Equivalence by coupling for heterogeneous SIS models*

Abstract

We consider the optimal allocation of (perfect) vaccine in an heterogeneous SIS model. Using a coupling approach, we explain how different models for the heterogeneity of the population lead to the same Pareto frontier in the cost/loss valuation of the vaccinations strategies. This covers in particular the elementary continuous representation of discrete models and the measure preserving transformation which appears in graphon theory.