统计方法用于计算和参数估计的小部分SIRC模型与沙门氏菌感染
1Mathematics Department, Faculty of Science, Al-Baha University, Saudi Arabia.
Heliyon
|December 13, 2024
概括
本研究引入了部分SIRC模型,用于动物群中的沙门氏菌感染,并结合了随机性来进行现实的流行病分析. 米尔斯坦方法有效地解决了这个模型,有助于了解疾病的传播和控制.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 随机过程 随机过程
背景情况:
- 沙门氏菌感染对动物群体构成重大威胁.
- 分数计算和随机微分方程为模拟复杂的流行病动态提供了先进的工具.
- 现有的模型可能无法完全捕捉疾病传播中固有的随机性.
研究的目的:
- 分析小数顺序SIRC (易受感染-恢复-易受感染) 的沙门氏菌在动物群中的流行病模型.
- 将随机分数微分方程 (在卡普托意义上) 纳入,以解释随机波动.
- 开发和验证用于解决拟议的随机分数模型的数值方法.
主要方法:
- 对溶液性质 (阳性,边界性,非阴性) 的确定性对应物的分析.
- 关于分数随机解的存在和唯一性的证明.
- 基于切断的伊托-泰勒扩展的米尔斯坦方法的应用,用于数值模拟.
- 确定性系统的稳定性分析 (本地,全球,Hyers-Ulam) 和灵敏度分析.
主要成果:
- 已经证明了分数随机解的存在和独特性.
- 密尔斯坦方法证明了对随机分数SIRC模型的近似解决方案的效率.
- 通过图表和错误表可视化的数值实验,为模型行为和方法准确性提供了洞察力.
- 随机模型提供了对沙门氏菌传播动态的更现实的表示.
结论:
- 开发的随机分数SIRC模型为了解动物种群中的沙门氏菌流行病提供了一个强大的框架.
- 密尔斯坦数值方法对于模拟和分析这种随机分数流行病模型是有效的.
- 纳入随机性增强了流行病建模的现实性,有助于更好地评估控制策略和为预防疾病做出明智决策.
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