Targeted Vaccination Strategies for Infinite-Dimensional Compartmental Models

In classical homogeneous compartmental models, the critical proportion of the population needed to be immune to eradicate the disease is given by the formula: 1 - 1/R0, where R0 is the basic reproduction number. This so-called herd immunity threshold can be lower in heterogeneous models by targeting specific sub-groups of the population.In this talk, we formalize and study the problem of optimal allocation strategies for a (perfect) vaccine in infinite-dimensional compartmental models. 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. We prove the existence of Pareto optimal strategies, describe the corresponding Pareto frontier, and study its convexity and stability properties. We also show that vaccinating according to the profile of the endemic state is a critical allocation, in the sense that, if the initial reproduction number is larger than 1, then this vaccination strategy yields an effective reproduction number equal to 1.In the second part of of the talk, we illustrate the theoretical framework developed previously with many examples.