|
摘要: |
本文讨论了基于媒体报道下的一类SIRS传染病模型的持久与灭绝. 该模型存在两个平衡点:无病平衡点和地方病平衡点. 本文首先给出了一个控制疾病持久与灭绝的临界值$\mathcal{R}_0$: 当$\mathcal{R}_0\leq1$时,无病平衡点呈全局渐进稳定, 这表示疾病是灭绝的; 而当$\mathcal{R}_0>1$时, 地方病平衡点呈全局渐进稳定, 这说明疾病是持久的. 最后通过数值分析验证了本文的结论. |
关键词: SIRS模型 媒体报道 基本再生数 全局渐进稳定性. |
DOI: |
分类号:O175.13 |
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目) |
|
A STUDY OF AN SIRS EPIDEMIC MODEL WITH MEDIA COVERAGE |
zhanglin,李存林
|
Abstract: |
This article aims to research the extinction and persistence of an SIRS epidemic model with media coverage. The model exists two equilibria: disease-free equilibrium and unique endemic equilibrium. We show $R_0$ to govern the extinction and the persistence of the disease. When $R_0\leq1$, the disease-free equilibrium is globally asymptotically stable which means the disease will die out. When $R_0>1$, the endemic equilibrium which is globally asymptotically stable means the persistence of the disease. Finally, Finally, the conclusion of this paper is verified by numerical analysis. |
Key words: SIRS model media coverage basic reproduction number global asymptotic stable. |