Herd Immunity Threshold Calculator

What Is Herd Immunity? Herd immunity (also called population immunity or community immunity) occurs when enough people in a population are immune to a disease — through vaccination or prior infection — that transmission is effectively halted. When enough people are immune, the disease can no longer spread efficiently and dies out, even protecting those who cannot be vaccinated (newborns, immunocompromised individuals).

The Basic Reproduction Number (R₀) R₀ (pronounced “R-naught”) is the average number of people an infected person will infect in a completely susceptible population.

• R₀ < 1: The disease will die out on its own
• R₀ = 1: The disease is endemic (stable)
• R₀ > 1: The disease will spread

Well-known R₀ values (approximate):

• Seasonal influenza: 1.2–1.4
• SARS-CoV-1: 2–3
• COVID-19 (original strain): 2–3; Omicron: 8–15
• Polio: 5–7
• Mumps: 4–7
• Rubella: 5–7
• Smallpox: 5–7
• Measles: 12–18 (one of the highest known)

Herd Immunity Threshold (HIT) Formula HIT = 1 − (1 / R₀)

This gives the minimum proportion of the population that must be immune to stop transmission.

Vaccination Coverage Needed If the vaccine is not 100% effective, more people need to be vaccinated: Vaccination coverage needed = HIT ÷ (vaccine efficacy / 100)

Worked Examples COVID-19 (R₀ = 5, 90% vaccine efficacy): HIT = 1 − 1/5 = 80% Coverage needed = 80% ÷ 0.90 = 88.9%

Measles (R₀ = 15, 97% vaccine efficacy): HIT = 1 − 1/15 = 93.3% Coverage needed = 93.3% ÷ 0.97 = 96.2% (This is why 96%+ measles vaccination is required for herd immunity)

Important Limitations Real-world herd immunity is more complex:

• Immunity wanes over time for both vaccines and natural infection
• R₀ varies with behavior, population density, and variants
• Vaccine coverage must be distributed evenly — clustered unvaccinated groups create local outbreaks
• Some diseases have animal reservoirs, making true eradication impossible