# Endemic-epidemic models with discrete-time serial interval distributions for infectious disease prediction

## TL;DR

This paper introduces flexible weighting schemes based on discrete-time serial interval distributions into endemic-epidemic models, significantly improving infectious disease prediction accuracy in case studies of dengue and gastroenteritis.

## Contribution

It develops and compares parametric and nonparametric weighting methods within the endemic-epidemic framework for better disease spread modeling.

## Key findings

- Enhanced predictive performance over traditional models
- Parametric weighting schemes outperform nonparametric approaches
- Models show significant improvements in dengue and gastroenteritis case studies

## Abstract

Multivariate count time series models are an important tool for the analysis and prediction of infectious disease spread. We consider the endemic-epidemic framework, an autoregressive model class for infectious disease surveillance counts, and replace the default autoregression on counts from the previous time period with more flexible weighting schemes inspired by discrete-time serial interval distributions. We employ three different parametric formulations, each with an additional unknown weighting parameter estimated via a profile likelihood approach, and compare them to an unrestricted nonparametric approach. The new methods are illustrated in a univariate analysis of dengue fever incidence in San Juan, Puerto Rico, and a spatio-temporal study of viral gastroenteritis in the twelve districts of Berlin. We assess the predictive performance of the suggested models and several reference models at various forecast horizons. In both applications, the performance of the endemic-epidemic models is considerably improved by the proposed weighting schemes.