具有非线性传染率的SIQS传染病模型定性分析和数值模拟  

Study on a Kind of SIQS Epidemic Model with Nonlinear Incidence Rate and Numerical Simulation

作　　者：周艳丽[1,2] 张卫国[2] 

机构地区：[1]上海医疗器械高等专科学校基础教学部,上海200093 [2]上海理工大学理学院,上海200093

出　　处：《数学的实践与认识》2013年第19期281-286,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11071164);上海医疗器械高等专科学校校科研启动基金(A25001201-8)

摘　　要：研究了一类具有非线性接触率并带有隔离项的传染病数学模型·利用Poincare Bendixson定理并通过构造Liapunov函数证明了地方病平衡点和无病平衡点的全局稳定性,揭示了隔离对平衡点的影响.最后运用数值模拟对文中所得结论进行验证.A kind of SIQS epidemic model with nonlinear incidence rate is considered. By means of Liapunov function and Poincare-Bendixson theorem, we proved the global asymptotic stability for the endemic equilibrium and disease-free equilibrium. The influence of quarantine period to the disease is exposed. Through numerical simulation demonstrates the critical situation, the results showed that the disease-free equilibrium and the endemic equilibrium are global asymptotic stability.

关 键 词：非线性接触率 SIQS模型 LIAPUNOV函数 全局稳定性 数值模拟 

分 类 号：O175[理学—数学]