翻转分叉分析和通过采取控制措施对霍乱病进行数学建模
Aqeel Ahmad1,2, Fakher Abbas1, Muhammad Farman3,4
1Department of Mathematics, Ghazi University D G Khan, Dera Ghazi Khan, 32200, Pakistan.
Scientific reports
|May 13, 2024
概括
本研究开发了一种分数顺序的数学模型,以评估早期霍乱诊断和治疗策略. 模拟显示了有或没有药物的干预措施对疾病传播和控制的影响.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 了解疾病动态对于有效的公共卫生干预至关重要.
- 霍乱仍然是一个重大的全球健康问题,需要改进诊断和治疗策略.
- 数学建模为分析疾病传播和评估控制措施提供了一个框架.
研究的目的:
- 开发和分析霍乱的分数顺序数学模型.
- 评估早期诊断和治疗方法的有效性,有或没有药物干预.
- 调查拟议的SEIBR模型的稳定性和分支.
主要方法:
- 使用ABC运算符制定一个分数顺序的SEIR数学模型.
- 模型的定性和定量分析,包括稳定性分析和翻转分叉验证.
- 使用下一代方法推导基本生殖数 ().
- 应用Atangana-Toufik方案用于数值解决方案和错误分析.
- 对模型参数的灵敏度分析,以了解它们对疾病动态的影响.
主要成果:
- 分析了SEIBR模型的稳定性和翻转分叉.
- 基本的生殖数 () 是为了量化传播率而衍生出来的.
- 敏感性分析确定了影响霍乱传播的关键参数.
- 模拟表明了早期检测和治疗策略的影响,包括药物干预和没有药物干预.
- 该模型提供了对不同补救方法下的疾病行为的洞察.
结论:
- 分数顺序建模提供了一个强大的方法来理解复杂的疾病动态,如霍乱.
- 早期诊断和有针对性的干预,包括非药物方法,可以显著影响霍乱的传播.
- 开发的数学框架有助于设计有效的传染病控制策略和公共卫生政策.
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