具有常数输入的SEIR和SEIS组合传染病模型的分析

Analysis of SEIR and SEIS Combination Epidemic Model with Constant Recruitment

根据流行病不同阶段的特征,建立了易感者类具有常数输入的SEIR和SEIS组合传染病模型.该模型所考虑的传染率为βSI/φ(I),推广了非线性传染率βIpS/(1+α|q),并且当φ(I)≡1时,该传染率即为双线性传染率.最后采用Liapunov函数和Lasalle不变原理证明了所给模型的平衡点的稳定性。

A class of SEIR and SEIS combination epidemic model with constant recruitment was established according to epidemic＇s characteristics in different stages. The incidence rate of this model was βSI/φ（I）, which was a derivation of the nonlinear incidence rate βIPS/（1＋aIq）. And if φ（I） ≡ 1, the more, the incidence rate is a bilinear incidence rate. By means of Liapunov function and Lasalle invariance principle, the stability of the model＇s equilibrium point was proved.