具有暂时免疫和母体抗体保护的轮状病毒传播模型的分析  

Analysis of a Rotavirus Transmission Model With Temporary Immunity and Protection From Maternal Antibody

作　　者：卢琨 李建全 谭宏武 LU Kun;LI Jianquan;TAN Hongwu(Department of Mathematics,School of Arts and Sciences,Shaanxi University of Science&Technology,Xi’an 710021,P.R.China)

机构地区：[1]陕西科技大学文理学院数学系,西安710021

出　　处：《应用数学和力学》2020年第7期796-806,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11301314,11501443,11971281);陕西省榆林市科学技术研究与开发项目(2018⁃02⁃40)。

摘　　要：轮状病毒(RV)是目前世界范围之内导致儿童发生严重腹泻最主要的病原体.为研究轮状病毒的传播规律,基于被轮状病毒感染后的恢复者具有暂时免疫和母体抗体对新生儿具有保护的特点,建立了一类轮状病毒的传播感染模型,通过动力学分析得到了决定此传染病流行与否的基本再生数.在分析模型平衡点局部稳定性的基础上,通过构造Lyapunov函数证得当基本再生数不大于1时无病平衡点是全局稳定的,借助Fonda引理推得当基本再生数大于1时疾病持续生存于种群之中.Rotavirus is the leading cause of severe diarrhea in children worldwide. To study the spread of rotavirus, a rotavirus transmission model was proposed based on the characteristics of temporary immunity after infection and maternal antibody protecting the newborn. By means of dynamic analysis, the basic reproduction number deciding the persistence of the infection was obtained. Based on the local stability analysis of the feasible equilibria, it was proved that the disease-free equilibrium will be globally asymptotically stable if the basic reproduction number is no more than 1, through construction of appropriate Lyapunov functions. The disease will persist in the population if the basic reproduction number is more than 1 according to the Fonda lemma.

关 键 词：基本再生数 全局渐近稳定 持续生存 暂时免疫 轮状病毒 

分 类 号：O357.41[理学—流体力学]