摘要
借助极限理论和Fonda定理,研究了一类既有常数输入率又有因病死亡率的SEIS传染病模型.所考虑模型的传染率是非线性的,并且得到了该模型的基本再生数,当基本再生数小于1时,该模型仅存在唯一的无病平衡点,它是全局渐近稳定的,且疾病最终灭绝.当基本再生数大于1时,该模型除存在不稳定的无病平衡点外,还存在唯一的局部渐近稳定的地方病平衡点,并且疾病一致持续存在.
By means of limit theory and Fonda＇ s theorem, an SEIS epidemic model with constant recruitment and the disease-related rate is considered. The incidence term is of the nonlinear form,and the basic reproduction number was found. If the basic reproduction number is less than one, there ex- ists only the disease-free equilibrium which is globally asymptotically stable, and the disease dies out eventually. If the basic reproduction number is greater than one,besides the unstable disease-free equillibrium,there exists also a unique endemic equilibrium, which is locally asymptotically stable, and the disease is uniformly persistent.
出处
《应用数学和力学》
CSCD
北大核心
2006年第5期591-596,共6页
Applied Mathematics and Mechanics
基金
国家科技攻关计划资助项目(2004BA719A01)
关键词
传染病模型
平衡点
稳定性
持续性
epidemic models
equilibrium
stability
persistence
