾病传播动力学的研究  

Study on the Dynamics of Disease Transmission in Heterogeneous Populations

作　　者：张杰 刘茂省[1] ZHANG Jie;LIU Maoxing(School of science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《重庆理工大学学报（自然科学）》2020年第4期235-242,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(11571324、11701528);山西省自然科学基金项目(201601D021015);山西省回国留学人员科研项目的资助项目(2016-086)。

摘　　要：由于交通出行越发便利,人员迁移对疾病的传播产生了至关重要的影响。为了研究无出生和死亡的异质集合种群网络中SIS流行病模型中的反应扩散过程,首先确定了模型具有无病平衡点,并用下一代矩阵法表示出基本再生数;又由于邻接矩阵是随机的,给出了全局耦合网络来计算模型的无病平衡点和基本再生数;接着证明了无病平衡点的局部渐近稳定性,构建出Lyapunov函数证明了在基本再生数小于1且邻接矩阵不可约时,无病平衡点全局渐近稳定;之后证明了地方病平衡点的存在唯一性和全局渐近稳定性;最后通过数值模拟验证了理论结果。研究结果表明,人口迁移在传染病的传播过程中起到了很大的作用。As people’s living standards improve,travel has become more and more convenient.Among them,migration plays a crucial role in the spread of disease. This paper mainly studies the reaction diffusion process in the SIS epidemic model in a heterogeneous population networks without birth and death. It is first determined that the model has a disease-free equilibrium and the basic reproduction number is represented by the nextgeneration matrix method. Since the adjacency matrix is random,we give a global coupled network to calculate the disease-free equilibrium and the basic reproductionnumber of the model. Then the local asymptotic stability of the disease-free equilibrium is proved firstly. Next,the Lyapunov function is constructed to prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1 and the adjacency matrix is irreducible. It then proves the existence uniqueness and global asymptotic stability of the endemic equilibrium. Finally,the theoretical results are verified by numerical simulation. Studies have shown that migration plays a large role in the spread of diseases.

关 键 词：反应扩散过程 异质性 集合种群 基本再生数 稳定性 

分 类 号：O175[理学—数学]