具有隐性感染的年龄结构传染病模型的稳定性分析

Stability Analysis of Age structured Infectious Disease Models with Covert Infection

SARS、艾滋病病毒、COVID-19和口蹄疫等疾病都具有隐性感染的特点,在建模时考虑隐性感染更加符合实际情况。此外,年龄是影响疾病传播中传染率和恢复率的因素,对一些与年龄相关的疾病,在模型中引入年龄结构是非常有必要的。建立了一个考虑隐性感染的年龄结构的易感者-潜伏者-显性/隐形感染者-移出者(SEIAR)模型。首先通过分析得到基本再生数的表达式,基于阈值理论研究了无病平衡点和地方病平衡点的存在性和稳定性。然后利用特征方程和特征线法,证明了当基本再生数R_(0)<1无病平衡点全局渐进稳定;当R_(0)>1存在唯一的地方性平衡点,满足一定的条件时,地方病平衡点局部渐进稳定。研究结果表明,应采取降低隐性感染者的密度、提高疫苗成功接种率等措施来预防传染病的暴发,从而有效控制疫情。

Diseases such as SARS,HIV,COVID- 19 and foot and mouth disease all have the characteristics of covert infection,it is more realistic to consider the cover tinfection in modeling.In addition,age is afactor affecting the transmission of diseases such as infection rate and recovery rate,and it is very necessary to introduce an age structure into the model for some age- related diseases.A SEIAR model considering the age structure of recessive infection was established.Firstly,the expression of the basic regeneration number is obtained by analysis,and the existence and stability of the disease-free equilibrium point and the endemic equilibrium point are studied based on the threshold theory.Then,using the eigenequation and the eigenline method,it is proved that when the basic reproduction number R_(0)<1 the disease-free equilibrium point is globally asymptotically stable;when R_(0)>1 it has aunique endemic equilibrium point and meets certain conditions,the endemic equilibrium point is locally asymptotically stable.The results show that measures such as reducing the density of recessive infections and increasing the successful vaccination rate should be taken to prevent the outbreak of infectious diseases,so as to effectively control the epidemic.