Bayesian data assimilation for estimating instantaneous reproduction numbers during epidemics: Applications to COVID-19

Estimating the changes of epidemiological parameters, such as instantaneous reproduction number, Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to estimate the instantaneous reproduction number Rt during emerging epidemics, resulting in the state-of-the-art ‘DARt’ system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in describing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for making accurate and timely estimation for transmission dynamics based on reported data.Author summary: Monitoring the evolution of transmission dynamics is of great importance in response to the COVID-19 pandemic. The transmission dynamics of infectious disease is described by epidemiological models, but the model parameters may vary substantially due to differences in government intervention policies. Existing methods on estimating time-varying epidemiological parameters face problems such as lagging observation, averaging inference, and unreliable uncertainty. To address these issues, we have proposed the Bayesian data framework to provide a timely estimate with credibility interval. We have developed the ‘DARt’ system to monitor the instantaneous reproduction number Rt from daily COVID-19 reports. The accuracy and robustness of our system are validated in numerical simulations and in retrospective analyses of real-world scenarios. Our system provides the insights of impacts of different intervention polices and highlights the effectiveness of undergoing mass vaccination.