Exploiting deterministic algorithms to perform global sensitivity analysis of continuous-time Markov chain compartmental models with application to epidemiology

Henri Mermoz Kouye (1, 2, 3, 4) , Gildas Mazo (1, 2, 3) , Clémentine Prieur (4) , Elisabeta Vergu (1, 2, 3)

1 Université Paris-Saclay
2 INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
3 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]
4 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows

In this paper, we propose a generic approach to perform global sensitivity analysis (GSA) for compartmental models based on continuous-time Markov chains (CTMC). This approach enables a complete GSA for epidemic models, in which not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments) are quantified, but also those of intrinsic randomness and interactions between the two. The main step in our approach is to build a deterministic representation of the underlying continuous-time Markov chain by controlling the latent variables modeling intrinsic randomness. Then, model output can be written as a deterministic function of both uncertain parameters and controlled latent variables, so that it becomes possible to compute standard variance-based sensitivity indices, e.g. the so-called Sobol' indices. However, different simulation algorithms lead to different representations. We exhibit in this work three different representations for CTMC stochastic compartmental models and discuss the results obtained by implementing and comparing GSAs based on each of these representations on a SARS-CoV-2 epidemic model.

Mots clés: Stochastic compartmental models; continuous-time Markov chains; epidemic models; global sensitivity analysis; uncertainty quantification

Domaines: Méthodologie [stat.ME]; Modélisation et simulation

Henri Mermoz Kouye, Gildas Mazo, Clémentine Prieur, Elisabeta Vergu. Exploiting deterministic algorithms to perform global sensitivity analysis of continuous-time Markov chain compartmental models with application to epidemiology. 2024. ⟨hal-03565729v5⟩