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Mathematical models show large decline in U.S. COVID-19 cases by fall

Recent reports about the rapid progress of SARS-CoV-2 vaccine trials1 have provided hopeful news for the coming year, showing highly effective results against the virus with limited side effects thus far. Resources around the globe are focused on manufacturing and distributing these vaccines, with the goal of stopping the spread of the COVID-19 disease taking an unprecedented toll on the population and the economy.

The United States has seen the highest overall reported infections and deaths from this disease,2 and as these vaccines are becoming available, officials have set out an aggressive timeline to get Americans vaccinated in the coming months.

Chart 9months

But how fast will we see improvements in cases and deaths as these vaccines slow the spread of the virus? And when can we hope for an effective halt, allowing a safe return to pre-pandemic activities?

To answer these questions, Verisk has developed preliminary simulations that may assist in projecting feasible outcomes of vaccine implementation using advanced mathematical and epidemiological modeling embedded in the web-based Life Risk Navigator platform. These simulations charting the potential spread of new cases are based on the preliminary results of the Phase 3 clinical trials and used a range of variations in vaccine effectiveness and coverage, and initial growth rate of new cases. How many vaccines will be available and how they will get to where they're needed may impact how fast we can vaccinate a large portion of the population.

Given the assumptions detailed in this blog, our mathematical models expect the United States may achieve herd immunity by fall 2021.

Modeling the vaccine rollout

Assuming that mass vaccination—that is, vaccination of individuals beyond front-line workers and nursing home residents—starts on January 15, 2021, and that vaccinated individuals develop immunity 30 days after taking the first dose of vaccine, our simulations start on February 15, 2021.

Our modeling considers the underreporting of cases, which varies by state and changes over time. The number of new cases at the start is based on a moderate growth scenario, assuming there will be no changes in the daily total of new cases since late November 2020.

Other key assumptions in these scenarios include:

  • To account for uncertainties in how fast we can vaccinate large numbers of people, we initially defined two types of vaccine campaign periods of six or nine months in duration.
  • Although preliminary results of clinical trials show that the vaccine efficacy is over 90%, vaccine effectiveness in these scenarios was assumed to be between 60% and 90% to account for variations when implemented in a large population.3,4
  • The new case growth rate in the population was varied within scenarios based on the reported initial effective reproduction number, or R values, for day one in the simulations from the historical data. The numbers of newly infected individuals in all scenarios are similar, but the effective reproduction number ranges between 1.2 to 2 (1.2, 1.4, 1.6, 1.8, 2) taking into account the potential change in spread at the time that the mass vaccination starts. According to our estimations, as of November 20, the effective reproduction number for the United States is 1.5.
  • To evaluate how different vaccine coverage scenarios would impact the spread of SARS-CoV-2, we ran scenarios with 0%, 40%, 60%, and 80% coverage. Coverage is a function of individuals’ willingness to get vaccinated, as well as availability of vaccine over time. For instance, in a scenario with 60% vaccine coverage and a vaccination period of six months, 60% of the population is vaccinated over a course of six months. The 0% vaccine coverage is a point of comparison, providing a scenario where no vaccine is available.
  • No priority for vaccination by age or comorbidities is assumed in these scenarios.

While the developed immunity for any vaccine is assumed to be effective for twelve months in the model, after which people may be susceptible again and potentially eligible for another vaccination, this projection is only to the end of 2021.


Figures 1 and 2 below show the results for vaccination campaigns that run for 6 months and 9 months, respectively, for a vaccine that is 90% effective. Dashed lines are the no-vaccine scenarios and scenarios are color coded based on the effective reproduction number (Re) at the mass vaccination start date. In each cluster, the lighter the color, the higher the vaccine coverage.

According to Figure 1, with a six-month vaccine campaign on a vaccine that is 90% effective, we expect to observe a significant decline in the number of new SARS-CoV-2 infections by the beginning of summer 2021, with some variations based on the vaccine coverage and initial Re.

Figure 2 shows if the same vaccine has a longer nine-month campaign—potentially due to less capability for mass production or distribution of the vaccine—the significant decline in new cases may be observed slightly later, during early to mid summer 2020 to 2021. While not displayed here, scenarios for a vaccine that is 60% effective showed a similar pattern to Figure 2, with an extended time until we see meaningful decline in the cases.

Chart 9months
Click to enlarge  

Figure 1. Projected number of new SARS-CoV2 cases after vaccinating United States population with a 90% effective vaccine during a six-month vaccination campaign. There are some variations in Re and vaccine coverage. (Source: AIR Worldwide)

Chart 9months
Click to enlarge  

Figure 2. Projected number of new SARS-CoV2 cases after vaccinating United States population with a 90% effective vaccine during a nine-month vaccination campaign. There are some variations in Re and vaccine coverage. (Source: AIR Worldwide)

Overall, these simulations showed that upon mass vaccination, we may observe a significant decline in new cases by fall 2021, assuming our hypothesis in terms of vaccine effectiveness and coverage are valid.


This study assumes there will be minimal air travel to the United States from other countries, even during the vaccine campaigns. While this assumption of isolation may provide a good understanding about the overall impact of the vaccine in the United States, the ability to fully model the worldwide effect of the vaccines on this pandemic is hampered by the range of unknowns surrounding potential sources and timing of vaccine distribution to countries that lack existing, priority contracts with major vaccine distributors.

Given the sheer complexity of vaccine planning underway in the United States alone, even current projected timelines will undoubtedly change.5 Regulatory reviews may impact certain rollout times. Supply line problems, including manufacturing, packaging, storage, and distribution, will likely need to be considered for a project of this scale. And while the United States Center for Disease Control will set out recommendations, each state will determine how to best allocate the number of vaccines it eventually receives.

Finally, it must be noted that the United States population may be in a better or worse situation initially from the moderate scenario we modeled here. The new case growth rate at the starting point is a direct function of population behavior, including social distancing, wearing masks, and avoiding large gatherings. While we profoundly hope the United States growth rate will decline in the interim, we acknowledge the impact of holiday seasons may bring the opposite effect.

Overall, despite the devastating pandemic that we are experiencing, the potential of containment by the summer of 2021 is exciting news for the scientific community and the population at large. With several vaccine trails under evaluation, including those developed using mRNA, and some granted emergency-use authorization in the United States as early as mid-December, the scientific community could have a range of effective options to effectively immunize different populations in the coming months.

Though we are still developing an understanding of potential side-effects, the astounding accomplishment of a successful vaccine development within 12 months for an emerging disease like COVID-19 shows how recent cutting-edge technologies may usher in a new era of disease control.

  1. Craven, Jeff, “COVID-19 Vaccine Tracker,” Regulatory Affairs Professional Society, December 23, 2020,
    < >, accessed on January 5, 2021.
  2. Centers for Disease Control and Prevention, “CDC COVID Data Tracker,” January 21, 2020,
    < >, accessed on January 5, 2021.
  3. Polack, Fernando P., Stephen J. Thomas, Nicholas Kitchin, Judith Absalon, Alejandra Gurtman, Stephen Lockhart, John L. Perez, et al. “Safety and Efficacy of the BNT162b2 MRNA Covid-19 Vaccine.” New England Journal of Medicine 383, no. 27 (December 31, 2020): 2603–15. < >
  4. Baden, Lindsey R., Hana M. El Sahly, Brandon Essink, Karen Kotloff, Sharon Frey, Rick Novak, David Diemert, et al. “Efficacy and Safety of the MRNA-1273 SARS-CoV-2 Vaccine.” New England Journal of Medicine 0, no. 0 (December 30, 2020): null. < >
  5. Diaz, Jaclyn. “U.S. Likely Will Miss Goal Of Vaccinating 20 Million By The New Year.” NPR, December 31, 2020,
    < >, accessed on January 6, 2021.

Narges Dorratoltaj

Narges Dorratoltaj, Ph.D., MPH is a computational epidemiologist and leads the Life and Health modeling team at Verisk. She can be reached at

John-Paul Glutting

John-Paul Glutting, M.Sc. MPH, is a senior scientist at Verisk and develops pandemic models of infectious diseases transmission and dynamics in different geographical locations. He can be reached at

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