Multi-event dynamic capture-recapture model for big data: Estimating undetected COVID-19 cases in British Columbia, Canada

The accurate quantification of the impact of COVID-19 pandemic on both public health and the economy is essential for informed policy-making. However, the true scope of the pandemic remains challenging to ascertain due to undetected cases, particularly when relying on reported cases, which rely heavily on test availability and strategies. To accurately quantify COVID-19 cases in British Columbia (BC), we develop a Susceptible-Infectious-Recovered multi-event capture-recapture (SIRMECR) model to capture the dynamics of COVID-19. Specifically, we present a time-varying Markov model to estimate the number of undetected COVID-19 cases in five Health Authority Regions in BC, Canada, during the year 2020. We utilize individual-level information available from Population Data BC database to estimate the case detection probability, infection probability, survival probability, and recovery probability by incorporating testing volumes as covariates that improve the estimate of our parameters. We develop a Markov chain Monte Carlo (MCMC) algorithm to estimate SIRMECR model parameters. However, analyzing this big COVID-19 data set prompts a discussion on the computational challenges encountered. Therefore, we developed divide-and-conquer strategies to address the challenges. Our application provides an estimate of the total COVID-19 burden in year 2020 and found the percentage of undetected varying from 77.4 % to 84.0 %. More specifically, we validate our results through a simulation study and N-mixture model for Northern Health Authority Region of BC.