具有时滞的SIQR流行病模型的稳定性和永久性分析

Stability and Permanence Analysis of SIQR Epidemic Model with Time Delay

摘要: 本文主要研究带有分布时滞的SIQR的流行病模型，并确定了疾病是否灭亡的基本再生数R0。证明了当R0 < 1时，模型仅存在无病平衡点且无病平衡点是全局渐近稳定的，疾病最终灭亡；当R0 > 1时，模型存在两个平衡点，其中无病平衡点不稳定，地方病平衡点是局部渐近稳定的，且疾病将永久存在。

Abstract: In this paper, we mainly study the epidemic model of SIQR with distributed delay, and determine the basic regeneration number r of whether the disease is extinct or not. It is proved that when R0 < 1, the model only has a disease-free equilibrium and the disease-free equilibrium is globally as-ymptotically stable, and the disease eventually dies; When R0 > 1, the model has two equilibrium points, in which the disease-free equilibrium point is unstable, the endemic equilibrium point is lo-cally asymptotically stable, and the disease will exist forever.