Numerical methods in the context of compartmental models in epidemiology - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue ESAIM: Proceedings and Surveys Année : 2015

Numerical methods in the context of compartmental models in epidemiology

Peter Kratz
  • Fonction : Auteur
Brice Samegni Kepgnou
  • Fonction : Auteur

Résumé

We consider compartmental models in epidemiology. For the study of the divergence of the stochastic model from its corresponding deterministic limit (i.e., the solution of an ODE) for long time horizon, a large deviations principle suggests a thorough numerical analysis of the two models. The aim of this paper is to present three such motivated numerical works. We first compute the solution of the ODE model by means of a non-standard finite difference scheme. Next we solve a constraint optimization problem via discrete-time dynamic programming: this enables us to compute the leading term in the large deviations principle of the time of extinction of a given disease. Finally, we apply the {\tau}-leaping algorithm to the stochastic model in order to simulate its solution efficiently. We illustrate these numerical methods by applying them to two examples.

Dates et versions

hal-01231867 , version 1 (21-11-2015)

Identifiants

Citer

Peter Kratz, Etienne Pardoux, Brice Samegni Kepgnou. Numerical methods in the context of compartmental models in epidemiology. ESAIM: Proceedings and Surveys, 2015, 48, pp.169-189. ⟨hal-01231867⟩
160 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More