FAILURE MAP
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FA-65166 / Epidemic compartment models / Open access

Epidemic growth rate, doubling time and R: reproduction mapping · case 01

R ignores the two-stage structure of the generation interval.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The SIR one-stage formula replaces the stipulated SEIR mapping.

VERIFIED REPAIR

Restore the reproduction mapping rule: `rep = (1 + r * tl) * (1 + r * ti)`.

Unsuccessful approach: The fixed-generation-interval exponential mapping is a different contract.

Case contract

r is the least-squares slope of ln(count) against day index over days with positive counts (original day indices kept); doubling time ln2/r only when r>0 else None; latent time Tl=latent_fraction*Tg, infectious time Ti=Tg-Tl, R=(1+r*Tl)*(1+r*Ti); return [r rounded 6, doubling rounded 4, R rounded 6]; None with fewer than two positive days.

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.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(counts, generation_mean, latent_fraction):
    pts = [(d, math.log(c)) for d, c in enumerate(counts) if c > 0]
    if len(pts) < 2:
        return None
    n = len(pts)
    mx = sum(d for d, _ in pts) / n
    my = sum(y for _, y in pts) / n
    sxx = sum((d - mx) ** 2 for d, _ in pts)
    sxy = sum((d - mx) * (y - my) for d, y in pts)
    r = sxy / sxx
    doubling = round(math.log(2) / r, 4) if r > 0 else None
    tl = latent_fraction * generation_mean
    ti = generation_mean - tl
    rep = 1 + r * generation_mean
    return [round(r, 6), doubling, round(rep, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('regression: declining', ([50, 41, 30, 26, 18, 15], 4.0, 0.3), [-0.246645, None, 0.217822]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('regression: declining', ([50, 41, 30, 26, 18, 15], 4.0, 0.3), [-0.246645, None, 0.217822]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: noisy growth[0.372323, 1.8617, 2.861617][0.372323, 1.8617, 3.693365]Failed
regression: with reporting gap zero[0.437065, 1.5859, 3.622388][0.437065, 1.5859, 5.341617]Failed
regression: declining[-0.246645, None, 0.013421][-0.246645, None, 0.217822]Failed
control: flat[0.0, None, 1.0][0.0, None, 1.0]Passed
control: too few positivesNoneNonePassed
regression: exact doubling per day[0.693147, 1.0, 3.079442][0.693147, 1.0, 4.160461]Failed
regression: leading zeros[0.796555, 0.8702, 6.575882][0.796555, 0.8702, 14.037592]Failed

SHA-256 / 83b6e8446e249edc6c5395612c3f6b231c2ef23019c1d25d813be0e323c6f87b

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(counts, generation_mean, latent_fraction):
    pts = [(d, math.log(c)) for d, c in enumerate(counts) if c > 0]
    if len(pts) < 2:
        return None
    n = len(pts)
    mx = sum(d for d, _ in pts) / n
    my = sum(y for _, y in pts) / n
    sxx = sum((d - mx) ** 2 for d, _ in pts)
    sxy = sum((d - mx) * (y - my) for d, y in pts)
    r = sxy / sxx
    doubling = round(math.log(2) / r, 4) if r > 0 else None
    tl = latent_fraction * generation_mean
    ti = generation_mean - tl
    rep = math.exp(r * generation_mean)
    return [round(r, 6), doubling, round(rep, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('regression: declining', ([50, 41, 30, 26, 18, 15], 4.0, 0.3), [-0.246645, None, 0.217822]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('regression: declining', ([50, 41, 30, 26, 18, 15], 4.0, 0.3), [-0.246645, None, 0.217822]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: noisy growth[0.372323, 1.8617, 6.434132][0.372323, 1.8617, 3.693365]Failed
regression: with reporting gap zero[0.437065, 1.5859, 13.768562][0.437065, 1.5859, 5.341617]Failed
regression: declining[-0.246645, None, 0.37285][-0.246645, None, 0.217822]Failed
control: flat[0.0, None, 1.0][0.0, None, 1.0]Passed
control: too few positivesNoneNonePassed
regression: exact doubling per day[0.693147, 1.0, 8.0][0.693147, 1.0, 4.160461]Failed
regression: leading zeros[0.796555, 0.8702, 263.982259][0.796555, 0.8702, 14.037592]Failed

SHA-256 / cc4feeb8a4d1ad510943707482c2cfe9d467feb9de69bda644e1acd290191e57

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(counts, generation_mean, latent_fraction):
    pts = [(d, math.log(c)) for d, c in enumerate(counts) if c > 0]
    if len(pts) < 2:
        return None
    n = len(pts)
    mx = sum(d for d, _ in pts) / n
    my = sum(y for _, y in pts) / n
    sxx = sum((d - mx) ** 2 for d, _ in pts)
    sxy = sum((d - mx) * (y - my) for d, y in pts)
    r = sxy / sxx
    doubling = round(math.log(2) / r, 4) if r > 0 else None
    tl = latent_fraction * generation_mean
    ti = generation_mean - tl
    rep = (1 + r * tl) * (1 + r * ti)
    return [round(r, 6), doubling, round(rep, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('regression: declining', ([50, 41, 30, 26, 18, 15], 4.0, 0.3), [-0.246645, None, 0.217822]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('regression: with reporting gap zero', ([2, 4, 0, 9, 13, 0, 30], 6.0, 0.5), [0.437065, 1.5859, 5.341617]),
  ('regression: declining', ([50, 41, 30, 26, 18, 15], 4.0, 0.3), [-0.246645, None, 0.217822]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592])],
 [('regression: noisy growth', ([3, 5, 6, 10, 14, 19, 30], 5.0, 0.4), [0.372323, 1.8617, 3.693365]),
  ('control: flat', ([7, 7, 7, 7], 5.0, 0.5), [0.0, None, 1.0]),
  ('control: too few positives', ([0, 0, 4, 0], 5.0, 0.5), None),
  ('regression: exact doubling per day', ([1, 2, 4, 8, 16], 3.0, 0.5), [0.693147, 1.0, 4.160461]),
  ('regression: leading zeros', ([0, 0, 1, 3, 5, 12], 7.0, 0.6), [0.796555, 0.8702, 14.037592]),
  ('regression: no latency', ([10, 13, 17, 22, 28], 5.0, 0.0), [0.258533, 2.6811, 2.292666]),
  ('regression: two points', ([5, 9], 4.5, 0.25), [0.587787, 1.1792, 4.956834])]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: noisy growth[0.372323, 1.8617, 3.693365][0.372323, 1.8617, 3.693365]Passed
regression: with reporting gap zero[0.437065, 1.5859, 5.341617][0.437065, 1.5859, 5.341617]Passed
regression: declining[-0.246645, None, 0.217822][-0.246645, None, 0.217822]Passed
control: flat[0.0, None, 1.0][0.0, None, 1.0]Passed
control: too few positivesNoneNonePassed
regression: exact doubling per day[0.693147, 1.0, 4.160461][0.693147, 1.0, 4.160461]Passed
regression: leading zeros[0.796555, 0.8702, 14.037592][0.796555, 0.8702, 14.037592]Passed

SHA-256 / ab24af451f11396cf6aee6d4af248ceb30906cefd02e401737baf05c2a338a53

Verification & scope

Deterministic bounded teaching model with a stipulated contract; not a validated scientific or public-health modelling library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:31.409294+00:00.

Case digest / 8d51b6f53d6605788d503a448791923a999581b26cc26d997913198dc4053f23