结核病的碎形分数模型:存在和数值解决方案
Aziz Khan1, Kamal Shah1, Thabet Abdeljawad2
1Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia.
Scientific reports
|May 28, 2024
概括
这项研究使用了新的分数运算符来模拟结核病 (TB). 数学分析提供了有关结核病传播动态和疾病控制策略的见解.
科学领域:
- 数学生物学 数学生物学
- 流行病学 流行病学
- 分数微积分的计算.
背景情况:
- 结核病 (TB) 是一种由Mycobacterium TB引起的传染性空气传播疾病,主要影响肺部.
- 结核病通过感染者咳,打喷或说话时的呼吸道滴滴传播.
- 数学建模对于理解疾病动态和开发控制策略至关重要.
研究的目的:
- 开发和分析一个新的数学模型用于结核病的传播,使用一个分数的分数运算符.
- 调查拟议的结核病模型的解决方案的合理性,存在和局限性.
- 确定关键的流行病学参数,如平衡点和繁殖数.
主要方法:
- 制定一个五个部分的模型 (易受感染者,DS感染者,MDR感染者,隔离者,康复者).
- 微积分微积分计算的应用以建模TB动态.
- 对模型属性的分析,包括不变区域,正解和平衡点.
- 使用Adams-Bashforth-Moulton方法对解决方案的数值近似计算.
主要成果:
- 该研究确定了碎形分数结核病模型的解决方案的存在和独特性.
- 对不变区域和积极解决方案的分析确保了流行病学相关性.
- 生殖数量是为了评估疾病传播潜力而计算的.
- 数字模拟表明该模型能够捕捉TB传播动态.
结论:
- 碎形分数运算符为分析诸如结核病之类的复杂疾病动态提供了强大的工具.
- 该模型的分析为公共卫生干预和结核病控制提供了宝贵的见解.
- 进一步的研究可以探索不同的分数运营商,并纳入更复杂的流行病学因素.
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