The world has marveled at the speed with which science took on and solved the task of creating effective vaccines for Covid-19. But another often-overlooked science — the engineering and management science of operations research — is now equally important for getting vaccines into the arms of Americans.
Every day of increased vaccine coverage gives SARS-CoV-2, the virus that causes Covid-19, less opportunity to evolve into an even more formidable foe. Winning this race against Covid-19 with maximal speed and efficiency requires a vaccination strategy that ensures that every available dose is used as soon as it becomes available for injection.
That may seem like an impossible goal, but it is attainable if vaccine distributors appreciate and act on three key insights from operations research about the national vaccination campaign:
- Optimize the right thing: Maximally protecting the U.S. from Covid-19 requires a national vaccination strategy that prioritizes both coverage and speed.
- Use the right metric: The goal of this national vaccination strategy should not be a target of a specified number of people vaccinated by a certain date, but rather maximizing the number of people who are vaccinated as soon as possible from today’s date. We call this maximizing the number of vaccinated person-days across a campaign. Failing to do that will increase the number of unvaccinated person-days, each of which gives the virus that caused Covid-19 more room to cause suffering and to potentially mutate.
- Scale up, everywhere: The best way to maximize vaccinated person-days in any system with limited supply and uncertain demand is to design and open vaccination centers that are as large as realistically feasible given local conditions. To be sure, reaching vaccine-hesitant and historically underserved communities may require local vaccine distribution points, like churches and pharmacies, but the same logic applies to them as well: the larger, the better.
Individually optimizing vaccine delivery at pharmacies, churches, doctor’s offices, sports stadiums, or even at the state level, will not benefit the country as a whole without a strategy that links these efforts to the right national goal. As one of us (J.A.M.) has taught generations of supply chain managers, operations research shows that “local optimization leads to global disharmony.”
Governors are citing as a measure of success the percentage of state-allocated vaccines administered. Logistics companies are touting the efficiency and speed with which finished vaccine is being transported from manufacturing facilities to distribution and dispensing sites, though not necessarily into people’s arms. While these achievements are laudable, they do not provide the best measure of national progress toward population protection.
If the national goal is 100 million doses in 100 days, it matters — greatly — whether those doses go into arms on day 1 or on day 100.
One prominent editorial, published as the vaccination campaign got underway in January, calculated the number of public health staff needed to accomplish this task by assuming that the optimal strategy was a uniform dispensing campaign of 1 million doses a day across the country. Such an approach may seem to make sense from a planning perspective, allowing local officials to develop dispensing plans that are familiar from other public health activities like routine vaccination campaigns.
But fighting a novel and evolving pandemic is anything but routine: the absolute priority is getting the largest number of individuals vaccinated as soon as vaccine is delivered, meaning the 1 million shots a day approach makes sense only if this is the exact delivery schedule of vaccines nationwide. Every person scheduled for a Covid-19 shot tomorrow when the dose intended for them is actually available today —say due to limited operating hours or staff availability at the vaccination center — adds an unvaccinated person-day to the national ledger.
This is why efforts to use local distribution sites, which may be essential for incremental success at reaching hard-to-vaccinate communities, need to be part of a larger unified strategy to leave no ready dose unused. Linking smaller local centers into tightly integrated networks that are capable of coordinating vaccine dispensing on a daily basis may meet this need. Creating more interactive and responsive — not to mention accessible and comprehensible — vaccination scheduling systems is essential to enabling such networks to match daily supply with demand.
We can’t overstate the importance of maximizing vaccinated person-days at each and every dispensing location across the nation. To understand why, consider the following example. Imagine that a local pharmacy receives 100 doses of a Covid-19 vaccine each week but, due to staffing limitations, can offer only 25 vaccinations a day Monday through Thursday. Under these conditions, the 100 people who got the vaccine yield 250 vaccinated person-days that week (25 from Monday who add 25 shots times four days, plus 25 from Tuesday who add 25 times three days, and so on).
In contrast, if this pharmacy were supported with extra staff and perhaps had extended hours to deliver all 100 shots on Monday, the result would be 400 vaccinated person-days (100 times four days), a 60% relative increase in population protection against infection despite giving out the same total number of vaccinations per week. Completing all the vaccinations on one day at that pharmacy instead of spreading them through the week may not sound like a big deal. But multiply this by the 60,000 pharmacies and countless community and church sites in the U.S., and you have a wholesale change in our ability to end Covid-19.
Using the metric of unvaccinated person-days to assess vaccination dispensing strategies at the local, regional, state, and federal levels will increase transparency about vaccine usage and identify important opportunities to change dispensing practices to hasten the end of the pandemic.
But how can we maximize vaccinated person-days? Insights from operations research, using the same supply-chain mathematics that make it possible to order one of millions of items online and instantaneously find out whether it can be delivered today, suggest when it comes to vaccination centers, bigger is always better, even if smaller seems smarter.
Critical attention is now being paid to improving vaccine access in historically underserved and medically vulnerable populations. Outreach efforts here will likely require smaller, targeted, and possibly even mobile vaccination drives. But the incontrovertible math says that the path to increasing efficiency at vaccine dispensing sites, regardless of type or size, is the same: giving out more shots per day per site will minimize the number of unused doses per day, which will minimize the number of unvaccinated person-days and speed the nation towards more rapid population protection from Covid-19.
To test this idea, we considered a simulated 26-week vaccination campaign in a state with 1.3 million people using a vaccine that comes 100 doses to a box, like the Moderna vaccine. Vaccinating everyone in the state on day 1 would result in zero unvaccinated person-days over the 26-week campaign. Using nine large vaccination sites (averaging 200 shots per day) and four mass sites (averaging 2,000 shots per day) would lead to 24 million unvaccinated person-days by the end of the campaign. In contrast, using 181 simulated pharmacies and community centers (130 sites giving an average of 30 shots a day, 35 sites giving 100 shots a day, and 16 sites giving 150 shots a day) would result in 144 million unvaccinated person-days across the 26-week campaign, a more than six-fold difference in vaccination campaign efficacy.
While the specific simulation results vary with the details, the general finding — that larger sites achieve desired pandemic vaccination goals faster, especially when considering realistic logistics — is clear.
Federal, state and local public health officials on the front lines in the U.S. — and their counterparts worldwide — did not choose this battle. But now that they are in it, they need every advantage to win it. Operations research provides a framework that can help guide efficient progress toward population protection and can highlight potential inefficiencies in reaching that goal. It tells us, clearly and unequivocally, how to design operationally transparent systems that can get us quickest to herd immunity, including optimal strategies for vaccinating underserved and vulnerable populations.
Nathaniel Hupert is an associate professor and co-director of the Cornell Institute for Disease and Disaster Preparedness at Weill Cornell Medicine, Cornell University in New York City, and cofounder of the Oxford-based Covid-19 International Modeling Consortium John A. (“Jack”) Muckstadt is professor emeritus of operations research and information engineering at Cornell University and was formerly a member of the Board of Scientific Counselors at the U.S. Centers for Disease Control and Prevention. Michael G. Klein is assistant professor at the Lucas College and Graduate School of Business at San Jose State University, in San Jose, Calif.