具有阶段进程的SLI艾滋病模型的全局稳定性  

Global Stability of a SLI AIDS Model with Staged Progression

作　　者：王晓红 刘桂荣[2] WANG Xiao-hong;LIU Gui-rong(Department of Mathematics, College of Lvliang, Lvliang 033001, China;School of Mat hematical Sciences, Shanxi University, Taiyuan 030006, China)

机构地区：[1]吕梁学院数学系,山西离石033001 [2]山西大学数学科学学院,山西太原030006

出　　处：《数学的实践与认识》2019年第10期286-291,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11471197):动态重叠网络上疾病和信息传播动力学建模与分析;吕梁学院校内青年基金(ZRQN201515):基于同步理论的复杂公交网络模型研究

摘　　要：艾滋病的潜伏期很长,一般会经历几个潜伏阶段才会发病,故将其看作常数是不合理的.建立了一个具有现实分布的数学模型,即将潜伏期划分为n个阶段.对于一个一般的具有双线性发生率的n-阶段的阶段进程模型,研究了其动力学行为.首先给出了模型的基本再生数.进一步得到,当基本再生数小于1时,无病平衡点是全局渐近稳定的且疾病最终会消失;当基本再生数大于1时,唯一的地方病平衡点是全局渐近稳定的且疾病最终会成为一种地方病.The incubation period of AIDS is very long, and it usually goes through several latent stages, so it is not reasonable to think of it as a-constant.This paper formulates a mathematical model with the realistic distribution, i.e., divides the latent period into n stages.For a general n-stage stage-progression(SP) model with bilinear incidence, we analyze its dynamic behavior. First we give the basic reproduction number. Moreover, if the basic reproduction number is less than 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out;If the basic reproduction number is more than 1, the unique endemic equilibrium is globally asymptotically stable and the disease persists at the endemic equilibrium.

关 键 词：艾滋病 阶段进程 李雅普诺夫函数 全局稳定性 

分 类 号：O175[理学—数学] R512.91[理学—基础数学]