通过具有记忆效应的变量和常量顺序的碎形运算符对乙型肝炎传播动态的新调查
Sumit Gupta1, Pawan Kumar Jain2, Deepika Khandelwal3
1SKIT, JAIPUR.
Critical reviews in biomedical engineering
|March 3, 2026
概括
这项研究引入了一种具有记忆效应的小数级乙型肝炎病毒 (HBV) 模型. 降低分数顺序可以降低峰值病毒载量,但会延长感染持续时间,影响控制策略.
科学领域:
- 数学流行病学数学流行病学
- 分数微积分的微积分计算.
- 病毒学 病毒学
背景情况:
- 乙型肝炎病毒 (HBV) 构成了全球重大健康挑战.
- 现有的模型往往忽略了关键的记忆效应和疾病传播中的非局部相互作用.
- 了解慢性HBV动态需要复杂的数学框架.
研究的目的:
- 开发一种新的小数序乙型肝炎病毒 (HBV) 传播模型.
- 使用Caputo,Caputo-Fabrizio和Atangana-Baleanu-Caputo (ABC) 运算符结合记忆效应和非局部相互作用.
- 分析分数顺序对疾病动态和控制的影响.
主要方法:
- 使用卡普托,卡普托-法布里齐奥和ABC操作员开发一个小数级HBV模型.
- 使用固定点定理和Ulam-Hyers标准对解决方案存在,独特性,正性和稳定的数学分析.
- 使用Adams-Bashforth-Moulton和预测-校正方法进行数值模拟.
主要成果:
- 分数顺序显著影响HBV动态.
- 降低分数顺序 (α < 1) 会降低峰值病毒载量,特别是在早期干预的情况下.
- 减少的分数顺序延长了感染的持续时间,因为病毒衰变的速度较慢.
结论:
- 分数建模为慢性HBV动态提供了更深入的见解.
- 该研究强调了减少峰值病毒载量和感染持续时间之间的权衡.
- 这些发现为疫苗接种策略和长期HBV控制工作提供了信息.
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