Balancing the Benefits of Vaccination: an Envy-Free Strategy

TL;DR

This paper proposes an envy-free vaccination allocation strategy based on Sperner's Lemma, balancing direct and indirect benefits across age groups to optimize vaccine distribution during a pandemic.

Contribution

It introduces a novel envy-free allocation method for vaccines that adapts mathematical principles to ensure balanced benefits among heterogeneous populations.

Findings

Strategy maintains benefit balance throughout vaccination periods.

Application to diverse country data shows effective dose distribution.

Ensures ethical and efficient vaccine allocation.

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 (J.W. Wu, S.D. John, E.Y. Adashi, Allocating Vaccines in the Pandemic: The Ethical Dimension, The Am. J. of Medicine V.33(11): 1241 - 1242 (2020)). 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 to be 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.