FA-65071 / Epidemic compartment models / Open access

SIR with daily all-or-nothing vaccination campaign: efficacy application · case 01

Vaccine failures vanish from the population.

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

ROOT CAUSE

All vaccinees leave S although only effective doses move to V.

VERIFIED REPAIR

Restore the efficacy application rule: `s -= dose * efficacy`.

Unsuccessful approach: Removing the failure fraction from S inverts the all-or-nothing rule.

Case contract

Each day from day index start_day (inclusive), dose=min(doses_per_day, S) is given to susceptibles before transmission; dose*efficacy moves S->V; failed vaccinees stay in S; mixing uses the full pop; return [S, I, R, V, doses administered] rounded to 3.

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(beta, gamma, pop, i0, doses_per_day, start_day, efficacy, days):
    s, i, r, v = float(pop - i0), float(i0), 0.0, 0.0
    given = 0.0
    for day in range(days):
        if day >= start_day:
            dose = min(doses_per_day, s)
            s -= dose
            v += dose * efficacy
            given += dose
        inf = beta * s * i / pop
        rec = gamma * i
        s -= inf
        i += inf - rec
        r += rec
    return [round(s, 3), round(i, 3), round(r, 3), round(v, 3), round(given, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])]]
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: city campaign from day 5	`[3671.765, 262.702, 1065.533, 4500.0, 5000.0]`	`[4007.174, 324.024, 1168.803, 4500.0, 5000.0]`	Failed
regression: campaign from day 0	`[742.245, 52.578, 205.177, 800.0, 1000.0]`	`[872.113, 79.727, 248.159, 800.0, 1000.0]`	Failed
regression: supply exceeds susceptibles	`[0.0, 1.492, 1.221, 92.423, 97.287]`	`[0.0, 1.516, 1.233, 97.251, 102.369]`	Failed
control: late campaign never starts	`[777.374, 141.242, 81.385, 0.0, 0.0]`	`[777.374, 141.242, 81.385, 0.0, 0.0]`	Passed
regression: perfect vaccine small town	`[0.0, 10.271, 55.609, 434.12, 434.12]`	`[0.0, 10.271, 55.609, 434.12, 434.12]`	Passed
regression: poor vaccine	`[0.0, 51.345, 515.176, 973.392, 2433.479]`	`[237.471, 307.647, 1134.882, 1320.0, 3300.0]`	Failed
control: no doses	`[896.73, 54.094, 49.176, 0.0, 0.0]`	`[896.73, 54.094, 49.176, 0.0, 0.0]`	Passed

SHA-256 / 1a35cb629789ece00b9d4c4a619ae082f87b6382122c7f6f05fdaf0c9d828234

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(beta, gamma, pop, i0, doses_per_day, start_day, efficacy, days):
    s, i, r, v = float(pop - i0), float(i0), 0.0, 0.0
    given = 0.0
    for day in range(days):
        if day >= start_day:
            dose = min(doses_per_day, s)
            s -= dose * (1 - efficacy)
            v += dose * efficacy
            given += dose
        inf = beta * s * i / pop
        rec = gamma * i
        s -= inf
        i += inf - rec
        r += rec
    return [round(s, 3), round(i, 3), round(r, 3), round(v, 3), round(given, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])]]
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: city campaign from day 5	`[5595.024, 1353.148, 2551.827, 4500.0, 5000.0]`	`[4007.174, 324.024, 1168.803, 4500.0, 5000.0]`	Failed
regression: campaign from day 0	`[1116.656, 234.664, 448.679, 800.0, 1000.0]`	`[872.113, 79.727, 248.159, 800.0, 1000.0]`	Failed
regression: supply exceeds susceptibles	`[73.391, 4.837, 1.859, 378.352, 398.265]`	`[0.0, 1.516, 1.233, 97.251, 102.369]`	Failed
control: late campaign never starts	`[777.374, 141.242, 81.385, 0.0, 0.0]`	`[777.374, 141.242, 81.385, 0.0, 0.0]`	Passed
regression: perfect vaccine small town	`[141.969, 164.262, 193.769, 520.0, 520.0]`	`[0.0, 10.271, 55.609, 434.12, 434.12]`	Failed
regression: poor vaccine	`[32.671, 166.064, 860.79, 1293.651, 3234.127]`	`[237.471, 307.647, 1134.882, 1320.0, 3300.0]`	Failed
control: no doses	`[896.73, 54.094, 49.176, 0.0, 0.0]`	`[896.73, 54.094, 49.176, 0.0, 0.0]`	Passed

SHA-256 / e069dc0617370a3836131c3e32c5713e31faddceaeff5aa0f0e366ec8f2e210c

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(beta, gamma, pop, i0, doses_per_day, start_day, efficacy, days):
    s, i, r, v = float(pop - i0), float(i0), 0.0, 0.0
    given = 0.0
    for day in range(days):
        if day >= start_day:
            dose = min(doses_per_day, s)
            s -= dose * efficacy
            v += dose * efficacy
            given += dose
        inf = beta * s * i / pop
        rec = gamma * i
        s -= inf
        i += inf - rec
        r += rec
    return [round(s, 3), round(i, 3), round(r, 3), round(v, 3), round(given, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('regression: supply exceeds susceptibles',
   (0.3, 0.1, 100, 2, 80, 1, 0.95, 6),
   [0.0, 1.516, 1.233, 97.251, 102.369]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])],
 [('regression: city campaign from day 5',
   (0.4, 0.2, 10000, 20, 200, 5, 0.9, 30),
   [4007.174, 324.024, 1168.803, 4500.0, 5000.0]),
  ('regression: campaign from day 0',
   (0.5, 0.25, 2000, 10, 50, 0, 0.8, 20),
   [872.113, 79.727, 248.159, 800.0, 1000.0]),
  ('control: late campaign never starts',
   (0.3, 0.1, 1000, 5, 100, 50, 0.9, 20),
   [777.374, 141.242, 81.385, 0.0, 0.0]),
  ('regression: perfect vaccine small town',
   (0.6, 0.2, 500, 5, 40, 2, 1.0, 15),
   [0.0, 10.271, 55.609, 434.12, 434.12]),
  ('regression: poor vaccine',
   (0.45, 0.15, 3000, 30, 150, 3, 0.4, 25),
   [237.471, 307.647, 1134.882, 1320.0, 3300.0]),
  ('control: no doses', (0.4, 0.2, 1000, 10, 0, 0, 0.9, 10), [896.73, 54.094, 49.176, 0.0, 0.0]),
  ('regression: start day one', (0.35, 0.1, 800, 4, 30, 1, 0.7, 12), [519.85, 32.463, 16.687, 231.0, 330.0])]]
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: city campaign from day 5	`[4007.174, 324.024, 1168.803, 4500.0, 5000.0]`	`[4007.174, 324.024, 1168.803, 4500.0, 5000.0]`	Passed
regression: campaign from day 0	`[872.113, 79.727, 248.159, 800.0, 1000.0]`	`[872.113, 79.727, 248.159, 800.0, 1000.0]`	Passed
regression: supply exceeds susceptibles	`[0.0, 1.516, 1.233, 97.251, 102.369]`	`[0.0, 1.516, 1.233, 97.251, 102.369]`	Passed
control: late campaign never starts	`[777.374, 141.242, 81.385, 0.0, 0.0]`	`[777.374, 141.242, 81.385, 0.0, 0.0]`	Passed
regression: perfect vaccine small town	`[0.0, 10.271, 55.609, 434.12, 434.12]`	`[0.0, 10.271, 55.609, 434.12, 434.12]`	Passed
regression: poor vaccine	`[237.471, 307.647, 1134.882, 1320.0, 3300.0]`	`[237.471, 307.647, 1134.882, 1320.0, 3300.0]`	Passed
control: no doses	`[896.73, 54.094, 49.176, 0.0, 0.0]`	`[896.73, 54.094, 49.176, 0.0, 0.0]`	Passed

SHA-256 / a8f168ad0533278fef5a4231d60edd19c88f20da1fd4fe9e504a20593a3e33e8

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 2026-09-29T14:47:30.713542+00:00.

Case digest / 862ca4205fc3c46ed2f7a46333717fa43a6f76751f5630a33d30a9ee08e62f2a