稳定性分析和数字评估的COVID-19模型与疫苗接种
Mohammad Izadi1,2, Tayebeh Waezizadeh3,4
1Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. izadi@uk.ac.ir.
BMC medical research methodology
|April 27, 2024
概括
这项研究介绍了新型的新冠病毒19 (COVID-19) 传播的数学模型,其中包括疫苗接种的影响. 该模型以真实数据验证,使用准线性化和切比舍夫多项式方法准确预测疾病动态.
科学领域:
- 数学建模的数学建模
- 流行病学 流行病学
- 计算数学是指计算数学.
背景情况:
- 冠状病毒19 (COVID-19) 传播动态需要准确的预测模型.
- 了解疫苗接种的影响对于疾病控制至关重要.
- 非线性数学模型为研究疾病传播提供了一个框架.
研究的目的:
- 开发和分析一种用于COVID-19传播的新型非线性数学模型.
- 调查拟议模型的定性行为和稳定性.
- 用现实世界的数据和先进的数值方法预测COVID-19的动态.
主要方法:
- 一个新的八部分非线性数学模型,用于COVID-19的传播,包括疫苗接种.
- 定性行为分析:解决方案的边界性,基本复制数和平衡点稳定性.
- 使用克尔曼医学科学大学 (KUMC) 的真实数据进行参数估计.
- 使用组合光谱矩阵聚合方法的数值模拟.
- 非线性系统的线性化通过准线性化方法 (QLM).
- 应用转移的切比舍夫多项式的第二种 (SCPSK) 与域分割的长期解决方案.
- 对SCPSK基的统一收和上限估计的严格证明.
- 使用剩余错误函数验证准确性.
- 证明QLM-SCPSK算法的稳定性和指数趋同率.
主要成果:
- 拟议的数学模型有效地捕捉了COVID-19传播动态.
- 准线性化方法与SCPSK和域分割相结合,提供了准确和高效的长期预测.
- 数字结果证实了QLM-SCPSK技术的稳定性和高精度.
- 该方法表现出指数级的收率,表明高效率.
- 该研究成功预测了系统的动态行为.
结论:
- 开发的非线性数学模型,包括疫苗接种,是了解COVID-19传播的宝贵工具.
- QLM-SCPSK方法为解决这些复杂的流行病学模型提供了一个高度准确和高效的方法.
- 这种方法可以扩展到预测类似疾病动态在任意领域的行为.
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