A zero-inflated endemic-epidemic model with an application to measles time series in Germany

TL;DR

This paper introduces a zero-inflated endemic-epidemic model tailored for infectious disease count data with excess zeros, enhancing the existing HHH framework to improve forecasting accuracy.

Contribution

The paper develops a multivariate zero-inflated endemic-epidemic model with random effects, extending HHH to better handle zero-inflated surveillance data.

Findings

Zero-inflation improves probabilistic forecasts for measles counts.

Model parameters estimated efficiently via penalized maximum likelihood.

Simulation confirms proper convergence and confidence interval coverage.

Abstract

Count data with excessive zeros are often encountered when modelling infectious disease occurrence. The degree of zero inflation can vary over time due to non-epidemic periods as well as by age group or region. The existing endemic-epidemic modelling framework (aka HHH) lacks a proper treatment for surveillance data with excessive zeros as it is limited to Poisson and negative binomial distributions. In this paper, we propose a multivariate zero-inflated endemic-epidemic model with random effects to extend HHH. Parameters of the new zero-inflation and the HHH part of the model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. A simulation study confirms proper convergence and coverage probabilities of confidence intervals. Applying the model to measles counts in the 16 German states, 2005--2018, shows that the added zero-inflation improves probabilistic forecasts.