具有路途感染和出境健康检查的SIQS传染病模型(英文)  

An SIQS Epidemic Model with Transport-Related Infection and Exit Screening

作　　者：陈晓平[1,2] 刘贤宁[1,2] 陈显[1,2] 

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]三峡库区生态环境教育部重点实验室,重庆400715

出　　处：《西南大学学报（自然科学版）》2011年第5期14-21,共8页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10971168);教育部科学技术研究重点项目(109132);中央高校基本科研业务费专项资金(XDJK2009B012)

摘　　要：提出了SIQS模型,研究了路途感染和出境健康检查对疾病传播的影响,获得了如下结果:如果基本再生数R0γθ≤1,无病平衡点全局渐近稳定;如果基本再生数R0γθ>1,综合利用Routh-Hurwitz准则和Gersgorin圆盘定理,得到了地方性平衡点局部渐近稳定性;此外,还证明了如果地方性平衡点存在,疾病是持久的.数学结论表明,出境健康检查能减少感染者出境数量和路途感染的发生率,有利于疾病的消失.To understand transport-related infection and the effect of exit on disease spread,an SIQS model is proposed and some analytical results are obtained.If the basic reproduction number R0γθ≤1,there only exists the disease-free equilibrium which is proved to be globally asymptotically stable.Comprehensively use of Routh-Hurwitz criterion and Gersgorin＇s theorem shows that endemic equilibrium is locally asymptotically stable if the basic reproduction number R0γθ1.It is also shown that the disease is endemic in the sense of permanence if and only if the endemic equilibrium exists.The mathematical results suggest that exit health examination is helpful for disease extinction,since it reduces the number of infected exit personnel and the rate of disease incidence during travel.

关 键 词：SIQS传染病模型 路途感染 出境检查 稳定性 持续性 

分 类 号：O175.1[理学—数学]