Exploiting deterministic algorithms to perform global sensitivity analysis for 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 develop an approach of global sensitivity analysis for compartmental models based on continuous-time Markov chains. We propose to measure the sensitivity of quantities of interest by representing the Markov chain as a deterministic function of the uncertain parameters and a random variable with known distribution modeling intrinsic randomness. This representation is exact and does not rely on meta-modeling. An application to a SARS-CoV-2 epidemic model is included to illustrate the practical impact of our approach.

Mots clés: Compartmental models; continuous-time Markov chains; Gillespie algorithm; stochastic models; deterministic; global sensitivity analysis

Domaines: Statistiques [math.ST]

Henri Mermoz Kouye, Gildas Mazo, Clémentine Prieur, Elisabeta Vergu. Exploiting deterministic algorithms to perform global sensitivity analysis for continuous-time Markov chain compartmental models with application to epidemiology. 2022. ⟨hal-03565729v1⟩