一类考虑未就诊患者带分布时滞的SIS模型分析

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摘要：

传染性疾病一直对人类产生重要的危害.人体感染某些疾病后不会立即发病,部分染病的患者在初期时症状轻微,而未去医院就诊,并且此类病人经过一段时间后才具有传染性.为研究这些易被忽略的因素对传染病传播的影响,建立具有分布时滞并考虑未就诊患者SIS模型,计算出基本再生数R0,分析了无病平衡点和地方病平衡点的存在性和稳定性.通过Lyapunov函数证明,得到当R0<1时,无病平衡点全局渐近稳定,地方病平衡点不稳定;在给定阈值R*的基础上,当R0>R*>1时,疾病持久,并且在特定条件下,地方病平衡点局部稳定.另外,对离散化的时滞模型进行数值模拟,结果显示传染性潜伏时间越短,未就诊病人数的峰值越大;反之,未就诊病人数的峰值越小.

Infectious diseases have always taken a major toll on mankind.People infected with certain diseases will not immediately come on,some infected patients in the initial symptoms of mild did not go to the hospital will become infectious after a period of time.In order to investigate the influence of these easily neglected factors on the spread of infectious diseases,this study established a SIS model with distributed delay considering non visiting patients.Basic reproduction number was calculated,and the existence and stability of disease-free equilibrium and endemic equilibrium were analyzed.Lyapunov function is used to prove that the disease-free equilibrium is globally asymptotically stable,while the endemic equilibrium is unstable.On the basis of a given threshold,when the disease is persistent,and under certain conditions,the endemic equilibrium point is locally stable.In addition,the numerical simulation of the discretized time-delay model showed that the shorter the incubation time of infection,the greater the peak value of the number of untreated patients would be.On the contrary,the peak of the number of non visiting patients is smaller.

作者：

齐龙兴程光一包云婷

Qi Longxing;Cheng Guangyi;Bao Yunting(School of Mathematical Sciences,Anhui University,Hefei 230061,China)

机构地区：

安徽大学数学科学学院

出处：

《betway官方app 学报：自然科学版》 CAS 北大核心 2022年第2期7-15,F0002,共10页

Journal of Henan Normal University(Natural Science Edition)

基金：

国家自然科学基金(11401002) 安徽省自然科学基金(2008085MA02) 安徽省质量工程重点项目(2020jyxm0103).

关键词：

传染性疾病分布时滞未就诊患者基本再生数