具有自然年龄和染病年龄的MSIR传染病模型的稳定性  

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

作　　者：曹志远 郭俐辉[1] CAO Zhiyuan;GUO Lihui(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 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：《新疆大学学报（自然科学版中英文）》2024年第4期419-426,共8页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：新疆维吾尔自治区自然科学基金“双曲型偏微分方程组初边值问题解的存在性”(2022D01E42).

摘　　要：在总人口规模不变的假设下,建立一类具有自然年龄和染病年龄的MSIR传染病模型,并研究该模型平衡解的稳定性.首先,对模型做归一化处理,并在无病平衡解处线性化,证明当R_(1)<1时,无病平衡解是局部渐近稳定的.其次,利用双曲方程组的特征线方法和Fatou引理,证明当R_(1)<1时,无病平衡解是全局渐近稳定的.最后,利用介值定理证明当R_(1)>1时,模型存在唯一的地方病平衡解.Assuming total population remains constant,this paper establishes a class of MSIR epidemic models with both natural age and infection-age and studies the stability of the equilibrium solutions of this model.Firstly,by normalizing the model and linearizing it at the disease-free equilibrium,demonstrating that when R_(1)<1,the disease-free equilibrium is locally asymptotically stable.Subsequently,employing the method of characteristics for hyperbolic systems and Fatou’s lemma,it is proven that when R_(1)<1,the disease-free equilibrium is globally asymptotically stable.Finally,the existence of a unique endemic equilibrium solution is established using the intermediate value theorem when R_(1)>1.

关 键 词：MSIR传染病模型 染病年龄 平衡解 存在性 

分 类 号：O175.1[理学—数学] R51[理学—基础数学]