Data assimilation for estimating time-varying reproduction numbers.

The time-varying basic reproduction number, R0(t), is a key epidemiological metric that quantifies the transmissibility of an infectious pathogen at time t. Accurate estimation and uncertainty quantification of R0(t) are crucial for understanding disease dynamics and informing public health decision-making. In this study, we evaluate six methods for estimating R0(t) using synthetic data generated from a stochastic Susceptible-Infected-Recovered (SIR) model with imposed changes to pathogen transmissibility and empirical COVID-19 case data. The methods include ensemble filter methods and inflation techniques, which are employed to mitigate covariance underestimation and filter divergence. For synthetic data, we compare the ensemble adjustment Kalman filter (EAKF) with no inflation, fixed inflation, and adaptive inflation, and the ensemble square root smoother (EnSRS) with adaptive inflation. For empirical data, we also compare with EpiEstim and EpiFilter. Our results demonstrate that the EAKF and EnSRS methods with adaptive inflation outperform other approaches in accurately estimating R0(t), particularly in scenarios with abrupt changes in transmission rates. The adaptive inflation techniques effectively address covariance underestimation and filter divergence, leading to more robust and reliable estimates of R0(t). These findings highlight the potential of adaptive inflation methods for improving the accuracy of time-varying parameter inference, contributing to more effective public health responses.