当前位置: X-MOL 学术SIAM J. Appl. Dyn. Syst. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Analysis of Pandemic Closing-Reopening Cycles Using Rigorous Homotopy Continuation: A Case Study with Montreal COVID-19 Data
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2021-04-27 , DOI: 10.1137/20m1366125
Kevin E. M. Church

SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 745-783, January 2021.
Moving averages and other functional forecasting models are used to inform policy in pandemic response. In this paper, we analyze an infectious disease model in which the contact rate switches between two levels when the moving average of active cases crosses one of two thresholds. The switching mechanism naturally forces the existence of periodic orbits. In order to make unbiased comparisons between periodic orbits in this model and a traditional one where the contact rate switches based on more simplistic pointwise evaluations of active cases, we use a rigorous homotopy continuation method. We develop computer-assisted proofs that can validate the continuation and prove that the branch of periodic orbits has no folds and is isolated in the space of periodic solutions. This allows a direct, rigorous comparison between the geometric and quantitative properties of the cycles with a moving average threshold and a pointwise threshold. We demonstrate the effectiveness of the method on a sample problem modeled off of the COVID-19 pandemic in the city of Montreal.


中文翻译:

使用严格的同伦连续性分析大流行的关闭-重新打开周期:以蒙特利尔COVID-19数据为例

SIAM应用动力系统杂志,第20卷,第2期,第745-783页,2021年1月。
使用移动平均线和其他功能预测模型来为大流行应对中的政策提供信息。在本文中,我们分析了一种传染病模型,其中当活动病例的移动平均值超过两个阈值之一时,接触率在两个级别之间切换。切换机制自然会强制存在周期性轨道。为了在此模型的周期轨道和传统的接触率基于活动案例的更简单的逐点评估进行切换的传统轨道之间进行无偏比较,我们使用严格的同伦连续方法。我们开发了计算机辅助的证明,可以验证连续性,并证明周期轨道的分支没有折叠并且在周期解的空间中是孤立的。这样可以直接 使用移动平均阈值和逐点阈值对循环的几何和定量属性进行严格比较。我们在以蒙特利尔市COVID-19大流行为模型的样本问题上证明了该方法的有效性。
更新日期:2021-04-28
down
wechat
bug