具有年龄结构和水平传播的媒介传染病模型研究  

Analysis of vector-borne infectious disease model with age-structured and horizontal transmission

作　　者：梁霜霜 聂麟飞[1] 胡琳[1] LIANG Shuangshuang;NIE Linfei;HU Lin(College of Mathematics and System Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《华东师范大学学报（自然科学版）》2021年第3期47-55,共9页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(1961066,11771373);新疆维吾尔自治区高校科研计划(XJEDU2018I001)。

摘　　要：考虑到病毒变异和感染年龄的普遍存在性,提出了一类具有潜伏年龄和水平传播的媒介-宿主传染病模型,给出了基本再生数R_(0)的精确表达式,刻画了该模型无病平衡态和地方病平衡态的存在性.进一步,利用线性近似方法和构造合适的Lyapunov函数及LaSalle不变原理等方法,证明了当R_(0)<1时,无病平衡态E0是全局渐近稳定的,疾病也最终趋于灭绝;而当R_(0)>1时,地方病平衡态是全局渐近稳定的,疾病将持续下去而形成地方病.Considering the prevalence of variations in virus strains and the age of infection,a vector-borne infectious disease model with latent age and horizontal transmission is proposed.An exact expression for the basic reproduction number,R_(0),is given,which characterizes the existence of the disease-free equilibrium and the endemic equilibrium for this model.Next,by using a combination of linear approximation methods,constructing suitable Lyapunov functions,LaSalle invariance principles,and other methods,we prove that if R_(0)<1,then the disease-free equilibrium has global asymptotic stability,and the disease will eventually become extinct;if R_(0)>1,then the endemic equilibrium is globally asymptotically stable,and the disease will continue to form an endemic disease.

关 键 词：媒介传染病模型 年龄结构与水平传播 基本再生数 无病和地方病平衡态 稳定性与持久性 

分 类 号：O175[理学—数学]