宿主具有垂直传染的查加斯病模型的建立与分析  

The Host Has a Vertical Infection Chagas Disease Model and Analysis

作　　者：王学艳 李桂花[1] WANG Xue-yan;LI Gui-hua(School of Science, North University of China, Taiyuan 030051, China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2017年第21期314-320,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11201434;61379125);山西省回国留学人员科研资助项目(2013-087);山西省留学回国人员科技活动择优资助项目

摘　　要：查加斯病是由克氏锥虫寄生引起的,其传播媒介为锥蝽.带有病原体的锥蝽叮咬健康人是其主要的传播途径,本病也可以通过输血、母婴进行传播.建立了宿主具有垂直传染、不同的传染源采用不同传染率的查加斯病模型并进行了动力学性态分析.通过分析,给出了基本再生数R_0;当垂直传染率p=0时,若R_0<1,系统仅存在无病平衡点且局部渐近稳定,意味着疾病消亡;当R_0>1时,系统存在一个正平衡点且局部渐近稳定;当0<p≤1时,系统不存在无病平衡点,始终存在一个正平衡点,并证明了其是局部渐近稳定的.通过构造Lyapunov函数证明了模型的无病平衡点和正平衡点的全局稳定性,即疾病流行.最后通过数值模拟,验证了所得结论的正确性.Chagas disease is caused by the Trypanosoma cruzi parasites, and its vector is triatomine. The main mode of transmission is that triatomines with pathogens bite healthy people. The disease can also be spread through blood transfusion, and from mother to child vertical transmission. This paper established a Chagas disease model, which considers the vertical transmission in host population, and also uses different transmission rate for different transmission mode. Also the dynamic characteristic analysis for the model is conducted in the paper. Through the analysis, it was found that given the basic reproduction number R0, when the vertical infection rate p -- 0, if R0 〈 1, the system only exists the disease- free equilibrium E0 and is locally asymptotically stable, which means the disease will die; If R0 〉 1, there is a positive equilibrium point, which is locally asymptotically stable; When 0 〈 p ≤ 1, the system does not have disease-free equilibrium and it has a positive equilibrium point, which is proved to be locally asymptotically stable. By constructing the Lyapunov function, we can conclude that the disease-free equilibrium and the positive equilibrium are globally asymptotically stable, and diseases will be popular at the positive equilibrium point. Finally through the numerical simulation, the conclusion is verified.

关 键 词：媒介传染 垂直传播 稳定性 LYAPUNOV函数 

分 类 号：O175[理学—数学]