FA-65016 / Epidemic compartment models / Open access
Two-group next-generation matrix R0: determinant sign · case 01
Strong cross-coupling lowers R0 instead of raising it.
ROOT CAUSE
The off-diagonal product is added to the determinant.
VERIFIED REPAIR
Restore the determinant sign rule: `det = k[0][0] * k[1][1] - k[0][1] * k[1][0]`.
Unsuccessful approach: Assuming a symmetric K squares one off-diagonal entry.
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[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]),
('control: 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]),
('control: 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),
('regression: 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]),
('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: 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),
('regression: 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]),
('control: 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),
('regression: 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])]]
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], 2.95, 0] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Failed |
| regression: asymmetric core group | [[1.333333, 0.1, 3.0, 1.35], 1.341667, 0] | [[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 |
| control: 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 / 349a7cfad3d4349e6c61d4f842b265fbe89ba580b7f3eb208b9534f8bcbcc813
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[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[0][1]
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]),
('control: 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]),
('control: 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),
('regression: 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]),
('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: 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),
('regression: 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]),
('control: 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),
('regression: 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])]]
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], 3.880054, 1] | [[2.4, 0.75, 1.4, 3.5], 4.11297, 1] | Failed |
| regression: asymmetric core group | [[1.333333, 0.1, 3.0, 1.35], 1.442013, 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 |
| control: 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 / 5dea4a66ee3f5f2b2f063d8cc0c6718709a47daca2d6bcafb08d4caae2ca8c07
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]),
('control: 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]),
('control: 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),
('regression: 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]),
('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: 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),
('regression: 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]),
('control: 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),
('regression: 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])]]
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 |
| control: 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 / 9a50640595744f3552f66b7e2b1927445d01446031d7b5a5b142b87aef69ab02
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 2026-09-29T14:47:30.089316+00:00.
Case digest / e24eb23b9cb02099fd472513bf2c3fc726b6ca671baace64cb0ac5adea683dfa