# Balancing the benefits of vaccination: An envy-free strategy

## TL;DR

This paper proposes a fair vaccination strategy using envy-free allocation to balance benefits across different age groups during limited vaccine availability.

## Contribution

The novelty lies in applying envy-freeness and Sperner’s Lemma to optimize vaccine distribution under ethical and epidemiological constraints.

## Key findings

- The strategy maintains balance in allocating vaccine doses across age groups.
- Applications with age distribution data show consistent optimization of direct and indirect benefits.
- The method aligns with SIR models to reflect real-world epidemiological dynamics.

## Abstract

The Covid-19 pandemic revealed the difficulties of vaccinating a population under the circumstances marked by urgency and limited availability of doses while balancing benefits associated with distinct guidelines satisfying specific ethical criteria. We offer a vaccination strategy that may be useful in this regard. It relies on the mathematical concept of envy-freeness. We consider finding balance by allocating the resource among individuals that seem heterogeneous concerning the direct and indirect benefits of vaccination, depending on age. The proposed strategy adapts a constructive approach in the literature based on Sperner’s Lemma to point out an approximate division of doses guaranteeing that both benefits are optimized each time a batch becomes available. Applications using data about population age distributions from diverse countries suggest that, among other features, this strategy maintains the desired balance, throughout the entire vaccination period. We discuss complementary aspects of the method in the context of epidemiological models of age-stratified Susceptible - Infected - Recovered (SIR) type.