First or Second Doses First? Vaccine Allocation Under Limited Supply

Abstract

Many vaccines stimulate a relatively weak immune response when given as just one dose. However, there is a stronger immune response when a second dose is added. How to allocate limited two-dose vaccines, such as mRNA vaccines, between the first vs. second doses provoked a heated public debate during COVID-19 in January 2021. People who supported the "First Doses First" (FDF) policy believed that prioritizing first doses by delaying the second shot is a way to build some immunity among a larger population. Opponents of the FDF policy who advocate the "Second Doses First" (SDF) policy argued that giving priority to the second dose can lead to stronger immunity among those who receive both shots and decrease the risk of widespread disease transmission. In this paper, we study the optimal vaccine allocation between the first vs. second doses with a constant stream of vaccine supply by formulating it as an optimal control problem under disease transmission to minimize the total number of infections over a planning horizon. Specifically, we extend the SIR model to incorporate the role of vaccines by adding two compartments, i.e., people who have received one dose and those who have received two doses. With the delay between the first and second doses neglected, we demonstrate that the optimal vaccine allocation policy has a bang-bang structure: there exists a threshold on the one-dose vaccine efficacy that is higher than one-half of the two-dose vaccine efficacy, above (resp., below) which choosing the FDF (resp., SDF) policy is optimal. Using COVID-19 vaccination data, we calculate thresholds for different countries in January 2021 to recommend to governments whether to use the FDF or SDF policy. Lastly, we demonstrate that our model can be extended to account for boosters by studying how to allocate limited vaccines between the second and booster shots.

Note:
Funding Information: None.

Conflict of Interests: None.