基于媒体报道下的一类SIRS传染病模型研究  

A STUDY OF AN SIRS EPIDEMIC MODEL WITH MEDIA COVERAGE

作　　者：张林 李存林[2] 郭文娟 ZHANG Lin;LI Cun-lin;GUO Wen-juan(School of Mathematics and Computer Science,North Minzu University,Yinchuan 750021,China;School of Management,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]北方民族大学管理学院,宁夏银川750021

出　　处：《数学杂志》2018年第5期887-895,共9页Journal of Mathematics

基　　金：国家自然科学基金资助(71561001);北方民族大学研究生创新项目资助(YCX1779)

摘　　要：本文主要研究了基于媒体报道下的一类SIRS传染病模型的持久与灭绝问题.利用一个控制疾病持久与灭绝的临界值R_0,求得了该模型存在两个平衡点:无病平衡点和地方病平衡点.结果表明当R_0≤1时,无病平衡点呈全局渐进稳定,这表示疾病是灭绝的;而当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该结论.This article aims to research the extinction and persistence of an SIRS epidemic model with media coverage.By using the critical value R0 to govern the extinction and the persistence of the disease,we obtain that the model exists two equilibria:disease-free equilibrium and unique endemic equilibrium.The results show that if R0≥1,the disease-free equilibrium is globally asymptotically stable which means the disease will die out;if R0>1,the endemic equilibrium which is globally asymptotically stable means the persistence of the disease.Finally,the conclusion is verified by numerical analysis.

关 键 词：SIRS模型 媒体报道 基本再生数 全局渐进稳定性 

分 类 号：O175.13[理学—数学]