带有体检和免疫的乙肝动力学模型分析  

Analysis of a Hepatitis B Kinetic Model with Physical Examination and Immunization

作　　者：孙雅楠 薛亚奎[1] SUN Ya-nan;XUE Ya-kui(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》2020年第11期265-272,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年基金(11301491);山西省自然科学青年基金(2018010221040)。

摘　　要：研究了一类同时带有体检和免疫的乙肝传染病问题.通过分析体检和免疫对乙肝的影响,建立了合理的动力学模型,证明了模型地方病平衡点的存在性条件,计算了基本再生数R0,并证明了当R0≤1时,无病平衡点是全局渐近稳定的,当R0> 1时,地方病平衡点是全局渐近稳定的.最后通过数值模拟证明了结果的正确性,分析比较了体验和免疫分别对乙肝感染的影响效果.强调了体检和免疫对防控乙肝感染的重要性.In this paper,we study a class with a Physical examination and immunization of hepatitis B infection at the same time,through the analysis of the influence of physical examination and immune to hepatitis B,then to establish a reasonable dynamic model.We also calculate the basic reproduction number of R0 and prove the conditions of the existence of endemic equilibrium point.Then it is proved that when R0≤1,the disease-free equilibrium point is globally asymptotically stable,and when R0>1,the endemic equilibrium point is globally asymptotically stable.Finally,it is found through numerical simulation that periodic solutions are accurate.The numerical simulation results emphasize the importance of physical examination and vaccination for the prevention and control of the hepatitis B.

关 键 词：体检 免疫 基本再生数 LYAPUNOV函数 全局渐近稳定 

分 类 号：R512.62[医药卫生—内科学] O211.6[医药卫生—临床医学]