Equivalence by coupling for heterogeneous SIS models*

2025/09/05 by Delmas, Jean-François, Dronnier, Dylan, Zitt, Pierre-André
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.04898

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.

Citations

• Optimal Vaccination Strategies for an Heterogeneous SIS Model
• Vaccinating according to the maximal endemic equilibrium achieves herd immunity
• The effective reproduction number: convexity, concavity and invariance
• Graphons, cut norm and distance, couplings and rearrangements
• A deterministic model for gonorrhea in a nonhomogeneous population

Related

• Optimal Vaccination Strategies for an Heterogeneous SIS Model
• Topological Properties of the Effective Reproduction Number in an Heterogeneous SIS Model
• Targeted Vaccination Strategies for an Infinite-dimensional SIS Model
• Effective reproduction number: Convexity, invariance and cordons\n sanitaires
• Optimal vaccination: Various (counter) intuitive examples