具有年龄结构的SVIQR传染病模型的稳定性分析

Stability Analysis of SVIQR Infectious Disease Model with Age Structure

摘要: 讨论一类具有疫苗接种和隔离的年龄结构SVIQR传染病模型，得出基本再生数R0的表达式。证明了当R0 < 1时，无病平衡点全局渐近稳定；当R0 > 1时，无病平衡点不稳定；此时系统存在地方病平衡点，并且证明了地方病平衡点是唯一的并且局部渐进稳定。最终得出，隔离是消除传染病的有效方式，如果不能进一步降低传播率，那么就需要最大限度地提高疫苗接种率。

Abstract: A class of age-structured SVIQR infectious disease models with vaccination and isolatio-n was discussed. The expressions of basic regeneration number R0 were derived. It was proved that when R0 < 1, the disease-free equilibrium point was globally asymptotically stable; when R0 > 1, the dis-ease-free equilibrium point was unstable. And there exists endemic equilibrium state, and it was proved that endemic equilibrium point was unique and locally asymptotically stable. Ultimately, isolation was an effective way to eliminate infectious diseases; if transmission rates cannot be re-duced in future, then vaccination rates need to be maximized.