Modelling the COVID-19 infection trajectory: A piecewise linear quantile trend model*

Feiyu Jiang, Zifeng Zhao, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by COVID-19 infection curves) and automatically delivers both point and interval forecasts with minimal assumptions. Building on a self-normalized (SN) test statistic, this paper proposes a novel segmentation algorithm for multiple change-point estimation. Theoretical guarantees such as segmentation consistency are established under mild and verifiable assumptions. Using the proposed method, we analyse the COVID-19 infection curves in 35 major countries and discover patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. A simple change-adaptive two-stage forecasting scheme is further designed to generate short-term prediction of COVID-19 cumulative new cases and is shown to deliver accurate forecast valuable to public health decision-making.

Keywords

  • change-point detection
  • forecasting
  • quantile regression
  • self-normalization
  • time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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