在凸发病率下,高度非线性皮肤莱什曼病流行病模型的定性行为与真实数据
Manal Alqhtani1, Khaled M Saad1, Rahat Zarin2
1Department of Mathematics, College of Sciences and Arts, Najran University, Najran, Kingdom of Saudi Arabia.
Mathematical biosciences and engineering : MBE
|March 8, 2024
概括
这项研究提出了一种新的数学模型,用于人类性皮肤莱什曼病传播动态. 该模型分析了疾病的传播,稳定性和关键参数,为疾病控制策略提供了洞察力.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 寄生虫学的寄生虫学
背景情况:
- 人类感染性皮肤莱什曼病构成了重大的公共卫生挑战.
- 了解传播动态对于有效的控制策略至关重要.
研究的目的:
- 开发和分析一种新的数学模型,用于人类性皮肤莱什曼病传播.
- 调查疾病传播动态的定性特征和稳定性.
主要方法:
- 使用下一代方法来确定基本复制数 ($R_0$).
- 应用了卡斯蒂略-查韦斯方法和利亚普诺夫理论,用于在无病和特有平衡状态下进行稳定性分析.
- 采用中心多元理论用于分叉分析和最小方程用于参数估计.
主要成果:
- 在无疾病 (R_0 < 1$) 和特有 (R_0 > 1$) 平衡点建立了局部和全球稳定的条件.
- 敏感性分析确定了影响疾病传播值的关键参数.
- 分叉分析揭示了潜在的疾病动态过渡.
结论:
- 开发的数学模型为理解人类性皮肤莱什曼病传播提供了一个强大的框架.
- 稳定性分析和参数洞察力为公共卫生干预和疾病管理提供了宝贵的信息.
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