Efficacy Adjusted Herd Coverage
Estimate critical vaccine coverage under homogeneous immunity and a supplied effective vaccine efficacy; values above one indicate model infeasibility.
Description
Calculate a homogeneous-model immunity threshold, divide it by supplied efficacy, and show whether the resulting coverage exceeds one.
In a simple homogeneous transmission model, reducing susceptibility reduces the effective reproduction number. The critical immune fraction is 1−1/R0 when R0 exceeds one; at or below one, this model requires no additional immune fraction to reach the boundary.1
If a supplied efficacy fraction represents the reduction relevant to this transmission model, vaccination coverage multiplied by efficacy supplies the modeled effective immune fraction. Dividing the threshold by efficacy gives the corresponding coverage requirement. Efficacy against symptomatic disease is not automatically the same parameter.
Efficacy Adjusted Herd Coverage reports the threshold, required coverage, and feasibility at full coverage. A requirement above one is retained as an infeasible model result rather than clipped to 100%.
When to explore an efficacy-adjusted coverage threshold
Use the tool for a clearly labeled homogeneous-model scenario with a chosen R0 and compatible efficacy. It helps identify sensitivity to efficacy and distinguish an immunity fraction from vaccination coverage.
- Calculate a threshold and its coverage equivalent.
- Identify when full coverage would be insufficient under the assumptions.
- Check low-R0 and exact-full-coverage boundaries.
How to enter R0 and efficacy and calculate coverage
- Enter positive Reproduction number as the model R0.
- Enter Vaccine efficacy fraction greater than 0 and no greater than 1; enter 0.8 for 80%.
- Run the calculation and read Herd immunity fraction and Required coverage fraction.
- Read Feasible at full coverage and preserve any requirement above one as a model infeasibility result.
herdImmunityFraction = max(0, 1−1/R0); requiredCoverageFraction = herdImmunityFraction/efficacy; feasible = requiredCoverageFraction ≤ 1 The implementation clamps only the immunity threshold at zero. Equality at coverage one is feasible according to its inclusive comparison.
{
"input": {
"reproductionNumber": 4,
"vaccineEfficacyFraction": 0.8
},
"output": {
"herdImmunityFraction": 0.75,
"requiredCoverageFraction": 0.9375,
"feasibleAtFullCoverage": true
}
}R0 at most one returns zero threshold and zero required coverage. Efficacy zero is rejected even in that case. Nonpositive R0, efficacy outside its valid domain, malformed input, and nonfinite values produce errors.
Limitations and interpretation
- The calculation assumes homogeneous mixing and a simple efficacy-to-susceptibility effect; it does not model heterogeneous contacts, waning, variants, or prior immunity.
- The supplied efficacy must be relevant to the modeled transmission effect, not simply copied from a different clinical endpoint.
- Reaching the mathematical boundary corresponds to effective reproduction one, not a guarantee of elimination or absence of outbreaks.
- No real-world coverage recommendation, rollout schedule, uncertainty interval, or population feasibility assessment is supplied.
Alternative or Complementary methods
A peak screen compares a current susceptible state with a growth boundary. A trial-efficacy summary estimates a relative clinical outcome from supplied counts, whose endpoint must be considered before any use in a transmission model.
References
-
The Mathematics of Infectious Diseases — SIAM Review; H. W. Hethcote (2000)
Similar or alternative tools
- SIR Infectious Peak Screen
Compare supplied susceptibility and R0 with the instantaneous homogeneous SIR boundary.
- Trial Vaccine Efficacy
Calculate relative outcome efficacy from trial-arm case counts and group sizes.