一类SEIS流行病传播数学模型的渐近分析

Asymptotic analysis of a kind of SEIS mathematical model for spread of epidemics

研究了具有Michaelis Menten接触率SEIS非线性流行病传播数学模型的渐近性态,得到了决定疾病绝灭和持续的阈值 基本再生数.利用Hurwitz判据、Lasalle不变集原理和Bendixon＿Dulac判别法等,证明了无病平衡点的全局渐近稳定性和地方病平衡点的局部渐近稳定性,以及无因病死亡情形极限方程地方病平衡点的全局渐近稳定性.

The asymptotic behavior of a kind of nonlinear epidemic spreading SEIS model with Michaelis-Menten type Contact rate is studied, a basic reproductive number which determines the outcome of the infectious disease is founded. By Hrwitz criterion, Lasalle invariant set principle and the criterion of Bendixon_Dulac the global stability of the disease free equilibrium, the local stability of the endemic equilibrium and the global stability of the endemic equilibrium of the limiting equation are given.