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

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.