refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조

에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-11 11:05:56 +09:00
parent 6549ead309
commit c24165b8bc
6193 changed files with 1717 additions and 31 deletions
@@ -0,0 +1,257 @@
+---
+id: wiki-2026-0508-epidemiological-modeling
+title: Epidemiological Modeling
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [SIR model, SEIR, compartmental model, disease modeling, R0, agent-based epi]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.95
+verification_status: applied
+tags: [epidemiology, modeling, sir, public-health, simulation, forecasting, covid]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: Python
+  framework: scipy / NetworkX / Mesa / NumPyro
+---
+
+# Epidemiological Modeling
+
+## 매 한 줄
+> **"매 disease 의 population 의 spread 의 model"**. 매 SIR / SEIR (compartmental), 매 ABM (network), 매 statistical (R_t estimate). 매 R0, herd immunity, 매 NPI effect. 매 modern: 매 ML forecasting + 매 mobility data + 매 Bayesian inference.
+
+## 매 핵심
+
+### 매 compartmental
+- **SIR**: Susceptible → Infected → Recovered.
+- **SEIR**: + Exposed.
+- **SIRS**: 매 immunity 의 wane.
+- **SIRD**: + Dead.
+- **MSEIR**: + Maternal immunity.
+
+### 매 key parameter
+- **R0**: 매 basic reproduction number.
+- **R_t**: 매 effective (time-varying).
+- **β**: 매 transmission rate.
+- **γ**: 매 recovery rate.
+- **R0 = β / γ**.
+- **Herd immunity**: 매 1 - 1/R0.
+
+### 매 method
+- **ODE**: 매 mean-field, deterministic.
+- **Stochastic** (Gillespie): 매 small population.
+- **ABM**: 매 individual + network.
+- **Statistical**: 매 R_t from cases.
+- **ML / DL**: 매 forecasting.
+
+### 매 응용
+1. **Pandemic forecast**: 매 COVID, flu.
+2. **Vaccination strategy**: 매 priority.
+3. **NPI effect**: 매 lockdown, mask.
+4. **Travel ban**: 매 border.
+5. **Hospital capacity**: 매 ICU.
+6. **Animal**: 매 livestock disease.
+
+## 💻 패턴
+
+### SIR (ODE)
+```python
+import numpy as np
+from scipy.integrate import odeint
+
+def sir(state, t, beta, gamma, N):
+    S, I, R = state
+    dS = -beta * S * I / N
+    dI = beta * S * I / N - gamma * I
+    dR = gamma * I
+    return [dS, dI, dR]
+
+t = np.linspace(0, 200, 1000)
+N = 1_000_000
+sol = odeint(sir, [N - 1, 1, 0], t, args=(0.4, 0.1, N))
+```
+
+### SEIR
+```python
+def seir(state, t, beta, sigma, gamma, N):
+    S, E, I, R = state
+    dS = -beta * S * I / N
+    dE = beta * S * I / N - sigma * E
+    dI = sigma * E - gamma * I
+    dR = gamma * I
+    return [dS, dE, dI, dR]
+```
+
+### Stochastic Gillespie
+```python
+def gillespie_sir(N, I0, beta, gamma, t_max=200):
+    S, I, R = N - I0, I0, 0
+    t = 0
+    history = [(0, S, I, R)]
+    while I > 0 and t < t_max:
+        a1 = beta * S * I / N  # 매 infection rate
+        a2 = gamma * I         # 매 recovery rate
+        a0 = a1 + a2
+        if a0 == 0: break
+        tau = np.random.exponential(1 / a0)
+        t += tau
+        if np.random.rand() < a1 / a0:
+            S -= 1; I += 1
+        else:
+            I -= 1; R += 1
+        history.append((t, S, I, R))
+    return history
+```
+
+### R_t estimation (EpiEstim-style)
+```python
+def estimate_rt(case_counts, gen_time=5, window=7):
+    """매 simple Cori method approximation."""
+    rt = []
+    for t in range(window, len(case_counts)):
+        recent = case_counts[t - window:t]
+        infectees = sum(recent[-(window - i)] * np.exp(-(window - i) / gen_time) for i in range(window))
+        rt.append(case_counts[t] / max(infectees, 1))
+    return rt
+```
+
+### Network ABM (NetworkX)
+```python
+import networkx as nx
+import random
+
+def network_sir(G, beta=0.1, gamma=0.05, init_infected=5, steps=100):
+    state = {n: 'S' for n in G.nodes()}
+    for n in random.sample(list(G.nodes()), init_infected): state[n] = 'I'
+    
+    history = []
+    for _ in range(steps):
+        new_state = state.copy()
+        for n in G.nodes():
+            if state[n] == 'I':
+                if random.random() < gamma: new_state[n] = 'R'
+                for nb in G.neighbors(n):
+                    if state[nb] == 'S' and random.random() < beta:
+                        new_state[nb] = 'I'
+        state = new_state
+        history.append({'S': sum(1 for v in state.values() if v == 'S'),
+                        'I': sum(1 for v in state.values() if v == 'I'),
+                        'R': sum(1 for v in state.values() if v == 'R')})
+    return history
+
+G = nx.barabasi_albert_graph(1000, 3)
+hist = network_sir(G)
+```
+
+### Vaccination intervention
+```python
+def vaccinate(G, strategy='degree', frac=0.3):
+    n = int(G.number_of_nodes() * frac)
+    if strategy == 'degree':
+        targets = sorted(G.nodes(), key=G.degree, reverse=True)[:n]
+    elif strategy == 'random':
+        targets = random.sample(list(G.nodes()), n)
+    elif strategy == 'betweenness':
+        bc = nx.betweenness_centrality(G)
+        targets = sorted(bc, key=bc.get, reverse=True)[:n]
+    return set(targets)
+```
+
+### Bayesian SIR (NumPyro)
+```python
+import jax.numpy as jnp
+import numpyro
+import numpyro.distributions as dist
+
+def bayesian_sir(observed_cases, N):
+    beta = numpyro.sample('beta', dist.Uniform(0.1, 1.0))
+    gamma = numpyro.sample('gamma', dist.Uniform(0.05, 0.3))
+    sigma_obs = numpyro.sample('sigma', dist.HalfNormal(10))
+    
+    # 매 simulate SIR (deterministic given params)
+    predicted = simulate_sir_jax(beta, gamma, N, len(observed_cases))
+    numpyro.sample('obs', dist.Normal(predicted, sigma_obs), obs=observed_cases)
+```
+
+### Mobility-aware (commute)
+```python
+def metapopulation_sir(populations, mobility, beta, gamma):
+    """매 multi-region 의 commute matrix."""
+    n = len(populations)
+    S = populations.copy()
+    I = np.zeros(n); I[0] = 10
+    R = np.zeros(n)
+    for _ in range(200):
+        # 매 effective infectious in each region with commuters
+        I_eff = mobility @ I
+        new_I = beta * S * I_eff / populations
+        new_R = gamma * I
+        S -= new_I; I += new_I - new_R; R += new_R
+    return S, I, R
+```
+
+### NPI effect (intervention)
+```python
+def sir_with_npi(t, beta, gamma, lockdown_start, lockdown_end, lockdown_factor=0.3):
+    if lockdown_start <= t <= lockdown_end:
+        beta = beta * lockdown_factor
+    return beta, gamma
+```
+
+### Forecast (ML over compartmental)
+```python
+import xgboost as xgb
+
+def forecast_cases(history, window=14, horizon=7):
+    """매 ML residual on top of SIR."""
+    sir_pred = sir_simulate(history)
+    residuals = history - sir_pred
+    
+    X = sliding_window(residuals, window)
+    y = residuals[window:window + len(X)]
+    model = xgb.XGBRegressor().fit(X, y)
+    
+    return sir_pred[-horizon:] + model.predict(X[-1:])[:horizon]
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Quick estimate | SIR ODE |
+| Latency disease | SEIR |
+| Small outbreak | Gillespie stochastic |
+| Network spread | ABM on graph |
+| Real-time R_t | Cori / EpiEstim |
+| Forecast | Compartmental + ML residual |
+| Spatial | Metapopulation + mobility |
+
+**기본값**: 매 SEIR baseline + 매 Bayesian inference + 매 mobility data + 매 ML residual + 매 NPI scenario analysis.
+
+## 🔗 Graph
+- 변형: [[SEIR]] · [[Compartmental-Model]]
+- Adjacent: [[Bayesian Inference]]
+
+## 🤖 LLM 활용
+**언제**: 매 outbreak. 매 vaccination plan. 매 hospital capacity.
+**언제 X**: 매 individual diagnosis (different domain).
+
+## ❌ 안티패턴
+- **R0 의 over-trust**: 매 heterogeneity 의 ignore.
+- **Mean-field at small scale**: 매 stochastic 의 use.
+- **No data calibration**: 매 toy.
+- **Forecast far horizon**: 매 uncertainty 의 hide.
+- **Single model**: 매 ensemble 의 prefer.
+
+## 🧪 검증 / 중복
+- Verified (Anderson & May, Cori 2013, COVID-19 modeling literature).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-04-20 | Auto-reinforced |
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — SIR / SEIR / Gillespie / ABM / Bayes / NPI code |