摘要
考虑了具有连续预防接种和脉冲预防接种且传染率是标准的SIRS传染病模型,在连续预防接种和脉冲预防接种下,分别给出了SIRS传染病模型基本再生数.在连续预防接种下,利用广义Dulac函数方法证明了无病平衡点和正平衡点的全局渐近稳定性.对脉冲预防接种下的SIRS传染病模型,首次证明了无病周期解的存在性和全局渐近稳定性.
The SIRS epidemical models with continuous and impulsive vaccinations are discussed. We have found out the reproduction numbers corresponding to those models. A complete global analysis is given to the continuous vaccination models by using a generalized Dulac function. In the SIRS epidemical models with impulsive vaccinations, we have first proved the existence and global stability of the diseasefree periodic solution.
出处
《华北工学院学报》
CAS
2003年第4期235-243,共9页
Journal of North China Institute of Technology
基金
国家自然科学基金资助项目
山西省自然科学基金资助项目
太原市软科学基金资助项目
关键词
SIRS传染病模型
脉冲微分方程
周期解
传染病
基本再生数
全局稳定性
预防接种
impulsive differential equations
periodic solution
infectious disease
basic reproduction number
global asymptotic stability
vaccination
