Tag Archives: vaccination

An Engineering Perspective on Accelerating Vaccine Distribution

by Daniel Lenski


Key Points:

  • We can continuously prioritize vaccination of the most at-risk populations, and at the same time immediately offer remaining vaccine doses to lower-priority recipients.
  • We can plan for optimal inter-dose timing for 2-dose vaccines without holding back half the supply of those vaccines.
  • We can build a system to maintain consistent levels of availability and prioritization in all regions of the country for the months and years it will take to produce enough vaccines for near-universal immunization.
  • The field of industrial engineering offers well-studied and proven techniques to accomplish this.

The rapid design, development, and validation of multiple safe and highly effective vaccines for COVID-19, by scientists in the US and around the world, has been a stunning achievement. Our challenge has now pivoted to the task of inoculation against this pandemic disease.  How quickly can we produce and deliver sufficient vaccines to maximize protection of life and health, offering the hope of returning to more normal lives and economies? 

Vaccine manufacturers AztraZeneca, Pfizer, and Moderna expect to produce enough vaccine to inoculate only one-third of the world’s population in 2021,[1] and the US expects to receive enough to inoculate only 50 million Americans by the end of March.[2]  Production will certainly limit the rate at which we can achieve a high level of immunity in our populations, but the slow roll-out of vaccination in the USA underscores how much we must also optimize delivery.

As of January 11, 25.5 million doses have been provided by the US government, but only 9 million doses (35%) have been injected into the arms of willing and available recipients.[3] Vaccine stockpiles continue to grow, indicating clearly that delivery, not manufacture, is currently the bottleneck. Delays have been ascribed to insufficient guidance and funding for states and cities, limited and confusing schedules for vaccination appointments, and confusion about current prioritization schemes.  In an example of the floundering, one week ago New York governor Andrew Cuomo instituted harsh penalties both for providers who vaccinated ineligible recipients and for providers who allowed doses to expire or otherwise go to waste. These requirements of maximally efficient utilization and strict prioritization are both logical and important, but they are inevitably in tension with each other. In the absence of clear and simple guidance for how to resolve this conflict, it is unsurprising that these dual mandates have led to a very low pace of vaccination in New York.

How should a program of mass vaccination operate amid a deadly pandemic? What should its goal be, day in and day out, from individual vaccine providers to cities and states to the country as a whole? The goal, as I see it, is to get vaccine doses into every willing recipient[4] while consistently ensuring that the most vulnerable, at-risk groups have prioritized access, and at the same time dispensing vaccines as fast as they can be produced.  A vial of vaccine sitting in a freezer for days or weeks, awaiting the arrival of a high-priority recipient, does no good for anyone. In contrast, vaccinating any human right away will eliminate a vector for the spread of the disease, and move all of us one step closer to ending the pandemic.

The field of industrial engineering can provide us with crucial techniques and tools to sustain a balance between rapid delivery and prioritization for the months and years ahead.  From 2015-2020, I worked with semiconductor factories in the US and around the world providing advice and software.  Our services addressed problems such as: maximizing throughput by identifying and removing bottlenecks in multi-step processes; making efficient use of scarce resources, including time, labor, and raw materials; prioritizing completion of urgently-needed output; and adhering to constraints in the relative timing of critical steps to ensure quality and reliability.

The problems of vaccine delivery are strikingly similar: for maximum efficacy, the Pfizer vaccine’s two doses should be delivered 21-28 days apart[5]; it’s critical to vaccinate at-risk groups early on[6]; all currently approved vaccines require storage and transportation in expensive deep freezers, must be thawed in multi-dose batches, and expire wastefully if not dispensed quickly.

The tradeoff between prioritization and maximally efficient use of time and materials, illustrated by Governor Cuomo’s orders, is a glaringly obvious one to industrial engineers. If a strict sequential order is followed, the next recipient may not be available in time to use the next vaccine dose (leading to expiration and waste), while giving the vaccine on a purely first-come-first-served basis will maximize utilization but hinder rapid access for the highest-priority recipients. It is clear, however, that some members of high-priority vulnerable groups are either unable or hesitant to receive COVID-19 vaccination right now, while some members of low-priority populations are willing and eager to receive it immediately, but cannot due to lack of both eligibility and information about availability. Industrial engineering offers simple mechanisms to achieve an efficient and dynamic balance between these competing demands, such as by creating multiple priority queues at each vaccination provider and switching from higher- to lower-priority recipients immediately when the former are not present.

Experience from manufacturing can also clarify the problem of delivering second doses with optimal timing. Available quantities of Pfizer and Moderna vaccines in the USA were effectively halved by the initial plan to reserve a second dose of vaccine for each patient as soon as their first dose is administered. Some experts have recently suggested distributing all available 2-dose vaccines as first doses,[7] reasoning that rapidly dispensing single doses will save more lives than a predictable but slow pace of second doses, while virologists warn that the reduced efficacy of single doses could have grave consequences in the longer term, by allowing vaccine-resistant variants of the SARS-CoV-2 virus to evolve and spread. In fact, neither reserving second doses nor abandoning their correct timing is necessary. Because future delivery of vaccine supplies to the USA is relatively predictable (at least in terms of the lower bound), an optimal steady-state solution is for providers to limit the rate at which they dispense first doses to half the rate at which they expect to receive future doses, which will leave them with sufficient supplies to consistently vaccinate patients returning for their second doses during the optimal time window.[8]

Beyond the failure to balance between rapidly dispensing available vaccines and prioritizing them, along with a sub-optimal approach to reserving second doses, vaccine distribution in the USA appears gummed up by a pernicious combination of insufficient information about when and where COVID-19 vaccines are available, and complex paperwork and administrative requirements.[9]

If the incoming Biden administration were to ask me to design a plan for rapid distribution of COVID-19 vaccine, my proposal would include the following elements:

  • A national database to track vaccine inventory and rates of dispensation at the level of each provider, in near real-time. This will be crucial for determining the appropriate rates at which to resupply providers with more vaccine doses, so as to sustain and maintain inventory of vaccines across the country without developing geographical and temporal imbalances in inventory.
  • First-come-first-served vaccine dispensation at the level of individual providers, with the crucial addition of multiple queues for patient intake, so that the most vulnerable can always receive the vaccine before others, no matter when they decide to get it.
  • Training for all vaccination providers to implement the queuing system uniformly and consistently, along with minimal and consistent administrative requirements.
  • A website to track wait times for each queue, at each provider, in near real-time. The availability of wait times at nearby locations will likely be crucial to motivate a continuous high rate of vaccine delivery, by allowing many Americans to seek out the vaccine on short notice when wait times are short for their eligibility cohorts.

Ending the COVID-19 pandemic through mass vaccination will present an extraordinary range of challenges for physicians, public health officials, scientists, politicians, and society at large. The tools of industrial engineering certainly cannot help with many of these challenges; however, they can help us achieve and sustain one crucial goal at all scales: getting vaccine doses into every available, willing human being as fast as they can be produced, while continuously ensuring that the most vulnerable people have the most rapid and streamlined access to the vaccine. I know that President-Elect Joe Biden’s COVID-19 task force will include epidemiologists, physicians, and virologists.[10] I would encourage him also to appoint experts in industrial engineering and operations research, who can provide strategic guidance and tactical advice to speed up and smooth out nationwide vaccine distribution.


Appendix: A Specific Proposal

If the incoming Biden administration were to ask me to design a national vaccination program with the above goal of dispensing vaccines as rapidly as they are manufactured, while also continuously guaranteeing preferential access to prioritized populations, here’s what I’d propose. To simplify, I’ll assume that our present vaccine distribution bottlenecks are indeed overwhelmingly a “last mile” problem,[11] and that there are no major logistical impediments to reliably delivering vaccine supplies to providers anywhere in the country within timescales of 1-2 weeks.

First, establish a national database of vaccine-dispensing providers, and a mechanism to log daily inventory for each provider. Apportion newly-manufactured vaccine among the states and territories, and from there down to the level of individual providers. The first round of apportionment will take some guesswork; in the interests of speed and simplicity, my strong inclination would be to apportion the first round simply by population. Subsequent rounds should be adjusted up and down based on past demand and current inventory, in order to prevent geographical and temporal imbalances in inventory.

Second, each provider should dispense vaccines on a first-come-first-served basis, but with multiple priority queues with extremely simple selection criteria. Age is the simplest and most easily documented criterion, and so I have used only that below. Other criteria, such as health-risk factors, occupation, and race or ethnicity have been proposed. However, more complex prioritization runs the risk of slowing down the process for everyone[12], by turning “eligibility determination” into the rate-limiting step. Something like the following:

  • Monday-Wednesday: 6 queues. One for recipients over 80 years age, one for 70+, one for 60+, one for 50+, one for 40+, and one for everyone else.
  • Thursday: 5 queues. 80+, 70+, 60+, 50+, everyone else.
  • Friday: 4 queues. 80+, 70+, 60+, everyone else.
  • Saturday: 3 queues. 80+, 70+, everyone else
  • Sunday: 2 queues. 80+, everyone else.

These queues should literally be lines that people who want the vaccine wait in, clearly marked according to the age criteria. During operating hours, patients should be free to join the appropriate queue at any time. Providers should accept and vaccinate all available patients from higher-priority queues before accepting any from lower-priority queues, but should immediately switch over to lower-priority queues if a higher-priority queue is empty. Example: it’s Tuesday, and there are 10 people in the 80+ queue, 30 in the 70+ queue, and 100 in the everyone-else queue. Providers should vaccinate all of the 80+ patients, then immediately start vaccinating all of the 70+ patients, then immediately start vaccinating “everyone else.” If two more 80+ patients arrive after that initial queue has emptied, they would be accepted and vaccinated immediately. Available vaccine doses should be logged daily to the national database. Acceptance of patients from each queue should be logged in real-time so that it’s possible to publish intake rates in real-time for each and every provider.[13]

This scheme is intended to achieve the following results:

  1. No matter when a higher-priority person decides to get vaccinated, they’ll be able to get it with less waiting than all lower-priority individuals.
  2. Lower-priority individuals will not have to wait to receive the vaccine unless higher-priority recipients are waiting for it right now.
  3. Wait times will be relatively measurable and predictable, encouraging people to drop in and get vaccinated when lines are short, and stay home when lines are long for their priority groups.
  4. Vaccine will be dispensed continuously during the operating hours of each provider, ensuring minimal wasted or expiring doses. (Round-the-clock operation should be able to eliminate this entirely.)
  5. This weekly cycle is intended to prevent overcrowding of lower-priority patients if there’s sustained high demand from higher-priority groups. For example, given the above prioritization scheme, few 35 year-olds will want to line up on Tuesdays. However, those who do will probably have very good reasons to endure a long wait for the possibility of vaccination, e.g. an immune-compromised family member. By later in the weekly cycle, the wait times and intake rates for the younger age groups should be more predictable based on previous days.

[1]    https://www.nature.com/articles/d41586-020-03370-6

[2]    https://www.nytimes.com/live/2020/12/15/world/covid-19-coronavirus

[3]    https://www.nytimes.com/interactive/2020/us/covid-19-vaccine-doses.html

[4]    Appropriately spaced when 2 doses are required, and excepting those with contraindications.

[5]    https://www.biopharma-reporter.com/Article/2021/01/07/WHO-weighs-in-on-COVID-19-vaccine-second-dose-delay

[6]    Modeling from Israel indicates that vaccinating the most vulnerable 7.5% of the population would reduce overall death rates by 75%. https://twitter.com/dwallacewells/status/1340397154683269123

[7]    https://www.washingtonpost.com/opinions/2021/01/03/its-time-consider-delaying-second-dose-coronavirus-vaccine/

[8]    This problem gets more complex when the rate of future availability is unpredictable, or when there’s a large build-up of current inventory.

[9]    https://www.newsweek.com/senior-citizens-wanting-covid-vaccine-face-51-step-online-registration-process-1560622

[10] https://www.forbes.com/sites/judystone/2020/11/09/president-elect-biden-names-new-covid-19-task-force–whats-the-enthusiasm-about/?sh=723ade8a458f

[11]   https://www.reuters.com/article/health-coronavirus-vaccine-challenges-tr/analysis-covid-19-vaccines-raise-hope-but-the-last-mile-challenge-looms-idUSKBN28P124

[12] https://www.wsj.com/articles/vaccination-by-age-is-the-way-to-go-11610476439?mod=hp_opin_pos_3

[13]  Let’s say it’s Monday at 10 am. I should be able to pull up a page for the pharmacy at the corner of 10th & Elm street, and see that in the last hour:
80+ queue: 12 patients accepted, est. 2 currently in line (→ ~10 minute wait time)
everyone-else queue: 24 patients accepted, est. 20 currently in line (→ ~50 minute wait time)


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