A multivariate statistical approach to predict COVID‐19 count data with epidemiological interpretation and uncertainty quantification

Abstract

For the analysis of COVID‐19 pandemic data, we propose Bayesian multinomial and Dirichlet‐multinomial autoregressive models for time‐series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number . All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet‐multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

Mathematical Modeling to Predict COVID-19 Infection and Vaccination Trends

“…The authors established the asymptotic properties of the estimators and performed simulation studies to certify the current procedure [ 35 ]. Bartolucci et al [ 36 ] and proposed multinomial Bayesian and Dirichlet auto-regressive models for series of time-dependent data points centered on counting patients exclusive and exhaustive categorized on predefined groups. Specifically, they were allocated based on the severity and required treatments in either regular wards or intensive care units, along with individuals that passed away and went through the disease.…”

Explicit modeling of antibody levels for infectious disease simulations in the context of SARS-CoV-2

“… 84 UpgUmibUsi-MultiBayes NO European Covid-19 Forecast Hub GitHub repository has not been updated since January 2021. In their paper 42 from August 2021, their Bayesian multinomial and Dirichlet-multinomial autoregressive models are proposed. Here, time series of numbers of patients in exclusive categories (for example, hospitalized in regular wards, in ICU units, deceased) are estimated.…”

Modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model

“…For an overview on recent advances in mathematical epidemiology, computational modelling, physics-based simulation, data science, and machine learning applied to the COVID-19 pandemic, we refer the reader to ( Kuhl, 2021 ). Even limiting the focus to the Italian context, several contributions have been proposed to accurately describe the spatio-temporal spreading of the epidemic in Italy ( Bertuzzo et al, 2020 ; Della Rossa et al, 2020 ; Gatto et al, 2020 ; Giordano et al, 2020 ; Loli Piccolomini & Zama, 2020 ), to forecast its future evolution ( Bartolucci et al, 2021 ; Farcomeni et al, 2021 ; Parolini et al, 2021a ) and to quantify (and possibly optimize) the effects of containing measures, including both pharmaceutical and non-pharmaceutical interventions (NPIs) ( Bonifazi et al, 2021 ; Giordano et al, 2021 ; Marziano et al, 2021 ).…”