Dylan Dronnier

• PostDoc Position at University of Neuchâtel

This present results lay the foundations for the study of the optimal allocation of vaccine in the simple epidemiological SIS model where one consider a very general heterogeneous population. In the present setting each individual has a type x belonging to a general space, and a vaccination strategy is a function $\eta$ where $\eta$(x) $\in$ [0, 1]...

We study in a general mathematical framework the optimal allocation of vaccine in an heterogeneous population. We cast the problem of optimal vaccination as a bi-objective minimization problem min(C($\eta$),L($\eta$)), where C and L stand respectively for the cost and the loss incurred when following the vaccination strategy $\eta$, where the funct...

Motivated by the question of optimal vaccine allocation strategies in heterogeneous population for epidemic models, we study various properties of the effective reproduction number . In the simplest case, given a fixed non-negative matrix K , this corresponds mathematically to the study of the spectral radius R_{e}(\eta) of the matrix product \math...

In previous articles, we formalized the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-dimensional metapopulation model. The aim of the current paper is to illustrate this theoretical framework with multiple examples where one can derive the analytic expression of the optimal strategies. We discuss in particular the...

Motivated by the question of optimal vaccine allocation strategies in heterogeneous population for epidemic models, we study various properties of the \emph{effective reproduction number}. In the simplest case, given a fixed, non-negative matrix $K$, this corresponds mathematically to the study of the spectral radius $R_e(\eta)$ of the matrix produ...

We consider the simple epidemiological SIS model for a general heterogeneous population introduced by Lajmanovich and Yorke (1976) in finite dimension, and its infinite dimensional generalization we introduced in previous works. In this model the basic reproducing number $R_0$ is given by the spectral radius of an integral operator. If $R_0>1$, the...

We consider the bi-objective problem of allocating doses of a (perfect) vaccine to an infinite-dimensional metapopulation in order to minimize simultaneously the vaccination cost and the effective reproduction number $R_e$, which is defined as the spectral radius of the effective next-generation operator. In this general framework, we prove that a...

In this article, we introduce an infinite-dimensional deterministic metapopulation SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We identify the basic reproduction number R0 which determines whether there exists a stable endemic...

In previous articles, we formalized the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-dimensional metapopulation model. The aim of the current paper is to illustrate this theoretical framework with multiple examples where one can derive the analytic expression of the optimal strategies. We discuss in particular the...

This thesis is motivated by the mathematical modelling of heterogeneity in human contacts and the consequences on the dynamic and the control of contagious diseases.In the first part of the thesis, we introduce and study an infinite-dimensional deterministic SIS (Susceptible/Infected/Susceptible) model which takes into account the heterogeneity of...

We consider the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-metapopulation model (including SIS, SIR, SEIR,. . .), when the loss function is given by the effective reproduction number Re, which is defined as the spectral radius of the effective next generation matrix (in finite dimension) or more generally of the...

We formalize and study the problem of optimal allocation strategies for a (perfect) vaccine in the infinite-dimensional SIS model. The question may be viewed as a bi-objective minimization problem, where one tries to minimize simultaneously the cost of the vaccination, and a loss that may be either the effective reproduction number, or the proporti...

In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We identify the basic reproduction number $R_0$ which determines whether there exists a stable endemic steady stat...

In this work, we use an adjoint-weighted residuals method for the derivation of an a posteriori model and discretization error estimators in the approximation of solutions to hyperbolic systems with stiff relaxation source terms and multiscale relaxation rates. These systems are parts of a hierarchy of models where the solution reaches different eq...