Herd immunity threshold is one of the most misunderstood numbers in epidemiology. Public conversation treats it as a single ceiling that, once crossed, ends an outbreak permanently. The actual math says the threshold is disease-specific, depends on assumptions that rarely hold in real populations, and shifts when a virus evolves. The same equation that says measles needs 95 percent immunity says seasonal flu effectively never reaches herd immunity at all.
Understanding the threshold matters because vaccine policy depends on it. Measles surveillance in 2024 to 2025 found multiple US counties below 90 percent MMR coverage, and outbreaks followed. Polio elimination targets are tied to the threshold. Pandemic disease severity scoring and policy responses get sharper when you know how the number is built.
Key Takeaways
- Herd immunity threshold (HIT) is calculated from R0: HIT = 1 minus 1/R0. For measles (R0 = 12 to 18), HIT runs 92 to 95 percent. For seasonal flu (R0 = 1.2 to 1.5), HIT runs 17 to 33 percent.
- The simple formula assumes random mixing, lifelong immunity, and a homogeneous population. Real populations cluster, immunity wanes, and pathogens evolve. Real-world thresholds are higher than the simple formula predicts.
- Measles is the textbook example because R0 is high and immunity is durable. Even a 5 percent gap in coverage produces sustained outbreaks.
- Influenza never reaches herd immunity because the virus undergoes antigenic drift each season, so the immune population keeps shrinking faster than it grows.
- Vaccine-induced and infection-induced immunity behave differently for HIT calculations. Vaccines often produce more uniform immunity; natural infection often produces stronger but more variable immunity, including in some cases sterilizing immunity vaccines do not yet match.
What is herd immunity threshold?
Herd immunity threshold is the proportion of a population that needs to be immune for sustained transmission of a pathogen to stop in that population. Below the threshold, each case on average infects more than one further person and the outbreak grows. Above the threshold, each case on average infects fewer than one further person and the outbreak shrinks.
The phrase is not "no infections ever again." It is "the average new case fails to replace itself, so chains of transmission die out faster than they start." Imported cases can still seed local outbreaks above HIT; what changes is whether those outbreaks self-sustain. The classic example is measles in pre-2000 US: high vaccine coverage above HIT, occasional imported cases, but no sustained transmission.
How do you calculate herd immunity threshold from R0?
The simple formula is HIT = 1 - 1/R0, where R0 is the basic reproduction number, the average number of secondary cases produced by one case in a fully susceptible population. The intuition: at HIT, exactly 1/R0 of the population is still susceptible, so each case meets on average one susceptible contact and replaces itself.
| Disease | R0 | HIT (simple formula) |
|---|---|---|
| Measles | 12 to 18 | 92 to 94 percent |
| Pertussis | 12 to 17 | 92 to 94 percent |
| Diphtheria | 6 to 7 | 83 to 86 percent |
| Polio | 5 to 7 | 80 to 86 percent |
| Smallpox | 5 to 7 | 80 to 85 percent |
| SARS-CoV-2 (original) | 2.5 to 3.5 | 60 to 71 percent |
| SARS-CoV-2 (Omicron variants) | 8 to 12 | 87 to 92 percent |
| Seasonal flu | 1.2 to 1.5 | 17 to 33 percent |
The formula assumes well-mixed populations, perfect immunity, and a constant pathogen. Real populations have clustering (kids in school, dense neighborhoods, undervaccinated communities) and waning immunity. Real pathogens mutate. The effective threshold in practice runs 5 to 15 percent higher than the simple-formula number for most diseases. See R0 and transmission dynamics for the underlying mechanics.
Why does the threshold vary so much between diseases?
The threshold depends almost entirely on R0, and R0 depends on three things: how transmissible the pathogen is per contact, how many contacts the average infected person has, and how long they remain infectious. Measles has very efficient airborne transmission, productive infectious shedding for about a week, and contact patterns that include schools and households; that combination drives R0 high.
Seasonal flu transmits efficiently but infectious shedding is shorter, immunity from prior seasons confers partial protection against this year's strain, and antigenic drift means the virus changes faster than the population builds long-term immunity. SARS-CoV-2 sat in the middle for the original strain and shifted higher for Omicron variants because Omicron transmits more efficiently and partially escapes prior immunity, raising effective R0 even in populations with widespread prior infection or vaccination.
Why did "herd immunity" fail as a COVID-19 strategy?
Several governments and commentators in 2020 floated the idea of allowing controlled spread to reach herd immunity. The strategy assumed a fixed HIT around 60 percent, durable immunity from infection, and a stable virus. None of those held. Variants emerged that pushed effective R0 higher, vaccine and infection-induced immunity waned within months for transmission (though not for severe disease), and the calculated threshold moved upward through 2021 and 2022 as new variants reached fixation.
The deeper issue is that the simple HIT formula is a biological lower bound, not a policy ceiling. Reaching HIT through infection requires getting sick, and even at a 0.5 percent infection fatality rate, infecting 60 percent of a population implies hundreds of thousands of deaths in any large country. The vaccine-led strategies that worked focused on protecting against severe disease and reducing transmission incrementally rather than on hitting a numerical threshold.
How does vaccine immunity differ from infection immunity for HIT?
Vaccines and natural infection produce different immune responses, and the differences matter for herd immunity calculations. The textbook simplification is that one immune person is one immune person. Reality is more complicated.
Vaccine-induced immunity tends to be more uniform across a population (same antigen, similar dose, fewer outliers) but may be narrower (targeting one or a few proteins rather than the whole pathogen). Infection-induced immunity is broader (multiple antigens) but more variable (individual viral load, severity, and immune competence drive the response). For some pathogens, including measles and yellow fever, both routes produce essentially lifelong sterilizing immunity. For others, including SARS-CoV-2 and influenza, neither route produces durable sterilizing immunity.
The practical implication: you cannot directly substitute "fraction infected" for "fraction vaccinated" in the HIT formula. Outbreak modeling that treats them as equivalent overestimates the immunity wall. See vaccine efficacy explained for how the protection numbers from clinical trials translate to population-level immunity.
FAQ
If 95 percent of people are vaccinated for measles, does that mean 5 percent will still get measles?
No. It means the population is above herd immunity threshold for measles, so imported cases are unlikely to start sustained transmission. Within that 5 percent who are unvaccinated or unsuccessfully vaccinated, individuals are still personally susceptible if exposed. Herd immunity is a population property, not a personal one.
Can a population have herd immunity to one variant but not another?
Yes, and this is exactly what happened with SARS-CoV-2. Populations with widespread immunity to the original Wuhan strain were partially susceptible to Alpha, more susceptible to Delta, and substantially susceptible to Omicron. The threshold recalculates each time a new variant changes effective R0 or escapes prior immunity.
Why is influenza's threshold so low if R0 is in the 1.2 to 1.5 range?
The simple formula gives a low threshold, but real-world flu does not behave as if it had been suppressed at 30 percent population immunity. The reasons are antigenic drift each season, waning antibody titers within months, and partial cross-reactivity that protects against severe disease without preventing infection. Flu effectively never reaches sustained herd immunity, which is why annual vaccination matters.
Did smallpox eradication require 100 percent immunity?
No. Smallpox was eradicated through ring vaccination (vaccinating contacts of cases rather than the whole population) plus surveillance. Global immunity at eradication was nowhere near 100 percent. The strategy worked because R0 was relatively low, the disease had no animal reservoir, vaccine immunity was durable, and surveillance could find every case.
Can herd immunity protect immunocompromised people who cannot be vaccinated?
Yes, this is the strongest practical argument for high coverage. People who cannot mount a vaccine response (some cancer patients, organ transplant recipients, people on certain immune-suppressing drugs, infants too young for vaccines) rely on the surrounding immune population to stop transmission chains before they reach them. Coverage gaps disproportionately put these groups at risk.