As observed in the case of COVID-19, effective vaccines for an emerging pandemic tend to be in limited supply initially and must be allocated strategically. The allocation of vaccines can be modeled as a discrete optimization problem that prior research has shown to be computationally difficult (i.e., NP-hard) to solve even approximately. Using a combination of theoretical and experimental results, we show that this hardness result may be circumvented. We present our results in the context of a metapopulation model, which views a population as composed of geographically dispersed heterogeneous subpopulations, with arbitrary travel patterns between them. In this setting, vaccine bundles are allocated at a subpopulation level, and so the vaccine allocation problem can be formulated as a problem of maximizing an integer lattice function subject to a budget constraint. We consider a variety of simple, well-known greedy algorithms for this problem and show the effectiveness of these algorithms for three problem instances at different scales: New Hampshire (10 counties, population 1.4 million), Iowa (99 counties, population 3.2 million), and Texas (254 counties, population 30.03 million). We provide a theoretical explanation for this effectiveness by showing that the approximation factor of these algorithms depends on the submodularity ratio of objective function g, a measure of how distant g is from being submodular.

The authors have declared no competing interest.

Funding for this research was provided as part of the CDC MInD Healthcare group under cooperative agreement U01CK000594 and associated Covid19 supplemental funding. Authors BA and SVP were awarded the grant and all 4 authors were supported by the grant. URL: https://www.cdc.gov/hai/research/MIND-Healthcare.html Additional funding was provided by NSF Award Number 1955939. Author SVP was awarded this grant and authors JK and SVP were supported by the grant.

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The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

This study will only use openly (to academics in one case) available data. The first source is a synthetic population derived from the 2010 United States Census we refer to as the "FRED" dataset (https://fred.publichealth.pitt.edu/syn_pops), which is freely available on the open internet. We also use a human mobility dataset we refer to as "SafeGraph" (https://www.safegraph.com/). Limited samples of this dataset are available, which we used in a county-aggregated form.

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Our experimental framework, all data processing and algorithm code, and output analysis are available on Zenodo at link http://doi.org/10.5281/zenodo.13882892

http://doi.org/10.5281/zenodo.13882892