发表机构
Institute of Mathematical Sciences, University of the Philippines Los Baños（菲律宾洛斯巴尼奥斯大学数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出最小保峰复杂度（MPPC）框架，证明低维时变SIR模型能以适度动态复杂度再现多重流行波，并区分可表示性、最小复杂度、机制可识别性与预测有效性四个问题。
AI 中文摘要
多重流行波常被视为简单房室模型在结构上不充分的证据。然而，关键问题不在于简单模型能否再现多个峰值，而在于要保留观察到的流行波模式，最少需要多少时变结构，以及从这种表示中能合理地推断出什么。利用易感-感染-移除（SIR）模型，我们开发了一个保峰动态简约框架，将动力系统、反问题、统计推断和传染病建模联系起来。我们建立了时变传播下精确多波可表示性，刻画了流行峰值和复发的条件，并展示了仅基于发病率的时变传播率和移除率的不可识别性。我们的主要方法论贡献是最小保峰复杂度（MPPC）：一个正的时变传播函数的最小维度，其后验预测轨迹保留显著特征，包括峰值数量、时间、高度、谷底深度和整条曲线的一致性。我们使用峰值感知的近似贝叶斯计算来估计MPPC，并通过六个可复现的压力测试、菲律宾COVID-19报告病例的概念验证以及短期未来节点预测进行评估。在多样化的数据生成机制下，低维时变SIR模型能以适度的动态复杂度保留聚合流行波拓扑。然而，准确的轨迹压缩并不意味着恢复潜在机制或可靠的长期间反事实预测。因此，该框架区分了四个常被混淆的问题：可表示性、最小动态复杂度、机制可识别性和预测有效性，为复杂流行轨迹的简约建模提供了基础。
英文摘要
Multiple epidemic waves are often taken as evidence that simple compartmental models are structurally inadequate. Yet the key question is not whether a simple model can reproduce multiple peaks, but how much time-varying structure is minimally required to preserve observed epidemic-wave patterns and what can legitimately be inferred from such a representation. Using the susceptible-infectious-removed (SIR) model, we develop a framework for peak-preserving dynamic parsimony linking dynamical systems, inverse problems, statistical inference, and infectious-disease modeling. We establish exact multi-wave representability under time-varying transmission, characterize conditions for epidemic peaks and resurgence, and show the incidence-only non-identifiability of time-varying transmission and removal rates. Our main methodological contribution is minimal peak-preserving complexity (MPPC): the smallest dimension of a positive time-varying transmission function whose posterior-predictive trajectories preserve salient features, including peak count, timing, height, trough depth, and whole-curve agreement. We estimate MPPC using peak-aware approximate Bayesian computation and evaluate it through six reproducible stress tests, a Philippine COVID-19 reported-case proof of concept, and short-term future-knot projection. Across diverse data-generating mechanisms, low-dimensional time-varying SIR models can preserve aggregate epidemic-wave topology with modest dynamic complexity. However, accurate trajectory compression does not imply recovery of the underlying mechanism or reliable long-term counterfactual prediction. The framework therefore separates four often-conflated questions: representability, minimal dynamic complexity, mechanistic identifiability, and projection validity, providing a basis for parsimonious modeling of complex epidemic trajectories.
Comments53 pages, 8 figures
