具有非线性状态依赖的冲动控制的SIR模型的非平滑动态
Chenxi Huang1, Qianqian Zhang1, Sanyi Tang1
1School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China.
Mathematical biosciences and engineering : MBE
|December 5, 2023
概括
本研究引入了一个非平滑的SIR模型来分析传染病控制,结合有限的资源和反策略. 研究证实了在特定条件下的无病周期溶液的存在和稳定性.
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:
- 易受感染复原 (SIR) 模型是评估传染病控制策略的基石.
- 实施隔离和疫苗接种等现实世界的干预措施需要先进的模型,这些模型可以考虑人口动态和资源限制.
研究的目的:
- 开发和分析一个非平滑的SIR模型,包括有限资源和依赖状态的冲动反控制的非线性术语.
- 调查周期溶液的存在,稳定性和分支,特别是无病周期溶液 (DFPS).
主要方法:
- 通过添加一个代表资源限制的非线性术语来修改经典的SIR模型.
- 纳入依赖于国家的冲动反控制,基于易受影响的人口规模和增长率.
- 应用分析方法,包括普恩卡雷地图分析和离散地图的分叉定理,以研究周期性解决方案.
主要成果:
- 在某些条件下,确定了无病周期溶液 (DFPS) 的存在和稳定性.
- 证明了非微不足道的第1级周期解的潜在存在.
- 确定了可能不存在非微不足道的k次序周期解的条件.
- 在关键参数方面分析了DFPS周围的跨临界分叉.
结论:
- 开发的非平滑的SIR模型为了解资源有限的传染病动态提供了更现实的框架.
- 该研究证实了DFPS的稳定性,表明可以实现有效的疾病控制.
- 这些发现为复杂的振荡行为和分叉提供了洞察力,这对于完善公共卫生干预至关重要.
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