Abstract
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 the spillover effects of vaccination 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 these 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 a theoretical performance guarantee. Moreover, we characterize a finite sample welfare regret bound and examine how its uniform convergence rate depends on the complexity and riskiness of the social network. In the simulation, we illustrate the importance of considering spillovers by comparing our method with targeting without network information.
Highlights
Allocation of a resource over individuals who interact within a social network is an important task in many fields, such as economics, medicine, education, and engineering (Lee et al (2020), Banerjee et al (2013), among others)
One of the important policy decisions of this sort in pandemic times is how to allocate vaccines over heterogeneous individuals to control the spread of disease and protect the lives of vulnerable
It is crucial for the vaccine allocation rule to take into account the spillover effect of cutting transmission of the disease
Summary
Allocation of a resource over individuals who interact within a social network is an important task in many fields, such as economics, medicine, education, and engineering (Lee et al (2020), Banerjee et al (2013), among others). To optimize the empirical welfare of allocation policies, one naive approach is to evaluate the value of empirical welfare exhaustively for all possible combinations of vaccine allocations over individuals We refer to this as the brute-force approach. A greedy optimization algorithm in the current setting is to sequentially allocate a vaccine to an individual in the network who is most influential for improving the social welfare. Relying on the seminal result in discrete convex analysis shown by Nemhauser et al (1978), we show that the greedy algorithm delivers an allocation policy at which the value of the objective function is worse than the optimum only up to a universal constant factor, independent of the spillovers, size, and density of the SIR networks.
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