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建模一种通用霍乱流行病模型的行为,并采用无症状措施进行早期检测

Ali Hasan Ali^1,2, Aqeel Ahmad^3,4, Fakher Abbas³

¹Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.

|March 31, 2025

概括

数学模型有助于理解霍乱的传播. 早期检测和强大的免疫系统导致有效的恢复,改善疾病控制策略.

科学领域:

流行病学流行病学
数学生物学数学生物学
传染病的动态传染病的动态.

背景情况:

数学建模对于理解疾病动态至关重要,特别是对于像霍乱这样的传染病.
了解霍乱的传播需要强大的模型配方来分析人口水平的传播.

研究的目的:

评估一种新的SEIRB (感受性-暴露-传染性-恢复-细菌) 霍乱模型的稳定性.
导出关键的流行病学参数,如生殖数量,以量化疾病传播率.
通过敏感性分析评估各种参数对疾病传播的影响.

主要方法:

在SEIRB模型上进行了定性和定量分析.
使用全球衍生和利普希茨标准来验证解决方案的存在,并分析模型组件.
利亚普诺夫的第一个导数用于全球稳定性分析.
用一个带有Mittag-Leffler内核的分数-分数运算符用于强大的解决方案导出.

主要成果:

该研究验证了线性增长的积极解决方案的存在,并分析了该模型的全球稳定性.
敏感性分析确定了影响霍乱传播的关键参数.
模拟显示了症状和无症状病例的影响以及早期检测的有效性.
具有强大的免疫系统的个体在早期诊断时表现出高效的恢复.

结论:

早期检测和干预对于管理霍乱疫情至关重要.
数学建模,特别是像分数-分数运算符这样的高级运算符,为疾病控制提供了宝贵的见解.
了解个人免疫反应以及流行病学因素可以提高霍乱管理策略.

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