在可行的情况下,使用数学碎形-碎形模型来控制结核病的流行率,具有敏感性,稳定性和模拟性
Muhammad Farman1, Aamir Shehzad2, Kottakkaran Sooppy Nisar3
1Faculty of Arts and Sciences, Department of Mathematics, Near East University, Northern Cyprus, Turkey; Department of Computer Science and Mathematics, Lebanese American University, 1107-2020, Beirut, Lebanon.
Computers in biology and medicine
|June 20, 2024
概括
这项研究使用碎形-碎形方法模拟结核病 (TB) 动态,发现疫苗接种和减少接触显著降低了结核病的传播. 碎形-碎形模型为结核病流行病学和控制策略提供了卓越的见解.
科学领域:
- 数学建模的数学建模
- 流行病学 流行病学
- 分数微积分的微积分计算.
背景情况:
- 结核病 (TB) 仍然是一个重大的全球健康威胁,预计到2021年将有1060万例病例和160万例死亡.
- 耐多药结核病正在增加,这对当前的治疗策略构成了重大挑战.
- 结核病死亡率与COVID-19相比,突显了迫切需要采取有效的控制措施.
研究的目的:
- 调查疫苗接种对结核病动态的影响,使用一种新的六分区决定性模型.
- 采用带有功率定律内核的分数-分数运算符来分析TB传输.
- 评估控制策略的有效性,包括疫苗接种和减少接触.
主要方法:
- 为结核病开发一个六分区的分数-分数决定性模型.
- 对模型属性的分析,包括正边界解和不变区域.
- 评估基本的复制数和模型平衡.
- 敏感性分析的应用,以确定影响结核病动态的关键因素.
- 用固定点理论来证明解决方案的存在和独特性.
- 使用两步牛顿多项式技术来研究分数运算符的效应.
主要成果:
- 碎形-碎形模型在乌兰-海尔斯条件和一般化乌兰-海尔斯条件下表现出稳定性.
- 数字模拟表明,提高疫苗有效性和减少与感染者的接触可以显著降低结核病负担.
- 与普通整数顺序模型相比,分数-分数运算符表现出更好的记忆效应.
结论:
- 分数建模为结核病的复杂动态提供了宝贵的见解.
- 这种方法提高了对结核病流行病学的理解,并有助于制定有效的控制策略.
- 这项研究强调了碎形微积分在分析传染病动态方面的潜力.
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