对于ADHD作为神经生物学和遗传疾病的分数顺序SIR模型
Zeeshan Afzal1, Mansoor Alshehri2,3
1Department of Mathematics, Lahore Garrison University, Lahore Campus, Lahore, Pakistan. zeeshanciitlhr@gmail.com.
Scientific reports
|July 2, 2025
概括
这项研究使用分数SIR模型建模了注意力缺陷多动症 (ADHD) 传播的模型. 优化的干预措施显著降低了ADHD的患病率,强调了早期诊断和有效治疗策略的必要性.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 计算动力学是一种计算动力学.
背景情况:
- 注意缺陷多动症 (ADHD) 呈现出复杂的传播动态.
- 分数顺序模型提供了增强的能力,以捕捉疾病进展中的长期依赖和记忆效应.
研究的目的:
- 开发和分析ADHD的分数顺序易受感染恢复 (SIR) 流行病学模型.
- 为了研究分数顺序参数对ADHD传播动态的影响.
- 评估ADHD管理的最佳控制策略的有效性.
主要方法:
- 使用卡普托分数导数开发一个分数顺序的SIR模型.
- 使用拉普拉斯余电序列 (LRPS) 和隆格-库塔第四顺序 (RK4) 方法进行数值模拟.
- 稳定性分析,灵敏度分析,并整合最佳控制理论.
主要成果:
- 分数级参数α影响疾病传播和恢复率;较高的α加速过渡.
- 基本的复制数[公式:见文本]决定了ADHD的持续性或根除.
- 优化的干预措施显然可以降低ADHD患病率和相关成本,RK4比LRPS更准确.
结论:
- 分数顺序建模为ADHD传播动态提供了宝贵的见解.
- 早期诊断,有效治疗和及时干预对于控制ADHD至关重要.
- 这项研究强调了数学建模和最佳控制在ADHD公共卫生政策规划中的潜力.
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