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

Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling