On the parametrization of epidemiologic models -- lessons from modelling COVID-19 epidemic

TL;DR

This paper presents a Bayesian approach to parametrizing SIR-type epidemiologic models, accounting for data biases and time-dependent factors, demonstrated on COVID-19 data from Germany and Saxony.

Contribution

It introduces a principled, flexible method embedding model structure into a general IO-NLDS framework for improved parameter estimation and prediction in epidemiology.

Findings

Good prediction performance on German COVID-19 data

Ability to estimate effectiveness of interventions

Scenario analysis for future epidemic trajectories

Abstract

A plethora of prediction models of SARS-CoV-2 pandemic were proposed in the past. Prediction performances not only depend on the structure and features of the model, but also on its parametrization. Official databases are often biased due to lag in reporting of cases, changing testing policy or incompleteness of data. Moreover, model parametrization is time-dependent e.g. due to changing age-structures, new emerging virus variants, non-pharmaceutical interventions and ongoing vaccination programs. To cover these aspects, we develop a principled approach to parametrize SIR-type epidemiologic models of different complexities by embedding the model structure as a hidden layer into a general Input-Output Non-Linear Dynamical System (IO-NLDS). Non-explicitly modelled impacts on the system are imposed as inputs of the system. Observable data are coupled to hidden states of the model by appropriate data models considering possible biases of the data. We estimate model parameters including their time-dependence by a Bayesian knowledge synthesis process considering parameter ranges derived from external studies as prior information. We applied this approach on a SIR-type model and data of Germany and Saxony demonstrating good prediction performances. By our approach, we can estimate and compare for example the relative effectiveness of non-pharmaceutical interventions and can provide scenarios of the future course of the epidemic under specified conditions. Our method of parameter estimation can be translated to other data sets, i.e. other countries and other SIR-type models even for other disease contexts.