具有年龄结构的伪狂犬病模型分析  

Analysis of stage-structured pseudorabies virus model

作　　者：刘文娟[1] 刘俊利[1] 万槟萁 LIU Wen-juan;LIU Jun-li;WAN Bin-qi(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,西安710048

出　　处：《哈尔滨商业大学学报（自然科学版）》2018年第6期736-740,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：中央高校教育教学改革专项经费资助(310612176301);陕西省自然科学基础研究计划资助项目(2014JQ1038);陕西省教育厅专项科研计划项目(16JK1331)

摘　　要：根据伪狂犬病在猪的各年龄段传播特性的不同,建立了具有成年和幼年两个年龄结构的伪狂犬病模型,并分析了其动力学行为,寻求决定疾病绝灭与否的基本再生数.当基本再生数小于或等于1时,模型仅有唯一的无病平衡点,当基本再生数大于1时,模型还存在唯一的正平衡点,利用线性化方法和Liapunov函数方法,讨论了两个平衡点的全局渐近稳定性.In this paper, according to propagation characteristics of pseudorabies in differentage groups of pigs, a pseudorabies model with two age structures of adult and juvenile wasformulated and analyzed, the basic reproduction number which determines the extinction andpersistence of the disease was obtained. When the basic reproduction number was less thanor equal to unity, there was only the disease-flee equilibrium, when the basic reproductionnumber was greater than unity, there was also one unique positive equilibrium, by the lin-earization and Liapunov function methods, the global stability of the disease-flee equilibriumand the positive equilibrium were discussed.

关 键 词：伪狂犬病 基本再生数 全局稳定性 LIAPUNOV函数 无病平衡点 正平衡点 年龄结构 

分 类 号：O175.1[理学—数学]