What is R0 (basic reproduction number)?

R0 is the average number of people one infected person will infect in a completely susceptible population. An R0 above 1 means the disease spreads; below 1 it dies out. Measles has an R0 of 12-18, seasonal flu around 1.2-1.4, and COVID-19 variants range widely from 2 to over 10.

What is the herd immunity threshold (HIT)?

The HIT is the minimum proportion of a population that must be immune for an infectious disease to stop spreading. It is calculated as HIT = 1 - 1/R0. For example, with R0 = 4, HIT = 75% — meaning 75% of the population needs immunity to prevent exponential spread.

How does vaccine efficacy affect the required coverage?

If a vaccine is only 80% effective, it provides less protection per dose. The required vaccination coverage is HIT / vaccine efficacy. With HIT = 75% and 80% efficacy, you need 75% / 0.80 = 93.75% of the population vaccinated to achieve herd immunity.

Is herd immunity possible through natural infection?

Mathematically yes — the formula applies regardless of how immunity is acquired. However, relying on natural infection is dangerous because it requires a large portion of the population to become infected and potentially suffer serious illness, which is why vaccination is strongly preferred.

Why does measles require such high vaccination coverage?

Measles is one of the most contagious diseases known, with an R0 of 12-18. Plugging R0 = 15 into the formula gives HIT = 93.3%. Combined with less-than-perfect vaccine efficacy, practical coverage targets are set at 95% or higher with two doses.

What are the limitations of the HIT formula?

The formula assumes homogeneous mixing in the population, uniform vaccine efficacy, and that immunity is permanent. In reality, populations cluster, vaccine protection can wane, and some groups may have lower uptake — all of which can raise the effective threshold needed.

Herd Immunity Threshold Calculator

Enter R0 and vaccine efficacy to explore a simplified threshold model; this is not a real-world vaccination target or forecast.

Inputs

Enter R0 and optional vaccine efficacy to compute the herd immunity threshold.

Basic Reproduction Number (R₀)

Must be greater than 1. Common values: flu ~1.3, COVID-19 ~2–5, measles ~15.

Vaccine Efficacy (%)

How effective the vaccine is at preventing infection (1–100%). Leave at 100 to ignore.

Quick presets

Results

Herd Immunity Threshold (HIT)

—

Proportion of population needing immunity

Min. Vaccination Coverage

—

Accounting for vaccine efficacy

Max. Susceptible Remaining

—

Critical susceptible proportion (Sₜ = 1/R₀); it equals the unvaccinated share only at 100% vaccine efficacy.

0% 100%

Formula Reference

Herd Immunity Threshold

HIT = 1 − 1 / R₀

Vaccination Coverage

V_c = HIT / E_v

Susceptible Threshold

S_c = 1 / R₀

R₀ = basic reproduction number | E_v = vaccine efficacy (0–1) | HIT = herd immunity threshold | V_c = required vaccination coverage

Summary

Enter R0 and vaccine efficacy to explore a simplified threshold model; this is not a real-world vaccination target or forecast.

How it works

Enter the basic reproduction number (R0) for the disease.
Optionally enter the vaccine efficacy percentage (default 100%).
The calculator applies HIT = 1 - 1/R0 to find the immunity threshold.
It divides the HIT by vaccine efficacy to find the required vaccination coverage.
Results update instantly along with an interpretation of the outbreak risk.

Use cases

Estimate vaccination targets for epidemic control planning.
Understand why measles (R0 ~15) needs ~95% vaccination coverage.
Compare herd immunity thresholds across diseases with different R0 values.
Assess the impact of imperfect vaccines on required coverage rates.
Educate students and the public on the mathematics of disease transmission.
Support public health policy discussions on vaccination campaigns.

Frequently Asked Questions

Last updated: 2026-09-19 · Reviewed by Nham Vu