Who Should Get Vaccinated? Individualized Allocation of Vaccines Over SIR Network

How to allocate vaccines over heterogeneous individuals is one of the important policy decisions in pandemic times. This paper develops a procedure to estimate an individualized vaccine allocation policy under limited supply, exploiting social network data containing individual demographic characteristics and health status. We model spillover effects of the vaccines based on a Heterogeneous-Interacted-SIR network model and estimate an individualized vaccine allocation policy by maximizing an estimated social welfare (public health) criterion incorporating the spillovers. While this optimization problem is generally an NP-hard integer optimization problem, we show that the SIR structure leads to a submodular objective function, and provide a computationally attractive greedy algorithm for approximating a solution that has theoretical performance guarantee. Moreover, we characterise a finite sample welfare regret bound and examine how its uniform convergence rate depends on the complexity and riskiness of social network. In the simulation, we illustrate the importance of considering spillovers by comparing our method with targeting without network information.