{"abstract":"Small age bands receive inflated force of infection from large ones.","category":"Epidemic compartment models","checks":7,"contract":"lambda[a] = beta*susceptibility[a]*sum_b contacts[a][b]*infected[b]/sizes[b] (groups with zero size skipped); expected new infections susceptible[a]*(1-exp(-lambda[a])); return [lambdas rounded 6, new infections rounded 4, total rounded 4].","evaluation_group":"w2-epidemic-age-foi","failed_approach":"Dividing by the total population dilutes group-specific prevalence.","family":"w2-epidemic-age-foi-prevalence-denominator","id":"FA-65096","implementations":{"attempt":{"sha256":"fd14871efea6ab0086371120640008c6dd8a932a4d8ca1712c996e2dafb104de","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(beta, contacts, sizes, infected, susceptible, susceptibility):\n    g = len(sizes)\n    lam = []\n    for a in range(g):\n        pressure = 0.0\n        for b in range(g):\n            if sizes[b] > 0:\n                pressure += contacts[a][b] * infected[b] / sum(sizes)\n        lam.append(beta * susceptibility[a] * pressure)\n    new = [susceptible[a] * (1 - math.exp(-lam[a])) for a in range(g)]\n    return [[round(x, 6) for x in lam], [round(x, 4) for x in new], round(sum(new), 4)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"d9bfd4815c0da46e4e6561d1ead401e87aa40a6881d351f8beee206c893c94bb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(beta, contacts, sizes, infected, susceptible, susceptibility):\n    g = len(sizes)\n    lam = []\n    for a in range(g):\n        pressure = 0.0\n        for b in range(g):\n            if sizes[b] > 0:\n                pressure += contacts[a][b] * infected[b] / sizes[a]\n        lam.append(beta * susceptibility[a] * pressure)\n    new = [susceptible[a] * (1 - math.exp(-lam[a])) for a in range(g)]\n    return [[round(x, 6) for x in lam], [round(x, 4) for x in new], round(sum(new), 4)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"583941a7a400cbd8aef032786310a5b8ec2fbf9427b7c61628dc95c258842424","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(beta, contacts, sizes, infected, susceptible, susceptibility):\n    g = len(sizes)\n    lam = []\n    for a in range(g):\n        pressure = 0.0\n        for b in range(g):\n            if sizes[b] > 0:\n                pressure += contacts[a][b] * infected[b] / sizes[b]\n        lam.append(beta * susceptibility[a] * pressure)\n    new = [susceptible[a] * (1 - math.exp(-lam[a])) for a in range(g)]\n    return [[round(x, 6) for x in lam], [round(x, 4) for x in new], round(sum(new), 4)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])],\n [('regression: three age bands',\n   (0.05, [[10, 3, 1], [3, 8, 2], [1, 2, 4]], [200, 500, 300], [5, 20, 3], [180, 450, 290], [1.0, 0.8, 1.2]),\n   [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081]),\n  ('regression: asymmetric school contacts',\n   (0.1, [[12, 2], [5, 6]], [300, 700], [10, 5], [280, 690], [1.0, 1.0]),\n   [[0.041429, 0.020952], [11.363, 14.3067], 25.6697]),\n  ('control: no infection',\n   (0.3, [[4, 1], [1, 4]], [100, 100], [0, 0], [100, 100], [1.0, 1.0]),\n   [[0.0, 0.0], [0.0, 0.0], 0.0]),\n  ('regression: high pressure saturates',\n   (2.0, [[20, 5], [5, 20]], [50, 50], [30, 25], [20, 25], [1.0, 1.0]),\n   [[29.0, 26.0], [20.0, 25.0], 45.0]),\n  ('control: single group', (0.1, [[7]], [1000], [50], [900], [0.9]), [[0.0315], [27.9081], 27.9081]),\n  ('regression: reduced child susceptibility',\n   (0.08, [[15, 4], [2, 7]], [400, 600], [2, 30], [390, 550], [0.5, 1.0]),\n   [[0.011, 0.0288], [4.2665, 15.6141], 19.8806]),\n  ('regression: unequal sizes',\n   (0.04, [[6, 6], [1, 3]], [50, 950], [5, 5], [40, 900], [1.0, 1.3]),\n   [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005])]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-epidemic-age-foi-prevalence-denominator","generated_at":"2026-09-29T14:47:30.779164+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Compartmental epidemic calculations drive outbreak forecasts, vaccine targets and hospital planning; a single wrong flow, rate conversion or boundary silently changes every downstream number.","repair":"Restore the prevalence denominator rule: `infected[b] / sizes[b]`.","root_cause":"Prevalence in the infector group is divided by the infectee group size.","sha256":"863afda0a06bec6e815e8a4581c523b116c587f29457faecf58ff4d5351978c8","title":"Age-structured force of infection: prevalence denominator · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.629,"exit_code":1,"observations":[{"actual":[[0.00565,0.00724,0.00342],[1.0141,3.2462,0.9901],5.2505],"check":"regression: three age bands","expected":[[0.019,0.0166,0.0087],[3.3877,7.4083,2.5121],13.3081],"passed":false},{"actual":[[0.013,0.008],[3.6164,5.498],9.1144],"check":"regression: asymmetric school contacts","expected":[[0.041429,0.020952],[11.363,14.3067],25.6697],"passed":false},{"actual":[[0.0,0.0],[0.0,0.0],0.0],"check":"control: no infection","expected":[[0.0,0.0],[0.0,0.0],0.0],"passed":true},{"actual":[[14.5,13.0],[20.0,24.9999],44.9999],"check":"regression: high pressure saturates","expected":[[29.0,26.0],[20.0,25.0],45.0],"passed":false},{"actual":[[0.0315],[27.9081],27.9081],"check":"control: single group","expected":[[0.0315],[27.9081],27.9081],"passed":true},{"actual":[[0.006,0.01712],[2.333,9.3359],11.6689],"check":"regression: reduced child susceptibility","expected":[[0.011,0.0288],[4.2665,15.6141],19.8806],"passed":false},{"actual":[[0.0024,0.00104],[0.0959,0.9355],1.0314],"check":"regression: unequal sizes","expected":[[0.025263,0.006021],[0.9979,5.4027],6.4005],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: three age bands\", \"actual\": [[0.00565, 0.00724, 0.00342], [1.0141, 3.2462, 0.9901], 5.2505], \"expected\": [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081], \"passed\": false}, {\"check\": \"regression: asymmetric school contacts\", \"actual\": [[0.013, 0.008], [3.6164, 5.498], 9.1144], \"expected\": [[0.041429, 0.020952], [11.363, 14.3067], 25.6697], \"passed\": false}, {\"check\": \"control: no infection\", \"actual\": [[0.0, 0.0], [0.0, 0.0], 0.0], \"expected\": [[0.0, 0.0], [0.0, 0.0], 0.0], \"passed\": true}, {\"check\": \"regression: high pressure saturates\", \"actual\": [[14.5, 13.0], [20.0, 24.9999], 44.9999], \"expected\": [[29.0, 26.0], [20.0, 25.0], 45.0], \"passed\": false}, {\"check\": \"control: single group\", \"actual\": [[0.0315], [27.9081], 27.9081], \"expected\": [[0.0315], [27.9081], 27.9081], \"passed\": true}, {\"check\": \"regression: reduced child susceptibility\", \"actual\": [[0.006, 0.01712], [2.333, 9.3359], 11.6689], \"expected\": [[0.011, 0.0288], [4.2665, 15.6141], 19.8806], \"passed\": false}, {\"check\": \"regression: unequal sizes\", \"actual\": [[0.0024, 0.00104], [0.0959, 0.9355], 1.0314], \"expected\": [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.784,"exit_code":1,"observations":[{"actual":[[0.02825,0.01448,0.0114],[5.0138,6.4691,3.2872],14.7701],"check":"regression: three age bands","expected":[[0.019,0.0166,0.0087],[3.3877,7.4083,2.5121],13.3081],"passed":false},{"actual":[[0.043333,0.011429],[11.8742,7.8408],19.715],"check":"regression: asymmetric school contacts","expected":[[0.041429,0.020952],[11.363,14.3067],25.6697],"passed":false},{"actual":[[0.0,0.0],[0.0,0.0],0.0],"check":"control: no infection","expected":[[0.0,0.0],[0.0,0.0],0.0],"passed":true},{"actual":[[29.0,26.0],[20.0,25.0],45.0],"check":"regression: high pressure saturates","expected":[[29.0,26.0],[20.0,25.0],45.0],"passed":true},{"actual":[[0.0315],[27.9081],27.9081],"check":"control: single group","expected":[[0.0315],[27.9081],27.9081],"passed":true},{"actual":[[0.015,0.028533],[5.8063,15.4716],21.2779],"check":"regression: reduced child susceptibility","expected":[[0.011,0.0288],[4.2665,15.6141],19.8806],"passed":false},{"actual":[[0.048,0.001095],[1.8746,0.9847],2.8594],"check":"regression: unequal sizes","expected":[[0.025263,0.006021],[0.9979,5.4027],6.4005],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: three age bands\", \"actual\": [[0.02825, 0.01448, 0.0114], [5.0138, 6.4691, 3.2872], 14.7701], \"expected\": [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081], \"passed\": false}, {\"check\": \"regression: asymmetric school contacts\", \"actual\": [[0.043333, 0.011429], [11.8742, 7.8408], 19.715], \"expected\": [[0.041429, 0.020952], [11.363, 14.3067], 25.6697], \"passed\": false}, {\"check\": \"control: no infection\", \"actual\": [[0.0, 0.0], [0.0, 0.0], 0.0], \"expected\": [[0.0, 0.0], [0.0, 0.0], 0.0], \"passed\": true}, {\"check\": \"regression: high pressure saturates\", \"actual\": [[29.0, 26.0], [20.0, 25.0], 45.0], \"expected\": [[29.0, 26.0], [20.0, 25.0], 45.0], \"passed\": true}, {\"check\": \"control: single group\", \"actual\": [[0.0315], [27.9081], 27.9081], \"expected\": [[0.0315], [27.9081], 27.9081], \"passed\": true}, {\"check\": \"regression: reduced child susceptibility\", \"actual\": [[0.015, 0.028533], [5.8063, 15.4716], 21.2779], \"expected\": [[0.011, 0.0288], [4.2665, 15.6141], 19.8806], \"passed\": false}, {\"check\": \"regression: unequal sizes\", \"actual\": [[0.048, 0.001095], [1.8746, 0.9847], 2.8594], \"expected\": [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.576,"exit_code":0,"observations":[{"actual":[[0.019,0.0166,0.0087],[3.3877,7.4083,2.5121],13.3081],"check":"regression: three age bands","expected":[[0.019,0.0166,0.0087],[3.3877,7.4083,2.5121],13.3081],"passed":true},{"actual":[[0.041429,0.020952],[11.363,14.3067],25.6697],"check":"regression: asymmetric school contacts","expected":[[0.041429,0.020952],[11.363,14.3067],25.6697],"passed":true},{"actual":[[0.0,0.0],[0.0,0.0],0.0],"check":"control: no infection","expected":[[0.0,0.0],[0.0,0.0],0.0],"passed":true},{"actual":[[29.0,26.0],[20.0,25.0],45.0],"check":"regression: high pressure saturates","expected":[[29.0,26.0],[20.0,25.0],45.0],"passed":true},{"actual":[[0.0315],[27.9081],27.9081],"check":"control: single group","expected":[[0.0315],[27.9081],27.9081],"passed":true},{"actual":[[0.011,0.0288],[4.2665,15.6141],19.8806],"check":"regression: reduced child susceptibility","expected":[[0.011,0.0288],[4.2665,15.6141],19.8806],"passed":true},{"actual":[[0.025263,0.006021],[0.9979,5.4027],6.4005],"check":"regression: unequal sizes","expected":[[0.025263,0.006021],[0.9979,5.4027],6.4005],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: three age bands\", \"actual\": [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081], \"expected\": [[0.019, 0.0166, 0.0087], [3.3877, 7.4083, 2.5121], 13.3081], \"passed\": true}, {\"check\": \"regression: asymmetric school contacts\", \"actual\": [[0.041429, 0.020952], [11.363, 14.3067], 25.6697], \"expected\": [[0.041429, 0.020952], [11.363, 14.3067], 25.6697], \"passed\": true}, {\"check\": \"control: no infection\", \"actual\": [[0.0, 0.0], [0.0, 0.0], 0.0], \"expected\": [[0.0, 0.0], [0.0, 0.0], 0.0], \"passed\": true}, {\"check\": \"regression: high pressure saturates\", \"actual\": [[29.0, 26.0], [20.0, 25.0], 45.0], \"expected\": [[29.0, 26.0], [20.0, 25.0], 45.0], \"passed\": true}, {\"check\": \"control: single group\", \"actual\": [[0.0315], [27.9081], 27.9081], \"expected\": [[0.0315], [27.9081], 27.9081], \"passed\": true}, {\"check\": \"regression: reduced child susceptibility\", \"actual\": [[0.011, 0.0288], [4.2665, 15.6141], 19.8806], \"expected\": [[0.011, 0.0288], [4.2665, 15.6141], 19.8806], \"passed\": true}, {\"check\": \"regression: unequal sizes\", \"actual\": [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005], \"expected\": [[0.025263, 0.006021], [0.9979, 5.4027], 6.4005], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}