FA-65246 / Epidemic compartment models / Open access

Delay-adjusted case fatality ratio: delay direction · case 01

Outcome-known cases include people who fell ill after the observation window.

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

ROOT CAUSE

The onset-to-death delay looks forward in time.

VERIFIED REPAIR

Restore the delay direction rule: `if t - j >= 0: / known += cases[t - j] * f`.

Unsuccessful approach: Excluding index 0 drops the first day of cases from the known-outcome count.

Case contract

naive CFR = sum(deaths)/sum(cases); delay_pmf[j] is the probability that death occurs j days after onset (j from 0); known = sum_t sum_j cases[t-j]*pmf[j] over t in the series; adjusted = min(sum(deaths)/known, 1); return [naive rounded 6, adjusted rounded 6 or None when known is 0]; None when there are no cases.

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(cases, deaths, delay_pmf):
    total_cases = sum(cases)
    total_deaths = sum(deaths)
    if total_cases <= 0:
        return None
    naive = total_deaths / total_cases
    known = 0.0
    for t in range(len(cases)):
        for j, f in enumerate(delay_pmf):
            if t + j < len(cases):
                known += cases[t + j] * f
    if known <= 0:
        return [round(naive, 6), None]
    adjusted = min(total_deaths / known, 1.0)
    return [round(naive, 6), round(adjusted, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])]]
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 fixture	Actual	Expected	Outcome
regression: growing epidemic	`[0.025806, 0.02847]`	`[0.025806, 0.072727]`	Failed
regression: stable epidemic	`[0.03, 0.036735]`	`[0.03, 0.036735]`	Passed
control: long delay no outcomes	`[0.0, None]`	`[0.0, None]`	Passed
control: no cases	`None`	`None`	Passed
regression: adjusted exceeds one	`[0.076923, 0.08]`	`[0.076923, 1.0]`	Failed
regression: immediate deaths	`[0.093333, 0.093333]`	`[0.093333, 0.093333]`	Passed
regression: single day	`[0.025, 0.041667]`	`[0.025, 0.041667]`	Passed

SHA-256 / 9ef738e91728eb2f09f1d5dd631218b2fb4e97c90e98ca61fd5b3dde519c997a

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cases, deaths, delay_pmf):
    total_cases = sum(cases)
    total_deaths = sum(deaths)
    if total_cases <= 0:
        return None
    naive = total_deaths / total_cases
    known = 0.0
    for t in range(len(cases)):
        for j, f in enumerate(delay_pmf):
            if t - j > 0:
                known += cases[t - j] * f
    if known <= 0:
        return [round(naive, 6), None]
    adjusted = min(total_deaths / known, 1.0)
    return [round(naive, 6), round(adjusted, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])]]
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 fixture	Actual	Expected	Outcome
regression: growing epidemic	`[0.025806, 0.08]`	`[0.025806, 0.072727]`	Failed
regression: stable epidemic	`[0.03, 0.046154]`	`[0.03, 0.036735]`	Failed
control: long delay no outcomes	`[0.0, None]`	`[0.0, None]`	Passed
control: no cases	`None`	`None`	Passed
regression: adjusted exceeds one	`[0.076923, None]`	`[0.076923, 1.0]`	Failed
regression: immediate deaths	`[0.093333, 0.127273]`	`[0.093333, 0.093333]`	Failed
regression: single day	`[0.025, None]`	`[0.025, 0.041667]`	Failed

SHA-256 / 3d89faf406f58d80cf070b7f012395bb66f00f94519ddbf9b1af60ff713a1689

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cases, deaths, delay_pmf):
    total_cases = sum(cases)
    total_deaths = sum(deaths)
    if total_cases <= 0:
        return None
    naive = total_deaths / total_cases
    known = 0.0
    for t in range(len(cases)):
        for j, f in enumerate(delay_pmf):
            if t - j >= 0:
                known += cases[t - j] * f
    if known <= 0:
        return [round(naive, 6), None]
    adjusted = min(total_deaths / known, 1.0)
    return [round(naive, 6), round(adjusted, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: stable epidemic',
   ([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
   [0.03, 0.036735]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])],
 [('regression: growing epidemic',
   ([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
   [0.025806, 0.072727]),
  ('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
  ('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
  ('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
  ('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
  ('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
  ('regression: late surge',
   ([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
   [0.024242, 0.111111])]]
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 fixture	Actual	Expected	Outcome
regression: growing epidemic	`[0.025806, 0.072727]`	`[0.025806, 0.072727]`	Passed
regression: stable epidemic	`[0.03, 0.036735]`	`[0.03, 0.036735]`	Passed
control: long delay no outcomes	`[0.0, None]`	`[0.0, None]`	Passed
control: no cases	`None`	`None`	Passed
regression: adjusted exceeds one	`[0.076923, 1.0]`	`[0.076923, 1.0]`	Passed
regression: immediate deaths	`[0.093333, 0.093333]`	`[0.093333, 0.093333]`	Passed
regression: single day	`[0.025, 0.041667]`	`[0.025, 0.041667]`	Passed

SHA-256 / 01ee2c9d630e6727e1687eea9652a6ffb68915f863ebe60f5a37a8cf8474002c

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 2026-09-29T14:47:32.073739+00:00.

Case digest / a034417d4e900b7583f621f20f9e7225aa60bd1f9bb4bbd08d2e6af484eb57af