| 宋家城,周宇生.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[J].井冈山大学自然版,2025,(1):1-7 |
| 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 |
| 投稿时间：2024-07-01 修订日期：2024-08-11 |
| DOI：10.3969/j.issn.1674-8085.2025.01.001 |
| 中文关键词: 筛查效应 隔离措施 基本再生数 全局稳定性 局部稳定性 |
| 英文关键词: screening effects quarantine measures basic reproduction number global stability local stability |
| 基金项目: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) |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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