具有自然年龄和染病年龄的SIQRS传染病模型的稳定性  

The Stability of SIQRS Epidemic Model with Natural Age and Infection-Age

作　　者：王时雯 由守科[1] WANG Shi-wen;YOU Shou-ke(College of Mathematics and System Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《数学的实践与认识》2022年第2期163-171,共9页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金(2019D01C080,2021D01C003);新疆大学博士科研启动基金(62008034)。

摘　　要：研究一类具有自然年龄和染病年龄的年龄结构SIQRS传染病模型,在人口处于稳定状态的假设下,得到了阈值R_(1)和R_(2).首先,通过将模型在无病平衡解处线性化,证明了当R_(1)<1时无病平衡解是局部渐近稳定的.其次,利用特征线法和Fatou引理,证明了当R_(2)<1时无病平衡解是全局渐近稳定的.最后,根据Volterra积分方程的相关知识,证明了如果R_(1)>1,模型至少存在一个地方病平衡解.In this paper,we study a model of infectious disease with natural age and infection-age.Under the assumption that the population is stable,the threshold R_(1) and R_(2) are obtained.Firstly,by linearizing the model at the disease-free equilibrium solution,we prove that the disease-free equilibrium solution is locally asymptotically stable when R_(1)<1.Secondly,using the method of characteristics and Fatou lemma,we prove that the diseasefree equilibrium solution is globally asymptotically stable when R_(2)<1.Finally,according to the relevant knowledge of the Volterra integral equation,we prove that there exists at least one endemic equilibrium solution if R_(1)>1.

关 键 词：染病年龄 无病平衡解 地方病平衡解 

分 类 号：R181.3[医药卫生—流行病学] O175[医药卫生—公共卫生与预防医学]