冠状病毒疾病的部分流行病模型与疫苗接种和拥挤效应
Suhail Saleem1, Muhammad Rafiq2,3, Nauman Ahmed4,3
1Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan.
Scientific reports
|April 8, 2024
概括
这项研究介绍了COVID-19的分数顺序流行病模型,包括拥挤和接种疫苗. 该模型表明,控制策略有效地减少了感染,并提高了康复率.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 传染病建模传染病建模
背景情况:
- "COVID-19"疫情造成全球健康危机,传播受到人口密度和疫苗接种努力的重大影响.
- 了解冠状病毒传播的动态对于制定有效的控制策略至关重要.
研究的目的:
- 为COVID-19提出和分析一个分数顺序的易受感染,接种疫苗和康复 (SIVR) 流行病模型.
- 调查拥挤和疫苗接种对疾病传播动态的影响.
- 确保拟议的分数模型的数学有效性和稳定性.
主要方法:
- 开发一个分数顺序的SIVR模型,包括非线性发病率,拥挤和疫苗接种.
- 分析确定平衡点和应用固点理论存在和独特性.
- 使用雅科比矩阵,罗斯-赫尔维茨标准和利亚普诺夫函数进行稳定性分析.
- 使用下一代矩阵计算基本繁殖数.
- 为数值模拟开发和应用非标准有限差异 (NSFD) 方案.
主要成果:
- 该模型建立了无病和特有平衡点的局部和全球非对称稳定性的条件.
- 计算基本繁殖数 (R0),稳定性取决于其相对于1的值.
- 已经证明,NSFD方案能够保持模型解决方案的积极性和边界性质.
- 模拟表明,控制策略减少感染人口,增加康复人口.
- 分数顺序参数对病毒传播的影响以图形分析.
结论:
- 分数顺序SIVR模型为COVID-19传播动态提供了宝贵的见解,强调了拥挤和接种疫苗的重要性.
- 拟议的NSFD方案提供了一种可靠的数值方法来解决分数流行病模型.
- 控制策略有效地缓解了病毒的传播,并提高了康复率.
- 这项研究有助于理解和预测未来的病毒传播趋势.
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