A Scaled Poisson Bayesian Model for Viral Epidemic Monitoring

Monitoring an ongoing epidemic requires accurate, trustworthy and easy to use tools, capable of handling low quality data. Extending existing epidemiological models quantifying the propagation intensity via a time-varying reproduction number, this work proposes a scaled Poisson model, accounting for large intrinsic variability in infection counts. The associated scaled likelihood is plugged into a Bayesian model with a quasi-noninformative prior. A carefully designed Markov Chain Monte Carlo algorithm yields a point estimate and credibility intervals of the reproduction number. The accuracy and robustness to model misspecification and to scale parameter selection of the proposed estimator is demonstrated through intensive numerical experiments on COVID-19 case counts in different countries and during various phases of the pandemic.