The success of Operation Warp Speed in delivering two effective Covid-19 vaccines in record time has stoked public optimism for an end to the pandemic. The difficult science has seemingly been done, and what remains is a simple supply chain problem: how to get shots into arms in the fairest and quickest way.
Although the logistical challenges are certainly solvable, there’s a significant gap between a fairness-based public policy and the most effective solution for the nation as a whole. The goal of prioritizing health care and other first-line workers is politically noble, and thus easy to defend. Practically, however, a holistic view of our goals — public health, restoration of public service, and economic reopening — suggest that a more opportunistic delivery strategy may ultimately save more lives.
For the past 30-plus years, my professional focus has been in decision optimization, the discipline of applying mathematical methods to the solution of problems that arise in the public and private sectors. It is part of the field of operations research, an outgrowth of an effort to engage science to solve difficult tactical and operational issues during World War II.
While the mathematics involved can be quite complex, deciding on a set of objectives — determining what makes one approach better than another — is often the greatest challenge of decision optimization.
The national rollout of vaccines for Covid-19 has sparked much discussion about the best strategy for prioritizing vaccine recipients. As with any decision optimization issue, it is useful to break the problem down into three components: constraints, decision variables, and objectives.
The simplest element to nail down is probably constraints. The vaccine supply is currently limited, and only a certain number of individuals can be vaccinated each day — these are clearly limiting constraints.
Decision variables define the prioritization policy, such as who to vaccinate, when, and whether to offer first doses to all before offering second doses to some. These aren’t easy questions to answer, but they aren’t beyond our capabilities.
The most difficult component to grapple with by far is the objective, meaning how we will define success. As with most complex problems, there won’t be a single objective, but several.
Unfortunately, multiple objectives frequently work against each other, making the determination of appropriate objectives a political rather than a mathematical question. In the case of Covid-19 vaccine distribution, the best example of this is the objective of fairness, the concept that giving priority for getting vaccinated to an individual or group must provide net positive benefit to the population as a whole.
At the extreme, the fairest solution might be to wait until 330 million doses of Covid-19 vaccines are available, deliver them en masse to the entire U.S. population, and repeat the process when an additional 330 million doses become available. Putting aside the practical absurdity of such an approach, it clearly ignores two important goals: minimizing death and serious illness, and allowing public institutions such as schools and businesses to reopen as soon as possible.
As with any multi-objective problem, the challenge is balancing multiple goals — fairness, minimization of sickness and death, and restoring public services and commerce. The relative values of these objectives are difficult social, political, and economic questions, which are all necessary inputs for a decision optimization model. Determining the goals and their relative values makes it possible to develop an objective, mathematically justifiable distribution strategy.
In the early days of Covid-19 vaccine availability, vaccine shortages and surpluses both exist. While the overall demand for vaccine exceeds the number of doses available, the initial distribution strategy has often resulted in substantial number of doses remaining “on the shelf” in various locations. In a conventional business environment, this is expected, and sometimes even encouraged. Companies keep more inventory than they expect to sell because exact demand patterns are unpredictable. The cost of maintaining additional inventory is weighed against the potential of lost sales due to items being out of stock.
The situation with Covid19 vaccine is quite different. Taken as a whole, the vaccine is essentially a single product with a demand that currently exceeds its availability. As such, any doses that remain “in inventory” for longer than absolutely required represent an unnecessary threat to public health and economic recovery. So while delaying the vaccination of lower-priority individuals when doses sit idle may well contribute to the abstract goal of fairness, the greatest good is served by making vaccines available to the greatest number of individuals as quickly as possible.
The concept of fairness has played a large role in recent discussion regarding prioritization of people over 65 versus frontline workers. Clearly, individuals who are at greatest risk of infection should be given priority. But when we see significant numbers of front-line workers declining vaccination, we need to put aside abstract concerns over fairness to ensure that all doses are used rapidly.
The same holds true when there’s a mismatch between vaccines delivered and the people seeking vaccination. Say a primary clinic gets 1,000 doses, but there are few first responders and health care workers in the area who haven’t already been vaccinated. Instead of waiting for the okay to begin vaccinating the next tiers of people, or shipping back the doses to the distributor, it makes sense to use those doses for a wait list of individuals who are on call. Each dose delivered provides a benefit to the community. Each dose sitting in storage is a missed opportunity.
There is no question that maximizing the absolute number of doses must take precedence in distributing Covid-19 vaccines, along with prioritizing individuals and communities with the greatest need. These are consistent with the greater goal of efficiently reaching the entire population. Balancing these objectives is possible and will yield an outcome that best serves us all.
Martin Shell is founding director of Jumpstart Decision Sciences, an analytics consultancy based in greater Boston.