一类考虑筛查效应和隔离措施的传染病模型的稳定性分析  

STABILITY ANALYSIS OF A CLASS OF INFECTIOUS DISEASE MODELS CONSIDERING SCREENING EFFECTS AND QUARANTINE MEASURES

作　　者：宋家城 周宇生 SONG Jiacheng;ZHOU Yusheng(School of Mathematics and Statistics,Guizhou University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳贵州550025

出　　处：《井冈山大学学报(自然科学版)》2025年第1期1-7,共7页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(12162006);贵州省科技计划项目(黔科合基础-ZK[2023]一般037)。

摘　　要：本研究提出了一种新型传染病模型,该模型结合了筛查效应和隔离措施。首先,推导了该模型的正性和不变集。接着,应用下一代矩阵的方法计算模型基本再生数,对无病平衡点局部与全局的稳定性进行了分析。随后,研究了地方平衡点的全局稳定性,最后通过数值模拟验证了所得到理论的准确性。A novel infectious disease model that incorporates screening effects and quarantine measures is proposed in this paper.First,the positivity and invariant sets of the model was derived.Then,the next-generation matrix method was used to calculate the basic reproduction number,and analyze the local stability and global stability of the disease-free equilibrium.Subsequently,the global stability of the endemic equilibrium was investigated.Finally,the accuracy of the obtained theory was validated through numerical simulations.

关 键 词：筛查效应 隔离措施 基本再生数 全局稳定性 局部稳定性 

分 类 号：O175[理学—数学]