by Melis Tekant
figures by Aparna Nathan 

The pandemic caused by the novel coronavirus Severe Acute Respiratory Syndrome Coronavirus 2  (SARS-CoV-2) has arguably been the single most devastating global crisis in recent history. As of December 2020, the virus claimed the lives of 1.7 million people, and healthcare systems around the world have been stretched to their limits. Notably, the U.S. has been exceptionally hard hit, accounting for one in five cases worldwide, even though the U.S. only makes up 4.25% of the global population. This means that Americans have been infected at five times the per-capita rate of the global average. Behavioral modifications such as social distancing and mask wearing have helped curb the spread. Still, the only clear solution to suppressing widespread infections and achieving herd immunity – where the entire population is protected from a pathogen through immunized individuals – is for a vaccine that is effective and widely available to be distributed.

Figure 1. The average number of contacts (left), rate of hospitalizations (middle), and deaths (right) by age group, the latter two taking 18-29 year-olds as reference. Data from Mossong, et. al., 2008 and CDC.

Vaccines are here, but available only to a few

Pfizer-BioNTech and Moderna have recently received emergency use authorization by the U.S. Food and Drug Administration (FDA) for their COVID-19 vaccines, which the companies report to have over 94% efficacy. Yet, due to their limited availability, these vaccines are currently only administered to health care providers and long-term care residents. As production ramps up, the vaccines will become available to a gradually increasing fraction of the general public. Throughout this process, it is vital to optimally allocate the vaccines to particular demographic groups in order to minimize the pandemic’s many devastating impacts on public health, as well as on the social and economic fabric of society.

From a health policy standpoint, there are two main strategies for mitigating the worst effects of the pandemic on society: minimizing the number of deaths and slowing the rate of infections. Unfortunately, while young adults drive most of the transmission of the virus, it is seniors above the age of 60 who are most at risk of dying from COVID-19 (Figure 1). The discrepancy between the most vulnerable age group and the age group mainly responsible for the spread of infection in the community positions the public health objectives at odds with one another. During the initial vaccine roll-out when the number of available vaccines is much smaller than the total population, if older people are prioritized this vulnerable demographic group will be protected, but infections will continue to spread through the unvaccinated 20-49 year-olds. On the other hand, vaccinating younger people first will help curb the spread but will leave the older population unprotected (Figure 2). In order to achieve overall maximum positive impact to society, where deaths due to COVID-19 are minimized while the prevalence of the virus is also curtailed, an effective vaccine distribution strategy must be deployed.

Figure 2. Two approaches to vaccine distribution: Vaccinating older individuals (depicted with canes), or younger (without canes). Individuals are either susceptible but uninfected (black), vaccinated (blue), infected (red boundary), or dead (red). (icon credit: Adrien Coquet/Noun Project)

Using mathematical models to find an optimal vaccination strategy

The intricacies of such a strategy have prompted mathematicians to build models to capture the complex dynamics of disease spread across the different age groups in a population. One such study utilized a classical model for infectious diseases called SEIR, where the letters stand for Susceptible, Exposed, Infected, and Recovered. In this model, the infection spreads within the population with a rate dependent on factors such as the number of infected and susceptible people, and how infectious the disease is. Through the transmission of the pathogen, a susceptible individual becomes exposed. Though infected with the pathogen, this person might not immediately be contagious, during a term described as ‘incubation.’ For SARS-CoV-2, this duration is estimated to be around three days. After becoming infectious, the individual either recovers or dies. The recovered population is assumed to be immune to the disease. The likelihood of the outcomes are dependent on risk factors related to age and other health conditions of the individual. Vaccination helps shrink the susceptible population through immunization, with a rate dependent on the efficacy of the vaccine (Figure 3).

Figure 3. A schematic diagram for an SEIR (Susceptible-Exposed-Infected-Recovered) model. 

In their model, the authors adjusted the mortality rates, infection prevalence, and contact structure to correspond to the current estimates for the various age groups. While mortality and transmission rates came from current estimates, the contact structure, or how frequently people in a certain age group interact within and outside their own group, has been studied for over a decade. The landmark study on societal contact patterns conducted in 2008 tracked thousands of peoples’ social interactions. Scientists collected data on the age and sex of anyone the subject had any physical (e.g. shaking hands) or non-physical (e.g. talking) in-person interaction with over the course of a day (Figure 1). Though school-age children were found to have more contacts than other age groups, partial or full closure of schools can reduce this number dramatically, leading to 20-49 year-olds having the highest average number of contacts.

With these values in hand, the authors estimated the effect of age group-selected vaccine administration in reducing deaths and infections for varying vaccine efficacy. For all possible scenarios, administering only to seniors aged 75 years and up resulted in the highest reduction of deaths as well as ICU hospitalizations, while vaccinating adults aged 20 to 49 years produced the highest reduction in infections and non-ICU hospitalizations. Thus, the authors concluded that, for a highly effective vaccine with over 70% efficacy, seniors over 75 years should be vaccinated first to reduce deaths, followed by a complete shift to prioritize adults aged 20 to 49 years to curb transmission, after enough vaccines to cover about half the population became available. Using a modified framework, a different group drew parallel conclusions. In one case, they consider a high vaccine efficacy and a basic reproductive rate – which describes the average number of people one infected individual is expected to infect – of 1.3. This assumes a relatively low transmission rate of the virus. In comparison, measles is a highly infectious disease that has a basic reproductive rate of 12-18. In this case, the authors recommended vaccinating 60+ year-olds first, then switching to 20 to 49-year-olds, and then switching back to seniors again after about 20% of the total population was vaccinated.

In another study, Buckner et al. stressed the importance of dynamic prioritization. Since social contacts are mainly concentrated within the respective age groups, they argued that the benefits to vaccinating individuals solely within a demographic group diminish as more people within that group become immune to the virus. Adding years of life lost (standard life expectancy of individuals at a certain age times the number of deaths at that age) as another optimization constraint, their results suggested starting with seniors to reduce deaths, then moving onto younger seniors to minimize years of life lost, then vaccinating school-age children to curb infections.

While the different models generally agree, they remain rudimentary in capturing the intricate social dynamics of the U.S. For instance, neither geographical variation in population size and make-up, nor systematic healthcare and social inequities experienced by black, indiginous, and people of color (BIPOC) have been included in any of these models. These considerations, as well as others such as occupation, health conditions, and multigenerational households, provide additional complexities for prioritizing optimal vaccine distribution.

What are the U.S. government’s plans?

The first coronavirus shot was given on Monday, December 14, 2020, and millions more will be administered the vaccine in the upcoming months. The U.S. federal government will allocate doses to each state in proportion to their population, but the decision on how to distribute the vaccines will be left up to the individual states. The Centers for Disease Control and Prevention (CDC) have released guidelines outlining a ‘phased approach to COVID-19 vaccination‘ in which they highlight four demographic groups to prioritize for initial vaccination: healthcare personnel, non-healthcare essential workers, adults with high-risk medical conditions, and people over 65 years of age. 

During phase 1, expecting limited vaccine supply, the CDC recommends starting with those who have a risk of direct or indirect exposure to infectious patients or materials, and then vaccinating all who belong to the four demographic groups highlighted above, as well as individuals who might belong to other populations deemed critical by the CDC. In an effort to balance the goals of preventing deaths and preserving societal functioning, an advisory committee for the CDC recommends vaccinating those aged 75 years and older as well as the 30 million frontline essential workers, such as grocery store, public transit, and postal service workers, in phase 2. 

When a large number of doses become available, which is expected to happen by the summer of 2021, the next cohort of individuals recommended to receive the vaccine consist of critical groups that were not covered in the previous phases, such as those with occupations essential to the functioning of society and others at an increased risk of exposure, as well as the general population. After a significant ramp up of vaccine production, when more doses than the size of the entire population become available, the CDC emphasizes the need for ensuring equitable access to the vaccine for all. 

Though country-wide vaccination of high-risk health care workers and residents in long-term care facilities has already begun, the CDC guidelines for a vaccine rollout are highly general and nonbinding, meaning that if states choose not to follow the recommendations, they will not face any consequences. Thus, the exact timeline and approach to geographic or demographic prioritization each state will take in immunizing its residents is likely to differ.

556,000 doses were administered in the first week of the Pfizer-BioNTech vaccine release, but the path to herd immunity through widespread vaccination (estimated to be around 60-70% of the population) will be a long and arduous process. In addition to those discussed in this piece, there are many logistical issues to solve, such as transportation of the Pfizer-BioNTech vaccine requiring -94 degree Fahrenheit temperatures, the success rate of administering both doses (as both of the currently approved vaccines need to be administered twice in order to reach the quoted efficacy levels), and what percentage of the population will be willing to get the vaccine due to concerns about their efficacy or safety. Lastly, unresolved questions such as how long immunity from a vaccine lasts and whether the developed vaccines will be effective against mutants places further pressure on creating an effective and rapid vaccine roll-out strategy. Until herd immunity is achieved, we must continue adhering to social distancing guidelines, wear masks, and when the time comes, receive the vaccine, for ourselves, our families, and our communities.


Melis Tekant is a Ph.D. student in the Physics Department at Massachusetts Institute of Technology. You can find her on Twitter as @melistekant.

Aparna Nathan is a fourth-year Ph.D. student in the Bioinformatics and Integrative Genomics Ph.D. program at Harvard University. You can find her on Twitter as @aparnanathan.

Cover image: “Syringe and Vaccine” by NIAID is licensed under CC BY 2.0

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One thought on “Optimal Strategy for a COVID-19 Vaccine Roll-out

  1. I believe the reason the US looks so bad in the statistics is because it has the most comprehensive testing and recording system. If you are going to compare the US to other countries, you need to provide some sort of data on the other countries testing methods and tracking and show their system is as good as the US.

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