Introduction to statistical inference for infectious diseases

Britton, Tom; Giardina, Federica

Journal de la société française de statistique, Tome 157 (2016) no. 1, pp. 53-70.

Dans cet article, nous introduisons le modèle stochastique épidémique général pour la propagation des maladies infectieuses. Nous décrivons ensuite des méthodes pour l’inférence des paramètres du modèle tels que le nombre de reproduction de base $R_0$ et la couverture vaccinale $v_c$ à partir de différents types de données épidémiques telles que des informations sur l’état final de l’épidémie et des données temporelles ou des observations pour une épidémie en cours. La prise en compte d’hétérogénéités individuelles et des contacts hétérogènes est discutée. Nous fournissons également une vue d’ensemble des méthodes statistiques pour l’estimation des paramètres d’autres modèles épidémiques stochastiques. Dans la dernière section nous décrivons le problème de la détection précoce d’épidémies dans la surveillance des maladies infectieuses et les modèles statistiques utilisés dans ce contexte.

In this paper, we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then, we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$ assuming different types of data from an outbreak such as final outbreak details and temporal data or observations from an ongoing outbreak. Both individual heterogeneities and heterogeneous mixing are discussed. We also provide an overview of statistical methods to perform parameter estimation for other stochastic epidemic models. In the last section we describe the problem of early outbreak detection in infectious disease surveillance and statistical models used for this purpose.

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