摘要
研究了一类具有常数出生、垂直传染和一般接触率β(N)的SIS传染病模型。利用Bendixson-Dulac判别法证明了当垂直传染率0<p<1或p=0,R0>1时,地方病平衡点E*或E*1全局渐近稳定,疾病流行形成地方病。运用Liapunov函数方法证明了当p=0,R0≤1时,无病平衡点E0全局渐近稳定,疾病最终消失。并通过Matlab进行数值模拟。
A SIS epidemic model with constant birth,vertical transmission and general contact rate β（N）is studied.By using Bendixson-Dulac discriminance,it is proved that the endemic equilibrium E or E1 is globally asymptotically stable if 0〈p〈1 or p=0;R0〉1,respectively,and the disease spreads to the endemic.The disease-free equilibrium E0 is globally asymptotically stable by Liapunov function method if p=0;R0≤1 and the disease always dies out eventually.And numerical simulation is carried out by Matlab.
出处
《科学技术与工程》
2010年第1期176-179,共4页
Science Technology and Engineering
基金
陕西省教育厅科研计划项目(08JK432)资助
关键词
垂直传染
一般接触率
全局渐近稳定
基本再生数
闭轨线
vertical transmission general contact rate globally asymptotically stable basic reproductive number closed trajectory
