具有治疗和接种的SEIRS传染病模型的稳定性  

Stability in a SEIRS Epidemic Model with Treatment and Vaccination

作　　者：傅金波 FU Jin-bo(Minnan Science and Technology Institute,Quanzhou Fujian 362332 China)

机构地区：[1]闽南科技学院,福建泉州362332

出　　处：《生物数学学报》2020年第1期71-77,共7页Journal of Biomathematics

基　　金：福建省高等学校新世纪优秀人才支持计划(2018);泉州市科技计划项目(2018C094R);福建省2019省级线下一流本科课程(工程应用数学C)

摘　　要：根据传染病动力学原理,考虑染病者经治疗或自然恢复后均具有免疫力,建立了一类具有接种和治疗的SEIRS传染病模型.综合利用LaSalle不变集原理,Lyapunov函数,Routh-Hurwitz判据,微分方程轨道稳定和复合矩阵的相关理论,获得了该系统的无病平衡点和地方病平衡点全局渐近稳定的充分条件.研究结果表明:基本再生数是疾病消失和一致持续的阀值,当基本再生数小于等于1时,疾病逐渐绝灭;当基本再生数大于1时,疾病持续流行或成为一种地方病.同时采取接种和治疗措施,能够将疾病的传播和流行控制在一定范围内,甚至能够加快疾病的绝灭.In this paper,by using epidemic dynamic theory,considering the illness after treatment or natural recovery with immunity,a class of SEIRS epidemic model with treatment and vaccination is established.By using some methods,including LaSalle invariant set principle,Lyapunov function,Routh-Hurwitz bounded,the theory about asymptotically orbital in differential equations and compound matrix,some obtain the threshold conditions which guarantee the global asymptotic stable disease-free equilibrium and endemic equilibrium of the SEIRS epidemic model.The results show that:basic reproduction number is a threshold which disease disappeared and consistence,when the basic reproduction number is less than or equal to 1,the disease gradually disappeared;when the when the basic reproduction number is greater than 1,the infection persistent existence,the diseases continue to prevail and will become a local disease.Treatment and vaccination measures were taken at the same time,able to control the spread and prevalence of the disease within a certain range,can even accelerate the extinction of the disease.

关 键 词：SEIRS传染病模型 治疗措施 接种疫苗 全局渐近稳定性 

分 类 号：R51[医药卫生—内科学] O175[医药卫生—临床医学]