FA-65006 / Epidemic compartment models / Open access
Two-group next-generation matrix R0: infector infectious period · case 01
R0 is wrong whenever the groups recover at different rates.
ROOT CAUSE
The infectious period of the infectee group is used instead of that of the infector.
VERIFIED REPAIR
Restore the infector infectious period rule: `/ gamma[j] for j`.
Unsuccessful approach: Averaging the two recovery rates erases the group difference.
Case contract
K[i][j] = contact[i][j]*sizes[i]/sum(sizes)/gamma[j] (infections in group i caused by one infective in j); R0 is the dominant eigenvalue of the 2x2 K; lead group is the larger component of its eigenvector (ties and decoupled ties to group 0); return [flattened K rounded 6, R0 rounded 6, lead] or None for empty population or non-positive gamma.
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(contact, sizes, gamma):
total = sum(sizes)
if total <= 0 or min(gamma) <= 0:
return None
k = [[contact[i][j] * sizes[i] / total / gamma[i] for j in range(2)] for i in range(2)]
tr = k[0][0] + k[1][1]
det = k[0][0] * k[1][1] - k[0][1] * k[1][0]
disc = max(tr * tr - 4 * det, 0.0)
r0 = (tr + math.sqrt(disc)) / 2
if abs(k[0][1]) > 1e-12:
v = [k[0][1], r0 - k[0][0]]
elif abs(k[1][0]) > 1e-12:
v = [r0 - k[1][1], k[1][0]]
else:
v = [1.0, 0.0] if k[0][0] >= k[1][1] else [0.0, 1.0]
lead = 0 if abs(v[0]) >= abs(v[1]) else 1
return [[round(x, 6) for row in k for x in row], round(r0, 6), lead]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None)],
[('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0])],
[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('regression: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('regression: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None)]]
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: children and adults | [[2.4, 0.6, 1.75, 3.5], 4.11297, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Failed |
| regression: asymmetric core group | [[1.333333, 0.066667, 4.5, 1.35], 1.889453, 1] | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | Failed |
| control: decoupled equal groups tie | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | Passed |
| control: decoupled first dominant smaller group | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | Passed |
| control: decoupled second dominant | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | Passed |
| regression: one-way coupling | [[1.0, 0.0, 4.0, 3.0], 3.0, 1] | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | Failed |
| control: empty population | None | None | Passed |
SHA-256 / 7c2636197f87be2db1d034decec32cd29cd434912e0963c161cd55200e5ced45
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(contact, sizes, gamma):
total = sum(sizes)
if total <= 0 or min(gamma) <= 0:
return None
k = [[contact[i][j] * sizes[i] / total / ((gamma[0] + gamma[1]) / 2) for j in range(2)] for i in range(2)]
tr = k[0][0] + k[1][1]
det = k[0][0] * k[1][1] - k[0][1] * k[1][0]
disc = max(tr * tr - 4 * det, 0.0)
r0 = (tr + math.sqrt(disc)) / 2
if abs(k[0][1]) > 1e-12:
v = [k[0][1], r0 - k[0][0]]
elif abs(k[1][0]) > 1e-12:
v = [r0 - k[1][1], k[1][0]]
else:
v = [1.0, 0.0] if k[0][0] >= k[1][1] else [0.0, 1.0]
lead = 0 if abs(v[0]) >= abs(v[1]) else 1
return [[round(x, 6) for row in k for x in row], round(r0, 6), lead]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None)],
[('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0])],
[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('regression: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('regression: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None)]]
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: children and adults | [[2.666667, 0.666667, 1.555556, 3.111111], 3.931204, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Failed |
| regression: asymmetric core group | [[1.6, 0.08, 3.6, 1.08], 1.936322, 1] | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | Failed |
| control: decoupled equal groups tie | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | Passed |
| control: decoupled first dominant smaller group | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | Passed |
| control: decoupled second dominant | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | Passed |
| regression: one-way coupling | [[0.666667, 0.0, 5.333333, 4.0], 4.0, 1] | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | Failed |
| control: empty population | None | None | Passed |
SHA-256 / be491ae6746ddca10c5ddee220f25d1f83dd1bc32a1ab08277eb82254effd4c6
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(contact, sizes, gamma):
total = sum(sizes)
if total <= 0 or min(gamma) <= 0:
return None
k = [[contact[i][j] * sizes[i] / total / gamma[j] for j in range(2)] for i in range(2)]
tr = k[0][0] + k[1][1]
det = k[0][0] * k[1][1] - k[0][1] * k[1][0]
disc = max(tr * tr - 4 * det, 0.0)
r0 = (tr + math.sqrt(disc)) / 2
if abs(k[0][1]) > 1e-12:
v = [k[0][1], r0 - k[0][0]]
elif abs(k[1][0]) > 1e-12:
v = [r0 - k[1][1], k[1][0]]
else:
v = [1.0, 0.0] if k[0][0] >= k[1][1] else [0.0, 1.0]
lead = 0 if abs(v[0]) >= abs(v[1]) else 1
return [[round(x, 6) for row in k for x in row], round(r0, 6), lead]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None)],
[('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0])],
[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None),
('control: homogeneous mixing',
([[1.2, 1.2], [1.2, 1.2]], [250, 750], [0.4, 0.4]),
[[0.75, 0.75, 2.25, 2.25], 3.0, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('regression: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('regression: children and adults',
([[2.0, 0.5], [0.5, 1.0]], [300, 700], [0.25, 0.2]),
[[2.4, 0.75, 1.4, 3.5], 4.11297, 1]),
('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: unequal recovery',
([[0.8, 0.6], [0.3, 0.9]], [600, 400], [0.1, 0.5]),
[[4.8, 0.72, 1.2, 0.72], 5.001785, 0]),
('regression: only cross contacts',
([[0.0, 2.0], [1.0, 0.0]], [300, 300], [0.25, 0.5]),
[[0.0, 2.0, 2.0, 0.0], 2.0, 0])],
[('regression: asymmetric core group',
([[4.0, 0.2], [1.0, 0.3]], [100, 900], [0.3, 0.2]),
[[1.333333, 0.1, 3.0, 1.35], 1.889453, 1]),
('control: decoupled equal groups tie',
([[1.0, 0.0], [0.0, 1.0]], [500, 500], [0.5, 0.5]),
[[1.0, 0.0, 0.0, 1.0], 1.0, 0]),
('control: decoupled first dominant smaller group',
([[3.0, 0.0], [0.0, 0.5]], [300, 700], [0.5, 0.5]),
[[1.8, 0.0, 0.0, 0.7], 1.8, 0]),
('control: decoupled second dominant',
([[0.5, 0.0], [0.0, 3.0]], [400, 600], [0.5, 0.5]),
[[0.4, 0.0, 0.0, 3.6], 3.6, 1]),
('regression: one-way coupling',
([[1.0, 0.0], [2.0, 1.5]], [200, 800], [0.2, 0.4]),
[[1.0, 0.0, 8.0, 3.0], 3.0, 1]),
('control: empty population', ([[1.0, 1.0], [1.0, 1.0]], [0, 0], [0.2, 0.2]), None),
('control: invalid gamma', ([[1.0, 1.0], [1.0, 1.0]], [10, 10], [0.0, 0.2]), None)]]
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: children and adults | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Passed |
| regression: asymmetric core group | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | [[1.333333, 0.1, 3.0, 1.35], 1.889453, 1] | Passed |
| control: decoupled equal groups tie | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | [[1.0, 0.0, 0.0, 1.0], 1.0, 0] | Passed |
| control: decoupled first dominant smaller group | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | [[1.8, 0.0, 0.0, 0.7], 1.8, 0] | Passed |
| control: decoupled second dominant | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | [[0.4, 0.0, 0.0, 3.6], 3.6, 1] | Passed |
| regression: one-way coupling | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | [[1.0, 0.0, 8.0, 3.0], 3.0, 1] | Passed |
| control: empty population | None | None | Passed |
SHA-256 / 0e516881940d9fa795dfbea113b15f6e1b8d49cd0ce652b19e9bb76e118e9ed6
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 2026-09-29T14:47:30.084310+00:00.
Case digest / 91a3fcc8ae8ff4020617349e0867dc3073dec7d330bb300492f350efe5e64de8