# Expert shares equation that shows even a 100% vaccination rate is not enough to stop Delta variant

Friday, August 13, 2021
A Boston University professor explains why Delta has made it mathematically impossible to beat coronavirus now with just the vaccine.

SAN FRANCISCO (KGO) -- Earlier in the pandemic, experts had hoped if we can get 75% of Americans vaccinated, we can contain the coronavirus.

Thursday, we're at just over 50% vaccinated. But 75% is no longer enough. The Delta variant has changed the equation, literally.

A professor of epidemiology at Boston University recently tweeted equations that explain why Delta has made it mathematically impossible to beat the virus now with just the vaccine:

Dr. Ellie Murray was on ABC7 News 3 p.m. program "Getting Answers" Thursday to share her calculations.

First, we have to understand a virus' effective Reproductive Number, or Re, the number of people an infected person will transmit to. It needs to stay under one, as in each infected person transmits to fewer than one other person, for us to suppress and beat the virus.

With the original COVID-19 strain, each infected person passed it on to an estimated 3 people without intervention. At our nation's current 50% vaccination rate, and vaccine efficacy at 95%, the Re is 1.575, not good enough. But at 75% vaccination rate, a lofty goal that mirrors the Bay Area but far surpasses much of the nation, the Re is 0.86, enough to defeat the virus:

Re=3*(1-0.5*0.95) = 1.575
Re=3(1-.75*.95)=0.86 <1

However, the Delta variant is much more transmissible, so Dr. Murray replaced the 3 with an 8, the number of people one person might pass it on to without mitigation.

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The more the virus spreads, the more it has "ample opportunity" to mutate, Dr. Anthony Fauci told anchor "GMA" George Stephanopoulos Thursday.

She also brought the vaccine efficacy rate to 85%, while acknowledging the latest studies suggest the number could be even lower. And now, you can see the Re at 50% vaccination is 4.6, much too high. And even if we achieve a national 75% vaccination rate, the Re would still be 2.9. With one infected person infecting nearly 3 others, that will not end the pandemic.

Even if 100% of people got vaccinated, that would not bring the effective reproductive number under 1. Hence, other mitigation measures are needed, such as masking:

Re=8(1-.5*.85) = 4.6
Re=8(1-.75*.85)=2.9

Even if the 50% who've already gotten the shots received a booster, that would make only a small dent and not nearly as impactful as getting new people vaccinated.

Even if we can't get rid of the virus entirely, the vaccines can help get rid of the "disease" in the form of worst outcomes. She says the math shows that the end game is vaccinate, vaccinate, vaccinate.