{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 코로나19과 사회적 거리두기 \n", "\n", "\n", "문서이력\n", "* 작성자: 강병철 (bckang at d-if dot kr)\n", "* (2020-03-21) Nesse와 Hubbs의 자료를 근간으로 시뮬레이션 모형을 구현하였습니다.\n", "* (2020-03-22) 코로나19의 전염성에 대한 사회적 거리두기 SEIR 모델 코드를 공유합니다.\n", "* (2020-03-23) 초록을 보완했습니다.\n", "* (2020-03-24) 사회적 거리 두기의 강도에 따른 변화를 추가했습니다.\n", "\n", "배경\n", "* 코로나19의 방역을 위해서 사회적 거리 두기를 강하게 권장하고 있습니다.\n", "* 사회적 거리 두기가 어느정도의 방역 효과를 가지는지 모형을 통해서 평가합니다.\n", "\n", "내용\n", "* SEIR 모형에 대한 개요를 소개합니다(Nesse 자료 참고).\n", "* 사회적 거리 두기 모형 구현을 위해서 간략화된 SEIR 모형을 정리했습니다(Hubbs 자료 중심).\n", "* 매개 변수를 조사해서 정리했습니다(Hubbs 자료 중심).\n", "* 모형의 개요\n", " * 인구 N = 10,000 명\n", " * 인구 유입과 유출은 없음 (섬과 같은 상황)\n", " * 잠복 기간의 역수 $\\alpha = \\frac{1}{t_{incubation}} = 0.2$\n", " * 인구의 평균 접촉 속도 $\\beta = 1.75$\n", " * 평균 감염 기간의 역수 $\\gamma = \\frac{1}{t_{infectious}} = 0.5$\n", " * 사회적 거리 두기 $\\rho = 0.8$\n", "* 불필요한 오해가 없도록 실제 특정 국가를 상정하지 않고, 사회적 거리 두기의 상대적 효과만 보았습니다.\n", "* 간단한 모형으로 감염병의 전파 시뮬레이션을 코로나19에 적용했습니다.\n", "\n", "토론\n", "* 20% 정도의 사회적 거리 두기($\\rho$=0.8)가 성공해도 방역에는 상당한 효과가 있을 것으로 계산됩니다.\n", "* 70% 정도의 사회적 거리 두기($\\rho$=0.3)를 할 수 있으면 완전 격리와 비슷한 효과가 있습니다. (다만, $\\rho$가 0.3 근방에서 특이점이 있어 그 밑으로는 본 모형으로 해석하는 것은 의미가 없습니다.)\n", "* 다만 20%로 상정한 것은 60일 이상의 사회적 거리 두기를 실천해야 하므로 강한 사회적 거리 두기를 설정하지 않았습니다. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SEIR 모형\n", "\n", "### 아래는 Nesse의 웹 콘텐츠를 요약해서 설명합니다.\n", "\n", "먼저 SEIR은 전염병이 전파되는 과정의 상태를 나타내는 susceptible (S), exposed (E), infected (I), resistant (R)를 각각 뜻합니다. Nesse의 SEIR 모형 설명은 다음과 같습니다. \n", "\n", "> SEIR은 취약(S), 노출 (E), 감염 (I) 및 내성 (R)의 네 가지 상태 사이의 사람들의 흐름을 모델링합니다. 이러한 각 변수는 해당 그룹의 인원 수를 나타냅니다. 알파 및 베타 매개 변수는 사람들이 감염되기 쉬운 상태에서 노출 된 상태 (베타), 감염된 상태 (시그마), 감염된 상태에서 내성 (감마)으로 이동하는 속도를 부분적으로 제어합니다. 이 모델에는 두 가지 추가 매개 변수가 있습니다. 하나는 질병 상태에 영향을받지 않는 배경 사망률 (mu)이고 다른 하나는 예방 접종 (nu)입니다. 예방 접종은 사람들을 노출 또는 감염시키지 않고 감수성에서 직접 저항성으로 이동시킵니다.\n", "> SEIR은 대기 시간이 추가 된 SIR 모델과 다릅니다. 노출된 개인 (E)은 감염된 사람과 접촉했지만 감염되지 않았습니다.\n", "\n", "아래부터는 Nesse의 원래 방정식의 $\\sigma$를 $\\alpha$로 바꾸어 표기하니 원문을 읽을 때 주의하십시오. 사회적 거리두기가 포함된 모형을 설명할 때 참고한 Hubbs의 방정식과 표기법을 맞추기 위해서입니다.\n", "\n", "이에 대한 동적 시스템 방정식은 아래와 같습니다.\n", "\n", "$$\n", "\\frac{dS}{dt} = \\mu (N-S) - \\beta \\frac{SI}{N} - \\nu S\n", "\\label{eq:Sdot} \\tag{1}\n", "$$\n", "\n", "$$\n", "\\frac{dE}{dt} = \\beta \\frac{SI}{N} - ( \\mu + \\alpha ) E \n", "\\label{eq:Edot} \\tag{2}\n", "$$\n", "\n", "$$\n", "\\frac{dI}{dt} = \\alpha E - ( \\mu - \\gamma )I \n", "\\label{eq:Idot} \\tag{3}\n", "$$\n", "\n", "$$\n", "\\frac{dR}{dt} = \\gamma I - \\mu R - \\nu S \n", "\\label{eq:Rdot} \\tag{4}\n", "$$\n", "\n", "$$\n", "N = S + E + I + R\n", "\\label{eq:total_pop} \\tag{5}\n", "$$\n", "\n", "여기서, 각 모형의 상태변수는 아래와 같습니다.\n", "\n", "* $S$ susceptible; 취약 인구수.\n", "* $E$ exposed; 노출 인구수.\n", "* $I$ infected; 감염 인구수.\n", "* $R$ resistant; 내성 인구수.\n", "* $N$ number of population; 인구수.\n", "* $t$ time; 시간, 보통 단위는 일(day).\n", "\n", "전염원에 따라 달라지는 매개변수는 다음과 같습니다..\n", "* $\\alpha$ 노출된 사람이 감염되는 비율.\n", "* $\\beta$ 베타 감염되기 쉬운 접촉이 새로운 노출을 일으키는 빈도를 제어하는 매개 변수이다.\n", "* $\\gamma$ 감염률이 회복되어 내성 단계로 이동하는 속도.\n", "* $\\mu$ 자연 사망률 (질병과 무관) 이것은 일정한 크기의 인구를 모델링한다.\n", "* $\\nu$ 취약 인구의 백신 접종 속도.\n", "\n", "실제 시뮬레이션을 위해서는 미분방정식을 수치해석해야 하며, 각 상태변수에 대한 초기값과 코로나19에 맞는 매개변수가 설정되어야 합니다.\n", "\n", "\n", "### 참고 자료\n", "\n", "* Hans Nesse, http://www.public.asu.edu/~hnesse/classes/seir.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 사회적 거리두기가 적용된 모형\n", "\n", "### 간략화된 SEIR 모형\n", "\n", "Christian Hubbs는 아래의 수식을 확장된 SIR 모형이라고 설명하고 있습니다. 앞장에서 설명한 SEIR 모형에서 자연사망율 $\\mu$d와 백신율 $\\nu$를 0으로 두면 동일한 수식이 됩니다. Hubbs는 R을 Recovered라는 상태로 표현하고 감염후 면역을 획득하고 나은 상태라고 설명합니다. \n", "\n", "$$\n", "\\frac{dS}{dt} = - \\beta SI\n", "\\label{eq:Sdot_simple} \\tag{1.1}\n", "$$\n", "\n", "$$\n", "\\frac{dE}{dt} = \\beta SI - \\alpha E \n", "\\label{eq:Edot_simple} \\tag{2.1}\n", "$$\n", "\n", "$$\n", "\\frac{dI}{dt} = \\alpha E - \\gamma I \n", "\\label{eq:Idot_simple} \\tag{3.1}\n", "$$\n", "\n", "$$\n", "\\frac{dR}{dt} = \\gamma I \n", "\\label{eq:Rdot_simple} \\tag{4.1}\n", "$$\n", "\n", "$$\n", "N = S + E + I + R\n", "\\label{eq:total_pop_simple} \\tag{5.1}\n", "$$\n", "\n", "Hubbs는 사회적 거리 두기의 효과를 보고 싶어했으므로 이와 같이 간략한 버전도 충분한 의미가 있다고 생각됩니다. 매개변수에 대해서 쉽게 설명하고 현재의 코로나19의 값을 조사하여 제시하고 있습니다. \n", "\n", "\n", "* $\\alpha$ 잠복 기간의 역수 ( $\\frac{1}{t_{incubation}}$).\n", "\n", "* $\\beta$ 모집단의 평균 접촉 속도.\n", "\n", "* $\\gamma$ 평균 감염 기간의 역수. ( $\\frac{1}{t_{infectious}}$ ).\n", "\n", "Hubbs가 수식(1)~(5)의 설명을 구글번역하여 인용합니다.\n", "\n", "> 식(1)은 질병에 걸리기 쉬운 사람의 변화이며, 감염된 사람의 수와 감염자와의 접촉에 의해 조절됩니다. 식(2)는 질병에 노출된 사람들에게 제공합니다. 접촉 속도에 따라 자라며 인큐베이션 기간에 따라 감소하여 사람들이 감염됩니다.\n", "식 (3)은 노출 된 인구와 잠복기에 따라 감염된 사람들의 변화를 보여줍니다. 감염 기간에 따라 감소하므로 γ가 높을수록 사람들이 더 빨리 죽거나 회복하고 식 (4)의 마지막 단계로 넘어갑니다. 마지막 방정식 인 숫자 (5)는 모형에 출생 / 마이그레이션 효과가 없음을 나타내는 구속 조건입니다. 우리는 처음부터 끝까지 인구가 고정되어 있습니다.\n", "\n", "이 글에서 자세하게 설명하는 매개 변수중에 $R_0$가 있습니다. 이 값은 질병이 얼마나 빨리 퍼지는지를 식(6)으로 표현합니다.\n", "\n", "$$\n", "R_0 = \\frac{\\beta}{\\gamma}\n", "\\label{eq:R0} \\tag{6}\n", "$$\n", "\n", "### 사회적 거리 두기를 반영한 모형\n", "\n", "사회적 거리 두기는 대규모 집회, 신체 접촉 및 전염병 확산을 막기 위한 중요한 사회적 활동으로 여겨지고 있습니다. 앞의 모형에 따르면 이런 사회적 활동이 영향을 줄 매개 변수는 접촉 속도 $\\beta$입니다.\n", "\n", "Hubbs는 사회적 거리 두기를 표현할 수 있는 새로운 매개 변수 $\\rho$를 도입했습니다. $\\rho$는 0 ~ 1 사이의 일정한 값을 가지는 것으로 가정하고, 0 이면 모든 사람이 격리되어 있는 상황이고, 1이면 사회적 거리 두기를 하지 않는 상태입니다.\n", "\n", "모형에 반영하기 위헤서 식(1)과 (2)에 $\\rho$를 적용합니다.\n", "\n", "$$\n", "\\frac{dS}{dt} = - \\rho \\beta SI\n", "\\label{eq:Sdot_socdist} \\tag{1-mod}\n", "$$\n", "\n", "$$\n", "\\frac{dE}{dt} = \\rho \\beta SI - \\alpha E \n", "\\label{eq:Edot_socdist} \\tag{2-mod}\n", "$$\n", "\n", "\n", "\n", "\n", "\n", "### 코로나19의 매개 변수 \n", "이제 방정식에 넣을 매개 변수를 코로나19에 맞추어 결정하는 것이 필요합니다. 이를 통해서 코로나19의 확산 과정을 더 잘 이해할 수 있습니다. 핵심은 α, β 및 γ에 대한 값을 결정하여 어떻게 확산 되는지 보는 것입니다.\n", "\n", "Hubbs는 COVID-19에 대한 최근의 연구 자료(Hellewell et al. 2020)에서 일부를 추정하였습니다.\n", "\n", "* 잠복기가 5 일이므로, $\\alpha = 0.2$\n", "* $R_0 = 3.5$\n", "\n", "$\\beta$와 $\\gamma$ 값은 Liu Hong (2020)의 연구에서 추정치를 얻습니다. 이 논문은 훨씬 복잡한 동적 모형을 사용하지만, 1/$\\gamma$값을 2 일로 얻을 수 있으므로 $\\gamma = 0.5$입니다.\n", "\n", "이 값을 식(6)의 $R_0$에 대입하여 $\\beta = 1.75$의 추정치를 얻습니다.\n", "\n", "### 참고 자료\n", "* Christian Hubbs, https://towardsdatascience.com/social-distancing-to-slow-the-coronavirus-768292f04296\n", "* Hellewell et al. (2020), Lancet, https://www.thelancet.com/journals/langlo/article/PIIS2214-109X(20)30074-7/fulltext\n", "* Liu Hong (2020), arXiv, https://arxiv.org/pdf/2002.06563.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 코로나19의 SEIR 모형 시뮬레이션\n", "\n", "\n", "## SEIR 모형의 구현\n", "\n", "위에서 설명한 SEIR 모형을 아래처럼 구현 하였습니다. 두 개의 모형은 모두 초기값과, 매개변수, 시간데이터를 넣어주면 SEIR을 numpy 행열로 돌려줍니다." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# SEIR model\n", "# semi-implicit Euler method\n", "# Christian Hubbs의 글을 참고해서 모델을 구현하고 차트 출력 부분을 추가했습니다.\n", "# (https://towardsdatascience.com/social-distancing-to-slow-the-coronavirus-768292f04296)\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import ticker\n", "\n", "\"\"\"\n", "BASE SEIR model\n", "\"\"\"\n", "def base_seir_model(init_vals, params, t):\n", " S_0, E_0, I_0, R_0 = init_vals\n", " S, E, I, R = [S_0], [E_0], [I_0], [R_0]\n", " alpha, beta, gamma = params\n", " dt = t[1] - t[0]\n", " for _ in t[1:]:\n", " next_S = S[-1] - (beta*S[-1]*I[-1])*dt\n", " next_E = E[-1] + (beta*S[-1]*I[-1] - alpha*E[-1])*dt\n", " next_I = I[-1] + (alpha*E[-1] - gamma*I[-1])*dt\n", " next_R = R[-1] + (gamma*I[-1])*dt\n", " S.append(next_S)\n", " E.append(next_E)\n", " I.append(next_I)\n", " R.append(next_R)\n", " return np.stack([S, E, I, R]).T\n", "\n", "\"\"\"\n", "SEIR model with social distancing\n", "\"\"\"\n", "def seir_model_with_soc_dist(init_vals, params, t):\n", " S_0, E_0, I_0, R_0 = init_vals\n", " S, E, I, R = [S_0], [E_0], [I_0], [R_0]\n", " alpha, beta, gamma, rho = params\n", " dt = t[1] - t[0]\n", " for _ in t[1:]:\n", " next_S = S[-1] - (rho*beta*S[-1]*I[-1])*dt\n", " next_E = E[-1] + (rho*beta*S[-1]*I[-1] - alpha*E[-1])*dt\n", " next_I = I[-1] + (alpha*E[-1] - gamma*I[-1])*dt\n", " next_R = R[-1] + (gamma*I[-1])*dt\n", " S.append(next_S)\n", " E.append(next_E)\n", " I.append(next_I)\n", " R.append(next_R)\n", " return np.stack([S, E, I, R]).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 초기값과 매개 변수\n", "\n", "\n", "최대 100간을 시뮬레이션하고 인구는 1만명에 최초 감염자는 1명으로 가정하여 위에서 조사된 매개 변수값을 적용합니다." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "# initial var. and parameters\n", "t_max = 300\n", "dt = .1\n", "scale_x = 1 / dt\n", "t = np.linspace(0, t_max, int(t_max/dt) + 1)\n", "N = 10000\n", "init_vals = 1 - 1/N, 1/N, 0, 0\n", "alpha = 0.2\n", "beta = 1.75\n", "gamma = 0.5\n", "params_base = alpha, beta, gamma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 코로나19의 시뮬레이션\n", "\n", "정의된 초기값과 매개변수로 모형 함수를 호출합니다." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Run simulation\n", "results_base = base_seir_model(init_vals, params_base, t)\n", "\n", "# Plot results\n", "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "\n", "ax.plot(results_base)\n", "ax.legend(['Susceptible', 'Exposed', 'Infected', 'Recovered'])\n", "\n", "ax.set_xlabel('Time (Days)')\n", "ticks_x = ticker.FuncFormatter(lambda x, pos: '{0:g}'.format(x/scale_x))\n", "ax.xaxis.set_major_formatter(ticks_x)\n", "ax.set_ylabel('Population fraction')\n", "ax.set_title(r'SEIR model with $\\alpha={p[0]}, \\beta={p[1]}, \\gamma={p[2]}$'.format(p=params_base) )\n", "plt.xlim(200, 600) # \n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fraction of Infected population = 0.10024335877116862\n", "Day of peak Infected = 40.4\n" ] } ], "source": [ "# peak of Infected\n", "print('Fraction of Infected population = {}'.format(results_base[:,2].max()))\n", "print('Day of peak Infected = {}'.format(results_base[:,2].argmax()/scale_x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "가정된 인구(1만명)와 매개 변수에 따르면 최소 1명의 감염자에서 최대치가 되는 것은 40일 근방으로 나타나고 인구의 10% 정도가 감염되는 것으로 예측됩니다." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 사회적 거리 두기 모형의 시뮬레이션\n", "\n", "이제 사회적 거리 두기(Soc; Social Distancing)를 할 경우 코로나19의 전염 패턴은 어떻게 되는지 살펴보자. 앞의 기본적인 SEIR 모형에 매개 변수 $\\rho = 0.8$가 추가되고 기본 모형과 비교하기 위해서 base 모형과 함께 차트를 그립니다.\n", "이 경우는 20%의 사람들이 사회적 거리 두기를 정확히 하고 있는 것을 가정한 것입니다. " ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "rho = 0.8 \n", "params_soc = alpha, beta, gamma, rho\n", "# Run simulation\n", "results_soc = seir_model_with_soc_dist(init_vals, params_soc, t)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot results\n", "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "\n", "ax.plot(results_base, linestyle='-')\n", "ax.plot(results_soc, linestyle=':')\n", "ax.legend(['$S_{base}$', '$E_{base}$', '$I_{base}$', '$R_{base}$',\\\n", " '$S_{soc}$', '$E_{soc}$', '$I_{soc}$', '$R_{soc}$'])\n", "\n", "ax.set_xlabel('Time (Days)')\n", "ticks_x = ticker.FuncFormatter(lambda x, pos: '{0:g}'.format(x/scale_x))\n", "ax.xaxis.set_major_formatter(ticks_x)\n", "\n", "ax.set_ylabel('Population fraction')\n", "ax.set_title(r'SEIR model with $\\alpha={p[0]}, \\beta={p[1]}, \\gamma={p[2]}, \\rho={p[3]}$'.format(p=params_soc) )\n", "\n", "plt.xlim(0,1000)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Base SEIR 모형(실선)과 사회적 거리두기(soc) 모형(점선)의 결과를 함께 출력하였습니다. 전체적으로 노출과 감염 인구의 비율이 줄고 지연되는 것을 확인할 수 있습니다." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 사회적 거리 두기의 효과\n", "\n", "Base 모형과 비교하여 노출과 감염 인구비율에 주는 영향과 최대 감염자 발생일이 얼마나 늦추어지는지 확인했습니다." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Population and COVID-19\n", " N = 10000\n", " $\\alpha$ = 0.2\n", " $\\beta$ = 1.75\n", " $\\gamma$ = 0.5\n", "Effect of social distancing: $\\rho=0.8$\n", " Drop ratio of Exposed = 0.23380988793745305\n", " Drop ratio of Infected = 0.22279100659793027\n", " Delay days of peak infected = 9.9\n" ] } ], "source": [ "# Drop ratio of Exposed: with soc vs base\n", "r_E = results_soc[:,1].max() / results_base[:,1].max()\n", "# Drop ratio of Infected: with soc vs base\n", "r_I = results_soc[:,2].max() / results_base[:,2].max()\n", "# Delay days of Infected: with soc vs base\n", "d_I = ( results_soc[:,2].argmax() - results_base[:,2].argmax() ) / scale_x\n", "\n", "print('Population and COVID-19')\n", "print(r' N = {}'.format(N))\n", "print(r' $\\alpha$ = {}'.format(alpha))\n", "print(r' $\\beta$ = {}'.format(beta))\n", "print(r' $\\gamma$ = {}'.format(gamma))\n", "\n", "print(r'Effect of social distancing: $\\rho={}$'.format(rho))\n", "print(r' Drop ratio of Exposed = {}'.format(1-r_E))\n", "print(r' Drop ratio of Infected = {}'.format(1-r_I))\n", "print(r' Delay days of peak infected = {}'.format(d_I))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\rho = 0.8$인 사회적 거리 두기를 할 경우, 인구의 20%가 스스로 격리한 경우에 노출 인구와 감염자를 각각 23%, 22% 정도 줄일 수 있고, 감염자가 최대치가 되는 날을 10일 정도 지연시킬 수 있는 것으로 계산됩니다.\n", "\n", "앞서 설명한 것처럼 $\\rho$=1인 경우는 사회적 거리 두기를 하지 않은 경우이고, $\\rho$가 0인 경우는 각 개인이 완전 격리된 상태를 뜻합니다. 어느 정도의 사회적 거리 두기를 하면 방역에 효과가 있는지 모사해보기 위해서 0~1까지 구간을 나누어 최대 감염자 비율과 감염율 최대일을 얼마나 지연시키는지 확인해보았습니다." ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rhos= np.linspace(0, 1, 100)\n", "\n", "I_delayed=[]\n", "I_max=[]\n", "I_base_peak_day=results_base[:,2].argmax()\n", "\n", "for rho in rhos:\n", " params_soc = alpha, beta, gamma, rho\n", " # Run simulation\n", " results_soc = seir_model_with_soc_dist(init_vals, params_soc, t)\n", " I_delayed.append((results_soc[:,2].argmax() - I_base_peak_day)/scale_x)\n", " I_max.append(results_soc[:,2].max())\n", "\n", "fig = plt.figure(figsize=(12,8))\n", "\n", "plt.subplot(121)\n", "plt.plot(1 - rhos, I_max)\n", "plt.xlabel(r'(a) Social Distancing ($1 - \\rho$)')\n", "plt.ylabel(r'Population fraction of Infected ')\n", "plt.xlim(0, 0.7)\n", "\n", "plt.subplot(122)\n", "plt.plot(1 - rhos, I_delayed)\n", "plt.xlabel(r'(b) Social Distancing ($1 - \\rho$)')\n", "plt.ylabel(r'Delayed days of Infected peak [day] ')\n", "plt.xlim(0, 0.7)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "위의 그림은 인구의 약 70%가 사회적 거리 두기에 참여하면 사실상 전염을 막을 수 있고 250일 이상 지연시킬 수 있다는 것을 보여줍니다. 그러나 70% 라는 의미는 학교나 기간 산업이 거의 정지한다는 의미이기도 합니다." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 고찰\n", "\n", "지금까지의 시뮬레이션은 우리나라를 포함한 특정 국가의 통계를 사용하지 않았습니다. 사회적 거리 두기의 상대적 효과를 파악하는 것을 목표로 하고 불필요한 오해와 논쟁을 피하기 위해서입니다.\n", "시뮬레이션 결과에 따른면 20% 정도의 사회적 거리 두기($\\rho=0.8$)가 성공해도 방역에는 상당한 효과가 있을 것으로 계산됩니다. 다만 20%로 상정한 것은 60일 이상의 사회적 거리 두기를 실천해야 하므로 강한 사회적 거리 두기를 설정하지 않았습니다." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }