Herd Immunity Threshold
Calculate the percentage of a population that needs to be immune — through vaccination or prior infection — to indirectly protect the community from disease spread.
Herd Immunity Threshold
intermediateCalculate the vaccination coverage needed to achieve herd immunity
Formula
HIT = (1 - 1/R₀) / VE
How It Works
The herd immunity threshold (HIT) is the minimum proportion of the population that must be immune to a disease for herd immunity to take effect. It depends on two key parameters:
- R₀ (Basic Reproduction Number): The average number of secondary cases generated from one infected individual in a fully susceptible population. Higher R₀ = harder to achieve herd immunity.
- Vaccine Efficacy (VE): The proportion reduction in disease risk among vaccinated individuals compared to unvaccinated. No vaccine is 100% effective.
Formula:
HIT (%) = (1 − 1/R₀) × 100
Required Vaccination Rate (%) = HIT / Vaccine Efficacy
Example
For a disease with R₀ = 3 (similar to COVID-19 original strain) and a vaccine with 95% efficacy:
HIT = (1 − 1/3) × 100 = 66.7%
Required Vaccination = 66.7% / 0.95 = 70.2%
This means at least 70% of the population must be fully vaccinated to achieve herd immunity.
Note: For measles (R₀ ≈ 15), HIT ≈ 93% — requiring near-universal vaccination.
Frequently Asked Questions
What is herd immunity?
Herd immunity occurs when a large enough portion of a population is immune to a disease — either through vaccination or prior infection — making further spread unlikely. This indirectly protects those who cannot be vaccinated (e.g., immunocompromised individuals, newborns).
Why does vaccine efficacy matter?
No vaccine is 100% effective. If vaccine efficacy is lower, a higher vaccination coverage rate is needed to achieve the same level of population protection. This is why the required vaccination rate = HIT / vaccine efficacy.
What is a typical R₀ value?
R₀ varies by disease: Seasonal flu ≈ 1.3, COVID-19 (original) ≈ 2.5-3, Polio ≈ 5-7, Smallpox ≈ 5-7, Measles ≈ 12-18. Higher R₀ means more contagious and harder to achieve herd immunity.
Can herd immunity be achieved naturally?
Theoretically yes, but achieving herd immunity through natural infection would require a very large portion of the population to be infected, leading to high hospitalization and death rates. Vaccination is the safer and more effective path.