Fair Allocation of Potential COVID-19 Vaccines Using an Optimization-Based Strategy

Abstract

The fair allocation of resources among multiple stakeholders in any area is a complex challenge for decision-making. This paper presents an optimization strategy for the allocation of COVID-19 vaccines, when they are available, through different fairness schemes (social welfare, Nash, Rawlsian justice, and social welfare II scheme). The applicability of the proposed model is illustrated using the case study of Mexico, including the states of the country as stakeholders. We involve several parameters to guide the allocation, such as the size, risk profiles, and fraction of vulnerable groups in the population. Furthermore, different scenarios of the availability of potential COVID-19 vaccines were evaluated. The social welfare approach is the most commonly used scheme for the allocation of resources. However, we demonstrate that this scheme yields non-unique or multiple solutions (through the social welfare II approach). These social welfare approaches provide inequalities in the allocations that become critical when resources are scarce. Specifically, the social welfare scheme favors large stakeholders (greater population) in all scenarios. We also observe how the complexity of the allocation increases with the higher availability of vaccines. Hence, it is relevant to consider allocation schemes to identify fair solutions.

A Survey on Optimization and Machine Learning-Based Fair Decision Making in Healthcare

“…For example, some vaccine allocation algorithms set overall social welfare as their objective function. This objective may exacerbate demographic disparities since underrepresented populations may have less access to vaccines 14 . Many optimization-based ambulance allocation models set the overall survival rate as the sole objective 15 .…”

“…To ensure fairness towards vulnerable populations, the objective function of an algorithm can be set to maximize the smallest number of allocated resources across all population subgroups. 14 Such fair objective ensures each subgroup receives necessary medical support.…”

Fair and efficient vaccine allocation: A generalized Gini index approach

“…(2016) or Enayati and Özaltın (2020). Again in the context of COVID‐19, Munguía‐López and Ponce‐Ortega (2021) compare different fairness‐related objectives, as the Rawlsian criterion or the Nash solution from cooperative game theory, to the utilitarian objective where the sum of all individual utilities is maximized. The model does not specify an epidemiological model for representing the infection dynamics.…”

Optimization Model for Planning the Logistical Response to COVID-19 Vaccination

“…Reducing crowding and vaccine allocation coverage also represents a particular challenge in this type of complex supply chain (Gessler et al 2021). Governments of countries that carried out vaccination processes very rapidly highlight the importance of implementing technology and data that prioritizes segments of the target population such as older adults (Cylus et al 2021;Green et al 2021) even though there was uncertainty in generalizing policies that might work for one country, but in another country the same result was not evident (Freed 2021;Marchildon 2021;Munguía et al 2021;Perry et al 2021). Therefore, it is necessary that the population be vaccinated with full and booster doses before the disease has a greater impact than we are already having.…”