Inference in Gaussian state-space models with mixed effects for multiple epidemic dynamics

TL;DR

This paper introduces a Gaussian state-space model with mixed effects to jointly estimate parameters of multiple epidemics, explicitly accounting for inter-epidemic variability using a novel inference method, improving accuracy over separate analyses.

Contribution

It extends existing models to incorporate mixed effects for multiple epidemics and develops a coupled SAEM and Kalman filtering inference method.

Findings

The method outperforms separate dataset processing in simulations.

Application to influenza data reveals variability between seasons.

Parameter estimates show significant differences in transmission and reporting.

Abstract

The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different periods. The resulting possible inter-epidemic variability is rarely explicitly considered. Here, we propose to tackle multiple epidemics through a unique model incorporating a stochastic representation for each epidemic and to jointly estimate its parameters from noisy and partial observations. By building on a previous work, a Gaussian state-space model is extended to a model with mixed effects on the parameters describing simultaneously several epidemics and their observation process. An appropriate inference method is developed, by coupling the SAEM algorithm with Kalman-type filtering. Its performances are investigated on SIR simulated data. Our method outperforms an inference method separately processing each dataset. An application to SEIR influenza outbreaks in France over several years using incidence data is also carried out, by proposing a new version of the filtering algorithm. Parameter estimations highlight a non-negligible variability between influenza seasons, both in transmission and case reporting. The main contribution of our study is to rigorously and explicitly account for the inter-epidemic variability between multiple outbreaks, both from the viewpoint of modeling and inference.