摘要
讨论了一类带有时滞的SE IS流行病模型,并讨论了阈值、平衡点和稳定性.模型是一个具有确定潜伏期的时滞微分方程模型,在这里我们得到了各类平衡点存在条件的阈值R0;当R0<1时,只有无病平衡点P0,且是全局渐近稳定的;当R0>1时,除无病平衡点外还存在唯一的地方病平衡点Pe,且该平衡点是绝对稳定的.
An SEIS epidemic model with time delay is discussed in this paper, the basic reproduction number R0 is obtained for the epidemic model. The equilibrium and stability are also discussed in this paper. The epidemic model is a differential equation with fixed time delay. The equilibria are decided by R0. Only the disease-free equilibrium arises when R0 〈 1, and the disease-free equilibrium is globally asymptotic stability. The endemic equilibrium arises when R0 〉 1, and the endemic equilibrium is absolutely stability. The results above are proved in this paper.
出处
《数学的实践与认识》
CSCD
北大核心
2007年第24期83-88,共6页
Mathematics in Practice and Theory
关键词
传染病模型
时滞
平衡点
稳定性
绝对稳定
阈值
epidemic model
time delay
equilibrium
stability
absolutely stable
threshold
