对于一个具有一般分布式延迟的三维随机病毒感染模型的静止分布
Ying He1, Junlong Tao2, Bo Bi2
1School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China.
Mathematical biosciences and engineering : MBE
|December 5, 2023
概括
这项研究分析了一种随机病毒感染模型,证明存在一种独特的积极解决方案. 它还证明了在特定条件下的静止分布,突出了对疾病传播的随机效应.
科学领域:
- 数学建模的数学建模
- 流行病学 流行病学
- 随机过程是指随机的过程.
背景情况:
- 病毒感染带来了重大的公共卫生挑战.
- 了解疾病动态需要强大的数学模型.
- 随机模型捕捉了生物系统中固有的随机性.
研究的目的:
- 分析具有分布式延迟的随机病毒感染模型.
- 建立一个全球积极解决方案的存在和独特性.
- 调查静态分布的条件和随机性的影响.
主要方法:
- 模型转换的线性链技术.
- 连普诺夫函数用于稳定性分析.
- 数字模拟用于验证和影响评估.
主要成果:
- 对随机系统的全局正解的存在和独特性.
- 当随机复制数 ($R^s$) 大于0时,建立一个静态分布.
- 数值结果证实了分析结果,并说明了随机扰动对疾病传播动态的影响.
结论:
- 开发的随机模型为理解病毒感染动态提供了一个框架.
- 静态分布的存在表明,在某些条件下,疾病控制的可能性很大.
- 随机扰动在调节病毒传播模式方面发挥着至关重要的作用.
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