# Vaccine Strategies: Follow the Math

A set of simple ideas that highlight business math principles that would speed up our vaccination process.  Here’s a link to a PDF version as well.

By Lauren and Philip Siegel

A much used saying during the pandemic has been “follow the science”. But when it comes to vaccine distribution we should “follow the math”. Many public health tools including disease testing and contact tracing are governed by mathematical and statistical principles.  If we had followed the math, we would have seen many of the avoidable and predictable failures in those efforts sooner in the pandemic. The new vaccines for Covid–19 are an amazing scientific achievement.  But the distribution of these various vaccines is a project for capacity planning, queuing theory and optimization algorithms—strategies which are underpinned by mathematics, not science.

Vaccine distribution to date has been focused on priority orders of who gets the vaccine shots. Other considerations have included logistical challenges such as storage, transportation, temperature regulation, and dose preparation and tracking.   However, the important aspect of urgency has been lost in the shuffle. How do we get everyone vaccinated sooner rather than later to get societal immunity for everyone? We must pursue speed, minimization of wait times, and waste and error reduction wherever we can.

Here are 10 practical applications of math concepts, that we see used in everyday life, that can benefit the speed and accuracy of our vaccination process:

1. Optimize priority groupings to reduce time delays. We see this when airlines work to load a plane efficiently while still offering priority to passengers based on accommodation needs or customer loyalty. Recall how slowly boarding proceeds when groups are too big and disorganized or too small with announcements and wait time. We need to ensure the groups identified for vaccination priority aren’t so large it’s a free for all but aren’t so small that the process is in a seemingly endless slow down.
2. Continue to the next priority group before the preceding group ends to eliminate time gaps. Think Southwest airlines; if you are in group A1-30 and you aren’t ready to board they will still board group A31-60 and you should slide into that group without being offended. It keeps the process moving and your opportunity doesn’t expire even though you allowed others to move ahead while buying your sandwich for the flight.
3. Pursue strategies that eliminate wasting time slots. Think of a sold-out concert. Often people without tickets wait outside to get in because some percentage of the ticket holders do not show. We shouldn’t waste any percentage of vaccines just like the concert venue shouldn’t waste any seats that could be used by fans. The ticket is worth nothing after the concert; the time slot is worth nothing after it expires.
4. Run at least part of the vaccine “machine” 24/7. Gold mines run 24/7 because the cost of shutting down and starting up far outweighs the cost of maintaining operations through the night. It’s true with vaccination as well.   A constant flow of people means that vaccine won’t spoil overnight, we can increase access for people who might have work commitments or other difficulties with day-time appointments, and provide an alternative for high risk individuals who prefer visiting a vaccine site when its other-wise closed to the public.  The number of people vaccinated per site per day could dramatically increase.
5. Reduce variety and thus complexity. We can improve out-of-stock efficiency with fewer types of vaccines at each location.  In vending machines, there might be 15 kinds of chips, 10 candy bars and 5 snack cakes.  The machine needs constant restocking.  If the machine only holds two types of each snack, there will be more of each on hand, less need to restock, still some protection from running out of both types at the same time, and a much increased likelihood that you can get your same snack the second time you visit the machine.
6. Reduce variety to match onsite resources. Sandwich shops have refrigerators, pizzerias have a pizza oven.  Not every location needs every vaccine type or every kind of storage capability.  Above, reducing variety avoided out of stock. In this case we reduce variety to make sure each location has doses it is best equipped to handle and can develop expertise in staff which increases speed and eliminates mistakes.
7. Serve household clusters. Vaccinate households together after the first priority individual groups are offered vaccines.  If you are vaccinated, and any housemate is not, the household is less likely to go to a restaurant, visit the gym, or otherwise participate in the retail economy. Protecting whole households will get the economy moving sooner.
8. Hold less inventory. Reduce duplicate holding of safety stocks and second doses. The federal government is saving 50% plus 500,000 doses. Many vaccination locations are also saving second doses. We have safety stock on top of safety stock and less vaccines available to put in arms. Let’s use well known inventory math models to get the right amount of safety stock in the system.
9. Go mobile to increase access. Some of the vaccines will travel well in a refrigerated truck. We have mobile units for food and supply distribution to communities in need, and for testing; provide some vaccine this way to speed up the process.
10. Focus on the most important measure of distribution performance to track our progress. That is the percentage of vaccine doses produced that are in people’s arms. It is currently around 20%. It’s early, but we must do better.

Practical math, business math, and common sense can help guide us through the vaccination process if we are thoughtful, logical and proactive.   The basic things we all do in everyday life like the ways we board an airplane, fill a concert venue, stock a vending machine, gain efficiency and accuracy with focus and experience, and reduce wait times and complexity can help us get this vaccination endeavor done faster and with fewer errors. In summary, now is the time to follow the math.

Lauren and Philip Siegel are the co-founders of MathHappens Foundation, a non-profit focused on public math literacy. Lauren has given several seminars during the pandemic on the math and statistics behind pooled sample testing. Phil is a co-founder of Private Equity firm Tritium Partners and a Senior Advisor to the Covid-19 Global Response Centre at the Boston Consulting Group where he has co-authored several articles on response to the pandemic.

Update Jan 10:  Are we using the right experts to lead vaccine distribution?  See the follow up in this blog post.  https://www.mathhappens.org/vaccine-strategy-ii-we-arent-using-the-right-experts/

Update Jan 12:  US Vaccine Policy Changed and HHS remarks by Dr. Azar referenced airline boarding processes which are featured in two of these recommendations.

Update Jan 15: President – Elect Biden announces intention to increase number of sites, increase groups and add mobile delivery

Update Jan 17:  Pretty cool- We saw Anthony Fauci also use the airline metaphor (strategy #2) on Meet the Press today while discussing vaccine priority groups.   See that Video Here: https://drive.google.com/file/d/1AKlN5YmzoIWPhx10eu_D5wwB0PGOoyLc/view?usp=sharing

Update Jan 18: COVID-19 vaccine rollout hasn’t worked, but change is coming, vaccine panel predicts.  The panel made recommendations to apply strategies from Disney, banks and airlines.. “We spent so much time on science and manufacturing and politics and we completely dropped the ball on logistics,”..

Update Jan 19:  Washington state governor announces more operations initiatives including partnerships with Starbuck and Microsoft:  “Now, we are not a health care company,” Starbucks President and CEO Kevin Johnson said during the news conference. “But Starbucks does operate 33,000 stores at scale, serving 100 million customers a week and we have a world class team of human-centered design engineers who are working under the direction of the state and health care providers … to help support the creation of vaccination centers that can scale and … amplify the comfort, care and safety of every person who gets vaccinated.”

Microsoft President Brad Smith said they will provide technology expertise, adding he has “confidence that we can bring vaccines to everyone faster because of this initiative.”