一类带有分层接种的麻疹模型的稳定性分析  

Stability analysis of measles model with hierarchical vaccination

作　　者：王茉 刘俊利[1] WANG Mo;LIU Junli(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2020年第2期55-60,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11801431,11801432);陕西省自然科学基础研究计划项目(2018JM1011)。

摘　　要：为有效控制麻疹疾病的流行,建立并研究一类带有分层接种的SIRV1V2V3麻疹传染病模型。通过比较原理等方法确定模型解的非负性和有界性,计算得到模型的无病平衡点和基本再生数R0。利用线性化,Hurwitz判据等方法证明了当R0<1时,模型无病平衡点是局部渐近稳定的,且疾病绝灭。利用一致持久性理论证明了R0>1时麻疹疾病的持久存在性。最后对模型的理论结果进行数值模拟,并利用偏秩相关系数(PRCC)方法得到了影响麻疹疾病传播的主要因素。结果表明:降低感染率,提高恢复率和第一次接种覆盖率可以有效控制麻疹疾病的流行。In order to effectively control the epidemic of measles,a kind of SIRV 1V 2V 3 measles infectious disease model with hierarchical vaccination was established and studied.The nonnegativity and boundedness of the model solutions were determined by using comparison principle,the disease-free equilibrium and the basic reproduction number R 0 of the model were calculated.Using the methods of linearization and Hurwitz criterion,the local asymptotic stability of the disease-free equilibrium and the disease that was cured were proved when R 0<1.When R 0>1,the uniform persistence of measles was obtained by the persistence theory.Finally,numerical simulations were performed to verify the theoretical results,and the main factors that affect the spread of measles were studied by the method of partial rank correlation coefficients(PRCC).The results show that lower infection rate,increased recovery and first vaccination coverage could effectively control the prevalence of measles.

关 键 词：麻疹传染病模型 基本再生数 一致持久性 偏秩相关系数 

分 类 号：O175.1[理学—数学]