(CNN) — Vaccination alone might not be enough to end the Covid-19 pandemic, researchers reported Tuesday.

Even with a majority of the population vaccinated, the removal of pandemic precautions could lead to an increase in virus spread, the researchers reported in the medical journal JAMA Network Open.

Mehul Patel, an assistant professor of emergency medicine at the University of North Carolina at Chapel Hill, and colleagues used a mathematical model to simulate coronavirus spread among the approximately 10 million people of North Carolina.

They found that coronavirus infections, hospitalizations and deaths would continue to rise if pandemic precautions such as quarantine, school closures, social distancing and mask-wearing were lifted while vaccines were being rolled out.

“Our study suggests that, for a population of 10.5 million, approximately 1.8 million infections and 8,000 deaths could be prevented during 11 months with more efficacious COVID-19 vaccines, higher vaccination coverage, and maintaining NPIs (non-pharmaceutical interventions), such as distancing and use of face masks,” they wrote.

If vaccines with 50% efficacy were rolled out to 25% of adults, the model showed an average of 2.2 million new infections when precautions were lifted, and just under 800,000 new infections when they were maintained.

If vaccines with 90% efficacy were given to 75% of adults, the model showed an average of 527,409 new infections when precautions were lifted, and 450,575 new infections when they were maintained.

It would be better to give lower-efficacy vaccines to more people, they calculated. That would reduce the risk of virus spread more than giving higher efficacy vaccines to fewer people.

“Increasing that coverage by a substantial amount, regardless of vaccine efficacy, really is what appears to be driving the control,” Patel told CNN. “If the vaccine were only distributed to a minority of the population, we might even see surges that were to the magnitude of what we were seeing prior to vaccines being administered.”

In keeping with other research, the model showed a greater risk for Covid-19 hospitalization and death among Black people and those living in rural communities. The team noted that combining vaccination with pandemic precautions would lead to reduced infections, hospitalizations and deaths across all groups.

The US Centers for Disease Control and Prevention said last month that in most cases, it’s safe for vaccinated people to go maskless outdoors and indoors. The guidance was met with mixed reviews, with some public health experts arguing that the US is not far enough along in its Covid-19 vaccination effort to relax pandemic precautions.

The CDC recommendations don’t discount the importance of the precautions highlighted in the modeling study, Dr. Alexander Doroshenko, an assistant professor in the Department of Medicine at the University of Alberta in Canada, noted in a related commentary. Rather, they “emphasize the need for a balanced approach to allow vaccinated individuals to resume low-risk activities.”

In the near future, continued pandemic precautions could work in synergy with Covid-19 vaccination to end the pandemic, Doroshenko said.

Patel’s team did not seek to pinpoint exactly when it would be safe to lift precautions in the US, but Patel noted that as vaccine coverage approached 75% in their simulations, they saw the level of infection decline.

Just over half of the adult population in the US and about 40% of the total population has been fully vaccinated, according to the latest CDC data.

As Covid-19 vaccination coverage increases, many states are dropping pandemic precautions. California plans to eliminate all capacity limits and social distancing requirements when the state fully reopens on June 15. Other states are tying the end of pandemic restrictions to vaccination coverage.

They include Oregon, which announced plans to end major pandemic restrictions once 70% of eligible residents have received at least one Covid-19 vaccine dose.

Patel and colleagues say their findings suggest it will take a coordinated effort of maximizing vaccine coverage and practicing pandemic precautions “to reduce COVID-19 burden to a level that could safely allow a resumption of many economic, educational, and social activities.”

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