How Simple Models Can Reproduce Multiple Epidemic Waves: Peak Topology, Minimal Dynamic Complexity, and Inference for Time-Varying Transmission
Abstract
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.
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BibTeX
@misc{rabajante2026simple,
title = {{How Simple Models Can Reproduce Multiple Epidemic Waves: Peak Topology, Minimal Dynamic Complexity, and Inference for Time-Varying Transmission}},
author = {Jomar Fajardo Rabajante},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05556},
eprint = {2610.05556},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05556},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - How Simple Models Can Reproduce Multiple Epidemic Waves: Peak Topology, Minimal Dynamic Complexity, and Inference for Time-Varying Transmission
AU - Jomar Fajardo Rabajante
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05556
UR - https://arxiv.org/abs/2610.05556
AB - 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.
ER -