Bayesian Sequential Data Assimilation: Enhancing Forecasting in Epidemiology

Resumen:

We present a Bayesian sequential data assimilation framework for forecasting non-autonomous dynamical systems, with applications to epidemiology.

The method integrates a validated transmission model (formulated as a dynamical system) with an observation model (specified as a likelihood function). Forecasts are sequentially updated using a sliding window of data, where the posterior distribution from each step informs the prior for the next, allowing the model to dynamically adapt to changing epidemic conditions. This approach is particularly suited for epidemics, which are inherently non-autonomous due to factors like behavioral changes, viral evolution and climate, making long-term predictions unreliable.

We demonstrate that sequential data assimilation provides a robust alternative, balancing real-time data integration with mechanistic modeling. The framework's performance is illustrated using a SEIR-type model applied to COVID-19 data from several Mexican localities and to Monkeypox outbreak data.

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