Bayesian analysis of diffusion-driven multi-type epidemic models with application to COVID-19

Lampros Bouranis^(1,*), Nikolaos Demiris^1, Konstantinos Kalogeropoulos^2, Ioannis Ntzoufras^1

^1 Department of Statistics, Athens University of Economics and Business, Athens, Greece

^2 The London School of Economics and Political Science, London, United kingdom

^* Corresponding author ([email protected])

arXiv preprint: link

Summary

We consider a flexible Bayesian evidence synthesis approach to model the age-specific transmission dynamics of COVID-19 based on daily age-stratified mortality counts. The temporal evolution of transmission rates in populations containing multiple types of individual are reconstructed via an appropriate dimension-reduction formulation driven by independent diffusion processes assigned to the key epidemiological parameters. A suitably tailored Susceptible-Exposed-Infected-Removed (SEIR) compartmental model is used to capture the latent counts of infections and to account for fluctuations in transmission influenced by phenomena like public health interventions and changes in human behaviour. We analyze the outbreak of COVID-19 in Greece and Austria and validate the proposed model using the estimated counts of cumulative infections from a large-scale seroprevalence survey in England.

Installation

You can install the development version of the Bernadette R library from GitHub following these installation instructions.

Libraries and source files

The workflow is initialised by loading the required libraries and sourcing .R files via /R/1_Libraries.R.

Case Study: COVID-19 in Greece

• Single Brownian motion (SBM) model: see /Sampling/SingleBM_GR.R.

• Multi Brownian motion (MBM) model: see /Sampling/MultiBM_GR.R.

Case Study: COVID-19 in Austria

• Single Brownian motion (SBM) model: see /Sampling/SingleBM_AT.R.

• Multi Brownian motion (MBM) model: see /Sampling/MultiBM_AT.R.

Model validation: COVID-19 in England

See /Sampling/MultiBM_ENG.R.

Estimation of model information criteria

• Estimation of the Deviance information criterion (DIC) and the respective effective number of model parameters via /R/6_MCMC_diagnostics_SingleBM.R for the SBM model and via /R/6_MCMC_diagnostics_MultiBM.R for the MBM model.

• Estimation of the Pareto smoothed importance sampling Leave-One-Out information criterion and the respective effective number of model parameters via /R/5_LooIC.R.

Graphical outputs

Information about the non-pharmaceutical interventions implemented by European governments during the study period is available at /Data/.

The graphs available in the main text and the supplementary material can be reproduced by executing the code in /R/7_Model_Fit_graphs_generation.R.