Analysis on a tuberculosis model with partial immunity in migration population
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摘要：
为预防肺结核疾病的传播,利用传染病建模思想,建立了一类迁移人群具有部分免疫的饱和发生率的肺结核模型.分析表明当移入潜伏者和染病者的比例均为0时模型才存在无病平衡点和基本再生数R0.利用Lyapunov函数方法证明了当R0≤1时,无病平衡点P0是全局渐近稳定的;当R0>0时,无病平衡点P^0是不稳定的.同时模型存在唯一的全局渐近稳定的地方病平衡点P^*.数值模拟结果与理论结果相一致,并使用模型对我国未来几年肺结核疫情进行了预测.
In order to prevent the spread of tuberculosis,a kind of tuberculosis model with partial immunity in migration population and saturation incidence with the modeling idea of infectious disease is established.The analysis shows that the model has a unique disease-free equilibrium point P0 and the basic reproductive number R0 when migration population entering the incubation and infection population respectively are both zero.When R0≤1 the globally asymptotic stability of disease-free equilibrium point P0 is proved by the functions methods and the disease-free equilibrium point P* is unstable. Meanwhile,the model has a unique endemic equilibrium point which is globally asymptotically stable.Numerical simulation results are in accordance with the corresponding theoretical results obtained in this paper,and the model is used to forecast the epidemic trend of tuberculosis of China in the future years.
作者：
方舒 张太雷 刘俊利
Fang Shu;Zhang Tailei;Liu Junli(School of Science,Chang'an University,Xi'an 710064,China;School of Science,Xi'an Polytechnic University,Xi'an 710048,China)
机构地区：
长安大学理学院 西安工程大学理学院
出处：
《betway官方app 学报：自然科学版》 CAS 北大核心 2020年第3期12-18,共7页
基金：
国家自然科学基金(11701041) 陕西省自然科学基础研究计划(2018JM1011).
关键词：
迁移人群 部分免疫 非线性发生率 全局渐近稳定
migration population partial immunity nonlinear incidence rate globally asymptotically stable
分类号：
O175.1 [理学—基础数学]
