对具有和恢复率和奥恩斯坦-乌伦贝克过程的随机SIB霍乱模型的分析
Buyu Wen1, Bing Liu2, Qianqian Cui3
1School of Information Engineering, Liaodong University, Dandong 118003, Liaoning, China.
Mathematical biosciences and engineering : MBE
|July 28, 2023
概括
这项研究分析了一种随机霍乱模型,证明存在一种独特的全球解决方案. 它确定了静态分布的条件,并计算了通过模拟验证的概率密度函数.
科学领域:
- 数学流行病学数学流行病学
- 随机模型的建模
- 疾病动态 疾病动态
背景情况:
- 霍乱的传播动态很复杂,受到各种因素的影响.
- 与确定性模型相比,随机模型提供了更现实的疾病传播表征.
- 了解传染病的长期行为对于公共卫生干预至关重要.
研究的目的:
- 为了研究一种包含和恢复率的随机感受性-感染性-振动杆菌 (SIB) 霍乱模型.
- 分析拟议模型的全球解决方案的存在和独特性.
- 为了确定静态分布的条件并计算概率密度函数.
主要方法:
- 开发一个随机SIB霍乱模型,具有和恢复率和奥恩斯坦-乌伦贝克过程.
- 数学分析以证明全球解决方案的存在和独特性.
- 构建一个Lyapunov函数,以确定静止分布的标准.
- 对概率密度函数的分析计算.
主要成果:
- 对于任何初始条件来说,已被证明对随机SIB霍乱模型有一个独特的全球解决方案.
- 足够的标准来证明存在一个静态分布.
- 在静止条件下计算概率密度函数的表达式.
- 数字模拟证实了理论发现,并提供了特定的边际概率密度函数.
结论:
- 随机SIB霍乱模型为理解霍乱动态提供了一个强大的框架.
- 静止分布的衍生条件对于预测长期疾病患病率至关重要.
- 这项研究为霍乱流行病的概率行为提供了宝贵的见解.
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