US Vaccine Strategy Calculator — Herd Immunity & Coverage
Enter the disease R₀, vaccine efficacy, and current coverage to calculate whether herd immunity is achieved, how many more people need to be vaccinated, and how much the effective reproduction number Rₑ has been reduced.
Disease preset
%
%
Rₑ ≥ 1 — herd immunity not yet reached; the disease can still spread
- 1
Herd immunity threshold
1 − 1 ÷ 2.9 = 0.6552 - 2
Effective population immunity (VE × coverage)
85% × 60% = 51% - 3
Effective reproduction number (Rₑ)
2.9 × (1 − 0.51) = 1.42When Rₑ < 1 the outbreak cannot sustain itself in this population.
How does this calculator work?
Herd immunity threshold = 1 − 1/R₀. Required vaccination coverage = (1 − 1/R₀) / VE. Current Rₑ = R₀ × (1 − VE × coverage). When Rₑ < 1, herd immunity is achieved and the outbreak cannot sustain itself. For COVID original (R₀ 2.9, VE 85 %), you need ~82 % coverage; for measles (R₀ 15, VE 95 %), ~98 % coverage.
Formula
How this is calculated
The basic reproduction number R₀ ("R-naught") is the average number of secondary cases generated by one infectious individual in a completely susceptible population. When enough people are immune — through vaccination or prior infection — the effective reproduction number Rₑ drops below 1, meaning each case generates less than one new case and the outbreak dies out. This is herd immunity.
The herd immunity threshold is H = 1 − 1/R₀. For measles (R₀ ≈ 15), H = 93 %; for influenza (R₀ ≈ 1.5), H = 33 %. Because no vaccine is 100 % effective, the required vaccination coverage is higher than H: C_required = H / VE = (1 − 1/R₀) / VE. If VE × max_coverage < H, vaccination alone cannot achieve herd immunity at the societal level.
With current coverage c and vaccine efficacy VE, the effective reproduction number is Rₑ = R₀ × (1 − VE × c). This model assumes homogeneous random mixing and a fully susceptible baseline population — it is a simplified public health planning tool. In reality, age structure, waning immunity, natural immunity from prior infection, clustered vaccine hesitancy, and variant evolution all affect transmission dynamics. Figures for R₀, VE, and coverage are 2022–2024 approximate literature estimates and are user-editable.
Frequently asked questions
For the original COVID-19 strain (R₀ ≈ 2.9), the herd immunity threshold is about 65–70 %. For the Omicron variant (R₀ ≈ 9–12), the threshold rises to 89–92 %, making it extremely difficult to achieve through vaccination alone without accounting for prior immunity.
The herd immunity threshold H = 1 − 1/R₀ is the fraction of the population that must be immune. Because vaccines are not 100 % effective, more people need to be vaccinated than actually become immune. The required coverage is H ÷ VE — for H = 70 % and VE = 85 %, you need 70 ÷ 0.85 ≈ 82 % of the population vaccinated.
For diseases with very high R₀ (like measles at ~15), the threshold is ~93 % immune. With a 95 % effective vaccine, you need about 98 % vaccination coverage — nearly universal immunisation. For diseases where VE × possible coverage < H, vaccination strategy must be combined with other measures (antiviral treatment, behaviour change, natural immunity).
Also known as
TG we-Calculate Editorial Team. (2026). US Vaccine Strategy Calculator — Herd Immunity & Coverage [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/us-vaccine-strategy-calculator
TG we-Calculate Editorial Team. "US Vaccine Strategy Calculator — Herd Immunity & Coverage." TG we-Calculate. 2026. https://we-calculate.com/calculator/us-vaccine-strategy-calculator.
TG we-Calculate Editorial Team, "US Vaccine Strategy Calculator — Herd Immunity & Coverage," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/us-vaccine-strategy-calculator
@misc{wecalculate_us_vaccine_strategy_calculator, title = {US Vaccine Strategy Calculator — Herd Immunity & Coverage}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/us-vaccine-strategy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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