Herd Immunity: It May Not Mean What You Think It Means

Updated: Jul 2, 2020

As the pandemic begins to wear on our psyche, much of the conversation has turned to the seemingly simple concept of Herd Immunity. This core public health concept has been twisted by politicians (and many physicians who forgot their definitions) as an excuse to stop personal responsibility and swing the needle to get back to business without addressing the baseline economic issues which created this crisis, or the pending crisis of waves of illness sweeping American workers.


When discussing herd immunity, we usually have a vaccine to CREATE that immunity - very rarely is it used to expose naive (unexposed/not ill) patients to a novel disease without a cure. Measles has been a fantastic example of the success of herd immunity (prior to the anti vax movement).


Seems easy enough, but let’s do some math (and add a few definitions).



Herd Immunity: When the majority of a population is immune to an infectious disease, this provides indirect protection, or herd immunity, to those who are not immune. We use this strategy to protect those we cannot vaccinate (those who have immune disorders, are receiving chemotherapy, are temporarily immunosuppressed, or have allergies to vaccine ingredients)




Pcrit: minimum proportion of the population that needs to be immunized in order to obtain herd immunity


As there is currently no vaccine

Pcrit = 1-1/Ro


Ro (Reproductive Ratio): this number is the number of individuals an infected individual would infect and assumes no immunity or public health measures at play.

COVID-19 Ro: between 2-3


Re (Effective Reproductive Ratio): the number of secondary infections caused by one primary infection at a given time (how many people one person will infect)

-this number varies based on social factors - most significantly social distancing, precautions taken, the health of the population.


CFR (Case Fatality Rate): the number of deaths/total number of confirmed infections

-With COVID-19 the Case fatality rate is approximately: 126,203 / 2,537,636 = 4.97%

(WHO/CDC Data)


Infection Fatality Rate: the number of deaths/total number of infections (including asymptomatic or untested unconfirmed) - this number has yet to be confirmed due to previous low testing rates but estimates have been ranging from 0.5-3.6%


American Population: 328,200,000 (US Census Bureau)


So let's look at some scenarios:


Assume a low Re (social distancing/lockdown scenario):

  • Re = 0.8

  • Pcrit = 1-1/Re = -0.25

  • Since Re < 1, an infected individual will transmit the virus to fewer than 1 person. This means that we would be approaching herd immunity, and eventually, the virus would stop spreading. This would REQUIRE a vaccine to reduce the number of people susceptible to the infection.

  • KEY POINT: Ro of COVID-19 is between 2 and 3. This will require EXTREME measures or an effective vaccine distributed to the majority of the population to get the Re to reach 0.8.

Moderate Re (little social distancing, moderately dense population)

  • Re = 2.4

  • Pcrit = 1-1/(2.4) = 0.58 or 58% of the population

  • 58%* American population = 190,356,000 total infections

  • Deaths: 190,356,000 * 4.97% = 9,460,693 total deaths

  • Using lowest estimated IFR: 190,356,000*0.5% = 951,780 deaths


Current Re in Southwest Ohio is 1.6 (optional social distancing)

  • Re = 1.6

  • Pcrit = 1-1/(1.6) = 0.375 or 37.5% of the population

  • 37.5%*American population = 123,075,000 infections

  • Deaths: 123,075,000 * 4.97% = 6,116,827 total deaths

  • Using lowest estimated IFR: 123,075,000*0.5%=615,375 deaths


Worst Case Scenario assuming Re is at max (assumed) Ro

  • Re = 3.0

  • Pcrit = 1-1/3 = 0.67 or 67% of the population

  • 67% *American population = 219,894,000 infections

  • Deaths: 219,894,000 * 4.97% =10,928,731 total deaths

  • Using lowest estimated IFR: 219,894,000*0.5%=1,099,470 deaths


From the numbers, we can see that the concept of herd immunity, while not inaccurate, would result in the deaths of millions of Americans. Even with the difference in infection vs case fatality rate and the fact the Re does change as more people are infected/are recovered. However, we have used a simplified model since the number of infected/dead would not be significantly impacted by using Re rather than the modified Ro.


Sweden has used the herd immunity approach, doing little in the way of forced social distancing, which has led to an upswing in infections and deaths among the elderly. A country with a population of 10.23 million, Sweden has documented 67,777 cases with 5,310 deaths - this is a case fatality rate of 7.8%. They have not yet reached the peak of their epidemic. They also are far from achieving herd immunity (with only 0.66% of their population infected). Small analyses have been done on the Swedish approach (here). Until COVID-19 has completed its havoc, we will not know whether the strategy was as ineffective as it appears.


While math and modeling may not be the most exciting way to look at things, public health is a science - not an opinion. So next time someone attempts to say herd immunity is the answer, remind them that if life went back to ‘normal’ right now, we could lose up to 10 million Americans. We can only hope people continue to base their actions on data, math, and public health science available instead of citing the buzzword ‘herd immunity’ because that is more body bags than we can be comfortable counting.


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