具有种群扩散的包虫病传播模型的研究  

Research on Echinococcosis Transmission Model with Population Diffusion

作　　者：刘俊利[1] 刘璐菊[2] 冯进钤[1] LIU Jun-li;LIU Lu-ju;FENG Jin-qian(School of Science, Xi＇an Polytechnic University, Xi＇an 710048, China;School of Mathematics and Statistics, He＇nan University of Science and Technology, Luoyang, 471023, China)

机构地区：[1]西安工程大学理学院,陕西西安710048 [2]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《中北大学学报（自然科学版）》2017年第6期647-651,673,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11101323;11101127;11302158);陕西省自然科学基础研究计划资助项目(2014JQ1038);陕西省教育厅科研计划资助项目(16JK1331)

摘　　要：研究了具有种群扩散的包虫病传染病模型,建立了反应扩散模型.利用线性化等方法对模型进行了动力学分析,证明了最小波速的存在性和正平衡点的局部渐近稳定性.数值模拟研究了各参数对最小波速的影响,研究结果表明染病狗的扩散对包虫病的传播影响最大.加强对狗活动的限制会减小包虫病的扩散速度,但是要消灭包虫病,还需要结合其它有效的控制措施.A reaction-diffusion model was formulated to investigate the echinococcosis transmission with population diffusion. The dynamical behaviors of the model were analyzed by using the linearization method, and the existence of minimum wave speed and the local asymptotic stability of the positive equilibrium were proved. The impact of parameters on the minimum wave speed was investigated by numerical simulation. The simulation results illustrate that the diffusion of infected dogs is the most important factor that leads to the spread of echinococcosis. Imposing restrictions on the dog dispersal will reduce the diffusion speed of eehinococcosis. If we want to eliminate echinococcosis, other effective control measures are necessary.

关 键 词：最小波速 种群扩散 包虫病传播 基本自生数 

分 类 号：O175.2[理学—数学]