In this paper, we estimate the time-varying COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model Our measurement of the contact rate is constructed using data on actively infected, recovered and deceased cases We propose a new trend filtering method that is a variant of the Hodrick-Prescott (HP) filter, constrained by the number of possible kinks We term it the sparse HP filter and apply it to daily data from five countries: Canada, China, South Korea, the UK and the US Our new method yields the kinks that are well aligned with actual events in each country We find that the sparse HP filter provides a fewer kinks than the l1 trend filter, while both methods fitting data equally well Theoretically, we establish risk consistency of both the sparse HP and l1 trend filters Ultimately, we propose to use time-varying contact growth rates to document and monitor outbreaks of COVID-19