一类流行病数学模型的Hopf分支  

Hopf bifurcation of a class of epidemic mathematical model

作　　者：谭欣欣[1] 冯恩民[2] 沈伯骞[3] 

机构地区：[1]大连大学信息工程学院,辽宁大连116622 [2]大连理工大学应用数学系,辽宁大连116024 [3]辽宁师范大学数学系,辽宁大连116029

出　　处：《大连理工大学学报》2006年第1期135-140,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(10471014)

摘　　要：利用平面向量场极限环分支的Hop f分支理论,研究了一类具有非线性传染率kIp-1Sq的S IRS流行病传播动力学模型.首次给出了模型中指数为p≥2,q≥1的一般整数时,系统正平衡点的精确表达式,证明了此类系统至少可以存在两个极限环,并给出了Hop f分支的数值计算及模拟结果.该简化平衡点坐标表达式的方法适用于一般情形,从而使奇点焦点量的计算简洁、可行.A kind of SIRS epidemic models with nonlinear incidence rates kI^p-1S^1 is studied according to Hopf bifurcation theory for the limit cycle bifurcations of the planar vector fields, and an accurate expression of positive equilibrium for the general condition p ≥ 2,q≥1 in this model is given for the first time. It is proved that there are at least two limit cycles existing in this system by Hopf bifurcation theory. The numerical example and simulative result are also given. The method to simplify the expression of equilibrium is fit for general condition, and makes the calculation of the focus quantity concise and feasible.

关 键 词：流行病模型 HOPF分支 极限环 

分 类 号：O175.12[理学—数学]