具有冲动和马尔科夫切换的随机反应-扩散登革热模型的有限时间收缩稳定性
Wei You1, Jie Ren2, Qimin Zhang1
1School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China.
Mathematical biosciences and engineering : MBE
|November 3, 2023
概括
这项研究引入了一种登革热流行病模型,具有反应扩散,冲动和马尔科夫切换,以确保有限时间收缩稳定性 (FTCS). 结果揭示了FTCS的条件,突出了冲动和控制策略对登革热预防的影响.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 预防登革热需要在特定的时间范围内尽量减少感染.
- 有限时间收缩稳定性 (FTCS) 对于控制流行病传播至关重要.
- 现有的模型可能无法完全捕捉复杂的登革热动态.
研究的目的:
- 开发和分析一种新的登革热流行病模型,包括反应-扩散,冲动和马尔科夫切换.
- 为拟议的登革热模型的有限时间收缩稳定性 (FTCS) 建立足够的条件.
- 调查模型参数,控制策略和环境噪声对流行病稳定性的影响.
主要方法:
- 构建一个相当的系统来证明正确的解决方案的正确性.
- 应用平均脉冲间隔方法和有限脉冲间隔方法来推导FTCS条件.
- 数字模拟用于探索冲动,控制策略和噪声强度的影响.
主要成果:
- 我们成功地证明了登革热模型的积极解决方案的良好位置.
- 获得了足够的条件来保证登革热模型的有限时间收缩稳定性 (FTCS).
- 数字结果表明,冲动,控制策略和噪声强度显著影响FTCS.
结论:
- 提出的登革热模型具有反应-扩散,冲动和马尔科夫切换,为研究流行病控制提供了一个强大的框架.
- 对FTCS的衍生条件为设计有效的登革热预防和治疗策略提供了宝贵的见解.
- 冲动控制和噪声强度是影响登革热爆发的稳定性和可预测性的关键因素.
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