Construction of semi-Markov genetic-space-time SEIR models and inference

Soubeyrand, Samuel

Journal de la société française de statistique, Tome 157 (2016) no. 1, pp. 129-152.

Identifier les évènements de transmission d’une maladie infectieuse dans une population hôte est essentiel pour comprendre son épidémiologie et améliorer les mesures de lutte contre la maladie. Les hôtes infectés proches spatialement et temporellement sont souvent supposés être liés, mais les données temporelles et spatiales seules sont généralement compatibles avec de nombreux scénarios de qui a infecté qui. Pour inférer de manière plus précise qui a infecté qui au cours d’une épidémie causée par un pathogène à évolution rapide, des données génomiques sur le pathogène ont été associées aux données spatiales et temporelles. Cependant, la manière d’associer ces données reste aujourd’hui un défit en terme de modélisation et de statistique.

Une des approches récemment développées est basée sur une extension des modèles stochastiques Susceptible-Exposé-Infectieux-Retiré (SEIR). Dans cet article, nous présentons cette extension qui associe (i) un modèle SEIR individu-centré, spatial et semi-markovien pour la dynamique spatio-temporelle du pathogène, et (ii) un modèle markovien d’évolution temporelle des séquences génétiques du pathogène. Le modèle résultant est un modèle à espace d’états incorporant des vecteurs latents de grande dimension. Ensuite, nous décrivons un nouvel algorithme permettant de mener une inférence bayésienne approchée des paramètres du modèle et des variables latentes. Enfin, la capacité de l’algorithme d’estimation à reconstruire les arbres de transmission (c-à-d qui a infecté qui) est évaluée avec une étude simulatoire. Nous nous intéressons tout particulièrement aux performances de la méthode d’inférence lorsque seulement une fraction des données génomiques sur le pathogène est observée.

Identifying transmission links of an infectious disease through a host population is critical to understanding its epidemiology and informing measures for its control. Infected hosts close together in their locations and timings are often thought to be linked, but timing and locations alone are usually consistent with many different scenarios of who infected whom. To infer more reliably who-transmitted-to-whom over the course of a disease outbreak caused by a fast-evolving pathogen, pathogen genomic data have been combined with spatial and temporal data. However, the manner to combine these data remains today a modeling and statistical challenge.

One of the approaches recently proposed is based on an extension of stochastic Susceptible-Exposed-Infectious-Removed (SEIR) models. In this article, we present this extension that combines (i) an individual-based, spatial, semi-Markov SEIR model for the spatio-temporal dynamics of the pathogen, and (ii) a Markovian evolutionary model for the temporal evolution of genetic sequences of the pathogen. The resulting model is a state-space model including latent vectors of high dimension. Then, we describe a new algorithm that allows an approximate Bayesian inference of model parameters and latent variables. Finally, the capacity of the estimation algorithm to reconstruct transmission trees (i.e. who infected whom) is assessed with a simulation study. We especially investigate how the inference method performs when only a fraction of pathogen genomic data is available.

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