  The role of epidemiological models is crucial for informing public health
officials during a public health emergency, such as the COVID-19 pandemic.
However, traditional epidemiological models fail to capture the time-varying
effects of mitigation strategies and do not account for under-reporting of
active cases, thus introducing bias in the estimation of model parameters. To
infer more accurate parameter estimates and to reduce the uncertainty of these
estimates, we extend the SIR and SEIR epidemiological models with two
time-varying parameters that capture the transmission rate and the rate at
which active cases are reported to health officials. Using two real data sets
of COVID-19 cases, we perform Bayesian inference via our SIR and SEIR models
with time-varying transmission and reporting rates and via their standard
counterparts with constant rates; our approach provides parameter estimates
with more realistic interpretation, and one-week ahead predictions with reduced
uncertainty. Furthermore, we find consistent under-reporting in the number of
active cases in the data that we consider, suggesting that the initial phase of
the pandemic was more widespread than previously reported.
