一类带有非线性接触率的SIR传染病模型的稳定性  

Stability of SIR epidemical model with a class of nonlinear incidence rates

作　　者：杨洪[1] 魏俊杰 

机构地区：[1]黑龙江八一农垦大学理学院,黑龙江大庆163319 [2]哈尔滨工业大学(威海)理学院,山东威海264209

出　　处：《高校应用数学学报（A辑）》2014年第1期11-16,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11031002);黑龙江省教育厅科学技术项目

摘　　要：分析传染病模型的稳定性,并考虑到已感染者对易感染者的作用是非线性的.文中首先研究了传染病模型解的正性和最终有界性.在此基础上,当基本再生数满足一定条件时,构造一个满足条件的Lyapunov函数,证明了无病平衡点的全局稳定性.The stability of epidemical model is analyzed with consideration of the non-linear effect of infected person on susceptible person. Firstly, the positivity and ultimate boundedness of the solution for epidemical model are studied. On the basis, when the basic reproductive number satisfies certain conditions, it is proved that the disease-free equilibrium is global asymptotically stable by Lyapunov function.

关 键 词：传染病模型 非线性接触率 稳定性 

分 类 号：O175.13[理学—数学]