FA-64986 / Epidemic compartment models / Open access

SIS endemic equilibrium convergence: susceptible depletion · case 01

Prevalence grows exponentially without saturating.

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

ROOT CAUSE

Transmission ignores that only pop-I people are susceptible.

THE FAILURE

Transmission ignores that only pop-I people are susceptible.

Unsuccessful approach: Using the initial susceptible count freezes depletion at the seed level.

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 * pop and day < max_days:
        i += beta * i - 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]),
  ('regression: 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]),
  ('regression: 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]),
  ('regression: 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]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('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]),
  ('regression: 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]),
  ('regression: 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]),
  ('regression: 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]),
  ('regression: 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, 23, 662.4737]`	`[666.6667, 42, 657.0888]`	Failed
regression: subcritical dies out	`[0.0, 22, 4.9239]`	`[0.0, 21, 4.9755]`	Failed
regression: start above equilibrium	`[500.0, 100, 74536177069.8131]`	`[500.0, 17, 504.3274]`	Failed
control: already at equilibrium	`[500.0, 0, 500.0]`	`[500.0, 0, 500.0]`	Passed
regression: tight tolerance capped	`[400.0, 30, 4.3219]`	`[400.0, 30, 4.288]`	Failed
control: zero day cap	`[66.6667, 0, 1.0]`	`[66.6667, 0, 1.0]`	Passed
control: invalid gamma	`None`	`None`	Passed

SHA-256 / 84de6982d423088204e181f1dcc08eb1f11c18fcbc505f67c4331d3cbc6136a8

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 * pop and day < max_days:
        i += beta * i * (pop - i0) / 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]),
  ('regression: 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]),
  ('regression: 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]),
  ('regression: 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]),
  ('control: already at equilibrium', (0.4, 0.2, 1000, 500, 0.01, 50), [500.0, 0, 500.0]),
  ('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]),
  ('regression: 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]),
  ('regression: 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]),
  ('regression: 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]),
  ('regression: 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, 200, 4.157479163375589e+16]`	`[666.6667, 42, 657.0888]`	Failed
regression: subcritical dies out	`[0.0, 20, 4.8615]`	`[0.0, 21, 4.9755]`	Failed
regression: start above equilibrium	`[500.0, 100, 0.0]`	`[500.0, 17, 504.3274]`	Failed
control: already at equilibrium	`[500.0, 0, 500.0]`	`[500.0, 0, 500.0]`	Passed
regression: tight tolerance capped	`[400.0, 30, 4.3065]`	`[400.0, 30, 4.288]`	Failed
control: zero day cap	`[66.6667, 0, 1.0]`	`[66.6667, 0, 1.0]`	Passed
control: invalid gamma	`None`	`None`	Passed

SHA-256 / 1e621f960b060f612e6e540470ed8f9a959a6f7818bab829d3c1ee455678cb25

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 2026-09-29T14:47:29.845579+00:00.

Case digest / 7ad7216cc3f7b110199128532fa78c1feeb65e53ce4dbcce2d319ec76d3ad9e9