Sparse HP filter: Finding kinks in the COVID-19 contact rate.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Time Series Analysis

Background:

• Accurate estimation of time-varying transmission dynamics is crucial for understanding and controlling infectious disease outbreaks.
• Existing methods for estimating contact rates in epidemiological models may lack the precision to capture real-world event-driven changes.
• The Susceptible-Infected-Recovered (SIR) model is a fundamental framework for studying disease spread.

Purpose of the Study:

• To develop and validate a novel filtering technique for estimating the time-varying contact rate within a SIR model for COVID-19.
• To compare the performance of the proposed method against existing trend filtering techniques.
• To establish a method for documenting and monitoring COVID-19 outbreaks using contact growth rates.

Main Methods:

• Development of the 'sparse HP filter,' a variant of the Hodrick-Prescott filter constrained by the number of potential kinks.
• Application of the sparse HP filter to daily COVID-19 case data (infected, recovered, deceased) from Canada, China, South Korea, the UK, and the US.
• Theoretical establishment of risk consistency for both the sparse HP filter and a comparative trend filter.

Main Results:

• The sparse HP filter successfully identified key events influencing COVID-19 transmission dynamics across five countries.
• The proposed filter produced fewer kinks than a standard trend filter while maintaining comparable data-fitting performance.
• Both the sparse HP filter and the comparative trend filter demonstrated theoretical risk consistency.

Conclusions:

• The sparse HP filter offers a robust method for estimating time-varying COVID-19 contact rates.
• The alignment of filter-identified kinks with real-world events validates its utility in outbreak analysis.
• Time-varying contact growth rates derived from this method can serve as a valuable tool for monitoring and documenting infectious disease outbreaks.