Filtering and improved Uncertainty Quantification in the dynamic estimation of effective reproduction numbers

Area of Science:

• Epidemiology
• Biostatistics
• Mathematical Biology

Background:

• The effective reproduction number (R_t) is crucial for assessing infectious disease spread.
• Existing methods for estimating R_t often fail to adequately quantify uncertainty.
• Variability in contagion patterns highlights the need for more robust estimation techniques.

Purpose of the Study:

• To develop an improved Bayesian method for estimating the effective reproduction number (R_t).
• To enhance the uncertainty quantification in R_t estimation.
• To provide a reliable and accessible method for R_t estimation in disease surveillance and forecasting.

Main Methods:

• Elaboration on the Bayesian estimation of R_t, building upon the Poisson sampling model.
• Introduction of an autoregressive latent process to create a Dynamic Linear Model for log(R_t).
• Application of conjugate analysis for explicit and efficient Bayesian inference, employing a filtering approach.

Main Results:

• Demonstrated improved uncertainty quantification in the estimation of R_t.
• The proposed method offers a reliable approach for estimating disease transmissibility.
• Validation of the method using recent COVID-19 epidemic data from Mexico.

Conclusions:

• The developed Bayesian Dynamic Linear Model offers superior uncertainty quantification for R_t estimation.
• This method is reliable, accessible to non-experts, and suitable for integration into forecasting systems.
• The approach provides a valuable tool for understanding and managing infectious disease outbreaks, as exemplified by the COVID-19 pandemic in Mexico.