# A smoothing and bootstrap-based framework for early outbreak detection

## TL;DR

This paper introduces a new method for detecting disease outbreaks by improving the accuracy of transmission estimates using calendar-aware smoothing and bootstrap techniques.

## Contribution

The novel framework combines calendar-aware smoothing with bootstrap inference to enhance outbreak detection using the effective reproduction number (Rt).

## Key findings

- Calendar-aware smoothing, especially with MAH, improves the stability of Rt estimates.
- The proposed method outperforms existing algorithms in timeliness while maintaining low false positive rates.
- Simulation studies confirm the method's robustness across varying data conditions.

## Abstract

Timely detection of infectious disease outbreaks is critical for effective public health response. The effective reproduction number (Rt) is a key metric that captures transmission dynamics and signals the potential onset of outbreaks when it rises above 1. However, day-of-the-week and public holiday effects, along with random fluctuations in reported cases, can distort Rt estimates and reduce their usefulness for real-time surveillance. In this study, we present an Rt-based outbreak detection framework that integrates calendar-aware smoothing with bootstrap inference to quantify the uncertainty of smoothed Rt estimates. Using daily COVID-19 case data from Singapore, we evaluate several smoothing approaches—including a working-day moving average (MAH) that adjusts for public holidays—and compare the performance of the proposed method with established outbreak detection algorithms such as Early Aberration Reporting System (EARS), Bayesian-based detection methods (EpiEstim) and logistic regression–based approaches. In our framework, calendar-aware smoothing is not a generic pre-processing choice but a necessary, model-agnostic step that produces Rt inputs with reduced calendar artefacts. This makes subsequent inference and testing on Rt both more stable and more interpretable. Our results show that smoothing, particularly with MAH, improves the stability of Rt estimates and enables more reliable outbreak detection. The proposed method consistently demonstrates superior timeliness across observed and simulated outbreaks, while maintaining desired false positive rates. Simulation studies further confirm its robustness under varying sample sizes and case volumes, highlighting advantages over other methods. In conclusion, the proposed method offers a simple, interpretable, and theoretically grounded framework for early outbreak detection. Its consistent performance across real and simulated data suggests it may be broadly applicable to other infectious diseases with similar transmission dynamics.