Optimal allocation of limited vaccine to minimize the effective reproduction number

We examine the problem of allocating a limited supply of vaccine for controlling an infectious disease with the goal of minimizing the effective reproduction number R-e. We consider an SIR model with two interacting populations and develop an analytical expression that the optimal vaccine allocation must satisfy. With limited vaccine supplies, we find that an all-or-nothing approach is optimal. For certain special cases, we determine the conditions under which the optimal R-e is below 1. We present an example of vaccine allocation for COVID-19 and show that it is optimal to vaccinate younger individuals before older individuals to minimize R-e if less than 59% of the population can be vaccinated. The analytical conditions we develop provide a simple means of determining the optimal allocation of vaccine between two population groups to minimize R-e.

Automated summary

The study finds that in the case of limited vaccine supplies, an all-or-nothing approach is optimal. For certain situations, the conditions for the optimal effective reproduction number to be below 1 are determined. The optimal strategy for vaccine allocation depends on the vaccination rate and the age of the population.