FA-64991 / Epidemic compartment models / Open access

SIS endemic equilibrium convergence: tolerance scaling · case 01

Convergence takes far longer than required and often hits the day cap.

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

ROOT CAUSE

The relative tolerance is compared as an absolute number of people.

THE FAILURE

The relative tolerance is compared as an absolute number of people.

Unsuccessful approach: Scaling tolerance by the target makes a zero target unreachable.

Case contract

SIS with susceptibles pop-I; endemic target pop*(1-1/R0) if R0=beta/gamma>1 else 0; iterate daily Euler I += beta*I*(pop-I)/pop - gamma*I until |I-target| <= tol*pop or max_days steps; return [target rounded 4, days taken, I rounded 4] or None for non-positive beta, gamma or pop.

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, tol, max_days):
    if beta <= 0 or gamma <= 0 or pop <= 0:
        return None
    r0 = beta / gamma
    target = pop * (1 - 1 / r0) if r0 > 1 else 0.0
    i = float(i0)
    day = 0
    while abs(i - target) > tol and day < max_days:
        i += beta * i * (pop - i) / pop - gamma * i
        day += 1
    return [round(target, 4), day, round(i, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('regression: subcritical dies out', (0.1, 0.2, 500, 50, 0.01, 200), [0.0, 21, 4.9755]),
  ('regression: start above equilibrium', (0.4, 0.2, 1000, 900, 0.005, 100), [500.0, 17, 504.3274]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None)],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None),
  ('regression: fast dynamics', (0.9, 0.3, 300, 3, 0.02, 100), [200.0, 14, 197.4596]),
  ('control: near threshold', (0.21, 0.2, 10000, 100, 0.001, 60), [476.1905, 60, 155.2383])],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('regression: subcritical dies out', (0.1, 0.2, 500, 50, 0.01, 200), [0.0, 21, 4.9755]),
  ('regression: start above equilibrium', (0.4, 0.2, 1000, 900, 0.005, 100), [500.0, 17, 504.3274]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None),
  ('regression: fast dynamics', (0.9, 0.3, 300, 3, 0.02, 100), [200.0, 14, 197.4596]),
  ('control: near threshold', (0.21, 0.2, 10000, 100, 0.001, 60), [476.1905, 60, 155.2383])],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('regression: subcritical dies out', (0.1, 0.2, 500, 50, 0.01, 200), [0.0, 21, 4.9755]),
  ('regression: start above equilibrium', (0.4, 0.2, 1000, 900, 0.005, 100), [500.0, 17, 504.3274]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None)],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None),
  ('regression: fast dynamics', (0.9, 0.3, 300, 3, 0.02, 100), [200.0, 14, 197.4596]),
  ('control: near threshold', (0.21, 0.2, 10000, 100, 0.001, 60), [476.1905, 60, 155.2383])]]
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: gonorrhoea-like endemic	`[666.6667, 73, 666.657]`	`[666.6667, 42, 657.0888]`	Failed
regression: subcritical dies out	`[0.0, 80, 0.0098]`	`[0.0, 21, 4.9755]`	Failed
regression: start above equilibrium	`[500.0, 48, 500.0042]`	`[500.0, 17, 504.3274]`	Failed
control: already at equilibrium	`[500.0, 0, 500.0]`	`[500.0, 0, 500.0]`	Passed
control: tight tolerance capped	`[400.0, 30, 4.288]`	`[400.0, 30, 4.288]`	Passed
control: zero day cap	`[66.6667, 0, 1.0]`	`[66.6667, 0, 1.0]`	Passed
control: invalid gamma	`None`	`None`	Passed

SHA-256 / 9655ddbeff8b976d15fb524bb8b66c2cc08ac7c0353cf997c38656818c618762

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, tol, max_days):
    if beta <= 0 or gamma <= 0 or pop <= 0:
        return None
    r0 = beta / gamma
    target = pop * (1 - 1 / r0) if r0 > 1 else 0.0
    i = float(i0)
    day = 0
    while abs(i - target) > tol * target and day < max_days:
        i += beta * i * (pop - i) / pop - gamma * i
        day += 1
    return [round(target, 4), day, round(i, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('regression: subcritical dies out', (0.1, 0.2, 500, 50, 0.01, 200), [0.0, 21, 4.9755]),
  ('regression: start above equilibrium', (0.4, 0.2, 1000, 900, 0.005, 100), [500.0, 17, 504.3274]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None)],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None),
  ('regression: fast dynamics', (0.9, 0.3, 300, 3, 0.02, 100), [200.0, 14, 197.4596]),
  ('control: near threshold', (0.21, 0.2, 10000, 100, 0.001, 60), [476.1905, 60, 155.2383])],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('regression: subcritical dies out', (0.1, 0.2, 500, 50, 0.01, 200), [0.0, 21, 4.9755]),
  ('regression: start above equilibrium', (0.4, 0.2, 1000, 900, 0.005, 100), [500.0, 17, 504.3274]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None),
  ('regression: fast dynamics', (0.9, 0.3, 300, 3, 0.02, 100), [200.0, 14, 197.4596]),
  ('control: near threshold', (0.21, 0.2, 10000, 100, 0.001, 60), [476.1905, 60, 155.2383])],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('regression: subcritical dies out', (0.1, 0.2, 500, 50, 0.01, 200), [0.0, 21, 4.9755]),
  ('regression: start above equilibrium', (0.4, 0.2, 1000, 900, 0.005, 100), [500.0, 17, 504.3274]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None)],
 [('regression: gonorrhoea-like endemic', (0.3, 0.1, 1000, 10, 0.01, 200), [666.6667, 42, 657.0888]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('control: tight tolerance capped', (0.25, 0.2, 2000, 1, 0.0001, 30), [400.0, 30, 4.288]),
  ('control: zero day cap', (0.3, 0.1, 100, 1, 0.01, 0), [66.6667, 0, 1.0]),
  ('control: invalid gamma', (0.3, 0.0, 100, 1, 0.01, 10), None),
  ('regression: fast dynamics', (0.9, 0.3, 300, 3, 0.02, 100), [200.0, 14, 197.4596]),
  ('control: near threshold', (0.21, 0.2, 10000, 100, 0.001, 60), [476.1905, 60, 155.2383])]]
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: gonorrhoea-like endemic	`[666.6667, 44, 660.4971]`	`[666.6667, 42, 657.0888]`	Failed
regression: subcritical dies out	`[0.0, 200, 0.0]`	`[0.0, 21, 4.9755]`	Failed
regression: start above equilibrium	`[500.0, 20, 502.204]`	`[500.0, 17, 504.3274]`	Failed
control: already at equilibrium	`[500.0, 0, 500.0]`	`[500.0, 0, 500.0]`	Passed
control: tight tolerance capped	`[400.0, 30, 4.288]`	`[400.0, 30, 4.288]`	Passed
control: zero day cap	`[66.6667, 0, 1.0]`	`[66.6667, 0, 1.0]`	Passed
control: invalid gamma	`None`	`None`	Passed

SHA-256 / e42639d04a3432902f6d16cc87d760c1030197444f6c5b6ca3b692b262a1e864

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:47:29.971357+00:00.

Case digest / 36c3f53c9e2e1da579031d07003de19a2a1c4f3607532fb89241d4ebf866a4df