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SEIR R0 with vital dynamics and vaccine coverage: herd threshold · case 03

Herd immunity thresholds fall as R0 rises.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

R0 = beta*sigma/((sigma+mu)*(gamma+mu)); when R0<=1 return [R0,0.0,0.0]; herd threshold 1-1/R0; critical coverage threshold/efficacy, None if it exceeds 1 (exactly 1 is feasible); values rounded to 6; None for invalid rates or efficacy outside (0,1].

Why this case matters

Compartmental epidemic calculations drive outbreak forecasts, vaccine targets and hospital planning; a single wrong flow, rate conversion or boundary silently changes every downstream number.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: measles-like high R0	`[14.4, 0.069444, 0.073099]`	`[14.4, 0.930556, 0.979532]`	Failed

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