projeto.ipynb

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      "name": "Metodos_teste.ipynb",
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      "source": [
        "# Simulação do modelo SEIRD\n",
        "\n",
        "O SEIRD é um modelo comportamental que é amplamente usado para a modelagem de doenças infecciosas, o modelo funciona dividindo a pupolação em grupos e mostramos o comportamento desses grupos por meio de um gráfico\n",
        "\n",
        "Nós iremos parametrizar esses sistemas de equação, vamos selecionar os valores de acordo com pesquisas e fontes para melhor aproximar a modelagem do valor real, iremos ter os comportamentos representados em curvas e vamos plotar os valores ao final\n",
        "\n",
        "## Modelo SEIRD\n",
        "\n",
        "Os sistemas de equações são descritos abaixo:\n",
        "\n",
        "$\\displaystyle \\frac{dS}{dt} = -\\frac{\\beta S I}{N}$<br><br>\n",
        "$\\displaystyle \\frac{dE}{dt} = \\frac{\\beta S I}{N} - \\sigma E$<br><br>\n",
        "$\\displaystyle \\frac{dI}{dt} = \\sigma E -  \\gamma I - \\mu I$<br><br>\n",
        "$\\displaystyle \\frac{dR}{dt} = \\gamma I$<br><br>\n",
        "$\\displaystyle \\frac{dD}{dt} = \\mu I$<br><br>\n",
        "$N = S + E + I + R + D$<br><br>\n",
        "\n",
        "Onde temos as seguintes constantes:<br><br>\n",
        "\n",
        "$\\beta$: Taxa de transmissão dos infectados<br><br>\n",
        "$\\sigma$: Taxa de incubação do individuos (Duração média da incubação $1/\\sigma$)<br><br>\n",
        "$\\gamma$: Taxa de recuperação dos infectados $\\gamma$ = 1/duração<br><br>\n",
        "$\\mu$: Taxa de mortalidade"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "source": [
        "## Módulos e importações:\n",
        "\n",
        "* Numpy: Biblioteca de python para nos ajudar a resolve os cálculos complexos\n",
        "\n",
        "* Matplolib: Biblioteca usada para plotar o gŕafico ao final\n",
        "\n",
        "* Scipy: Biblioteca que usamos para resolver os sistemas de equações\n"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I9KdpL8hrQzr"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "source": [
        "### Função com os sistemas de equações\n",
        "\n",
        "Implementação em python das equações descritas acima."
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "702vEYg3uWTu"
      },
      "source": [
        "def deriv(y, t, N, beta, sigma, gamma, mu):\n",
        "  S, E, I, R, D = y\n",
        "\n",
        "  dSdt = -beta* S*I/N\n",
        "  dRdt = gamma * I\n",
        "  dIdt = sigma*E - gamma*I - mu*I\n",
        "  dEdt = beta*S*I/N - sigma*E\n",
        "  dDdt = mu*I\n",
        "  \n",
        "  return [dSdt, dEdt, dIdt, dRdt, dDdt]\n",
        "\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "source": [
        "### Condições iniciais do modelo:\n",
        "\n",
        "Nesse exemplo vamos tentar simular o contágio em pernambuco, usamos a população de pernambuco e os dois primeiros casos relatados, e uma estimativa que esses 2 casos expuseram 6 pessoas, um indice r0 com 2.81 que foi o pico da transmissão no inicio da pandemia relatado em abril/2020, executamos a projeção em 200 dias, aproximadamente 7 meses após o primeiro caso comfirmado em PE\n",
        "\n"
      ],
      "cell_type": "markdown",
      "metadata": {}
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    {
      "cell_type": "code",
      "metadata": {
        "id": "QLDZnBdRs64G"
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      "source": [
        "# N: Numero Total\n",
        "# I: Infectados\n",
        "# E: Expostos\n",
        "# S: Suscetíveis\n",
        "# R: Recuperados\n",
        "# D: Mortos\n",
        "# beta: taxa de transmissão\n",
        "# sigma: taxa de incubação (1/sigma)\n",
        "# gamma: chance de recuperação (1/duração)\n",
        "# mu: taxa de mortalidade\n",
        "\n",
        "# População de Pernambuco\n",
        "N = 9616621\n",
        "\n",
        "# Valores iniciais\n",
        "I0 = 2\n",
        "E0 = 6\n",
        "R0 = 0\n",
        "D0 = 0\n",
        "S0 = N - (I0 + R0 + D0 + E0)\n",
        "\n",
        "r0 = 2.81\n",
        "sigma = 1/5.2\n",
        "gamma = 1/2.9\n",
        "\n",
        "mu = 0.034\n",
        "beta = r0 * gamma\n",
        "\n",
        "days = 200\n",
        "\n",
        "t = np.linspace(0,days,days)\n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-sexCS2vvhBJ"
      },
      "source": [
        "\n",
        "y0 = S0, E0, I0, R0, D0\n",
        "\n",
        "ret = odeint(deriv, y0, t, args=(N, beta, sigma, gamma, mu))\n",
        "\n",
        "S, E, I, R, D = ret.T"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
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        "outputId": "f4e1cd96-4185-4c11-db13-486fa39ac08f",
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        "fig = plt.figure(facecolor = 'w')\n",
        "ax = fig.add_subplot(111, facecolor = '#dddddd', axisbelow = True)\n",
        "\n",
        "ax.plot(t, S/N, 'blue', alpha = 0.5, lw = 2, label = 'Suscetíveis')\n",
        "ax.plot(t, E/N, 'brown', alpha = 0.5, lw = 2, label = 'Expostos')\n",
        "ax.plot(t, I/N, 'red', alpha = 0.5, lw = 2, label = 'Infectados')\n",
        "ax.plot(t, R/N, 'green', alpha = 0.5, lw = 2, label = 'Recuperados')\n",
        "ax.plot(t, D/N, 'black', alpha = 0.5, lw = 2, label = 'Mortos')\n",
        "\n",
        "ax.set_xlabel('Tempo/Dias')\n",
        "ax.set_ylabel(f'Numero ({N})')\n",
        "# ax.set_ylim(0,1.2)\n",
        "ax.yaxis.set_tick_params(length = 0)\n",
        "ax.xaxis.set_tick_params(length = 0)\n",
        "ax.grid(b = True, which = 'major', c = 'w', lw = 2, ls = '-')\n",
        "legend = ax.legend()\n",
        "legend.get_frame().set_alpha(0.5)\n",
        "for spine in ('top', 'right', 'bottom', 'left'):\n",
        "  ax.spines[spine].set_visible(False)\n",
        "plt.savefig('sir.pdf')\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 5,
      "outputs": [
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "source": [
        "### Progressão da doença com números atuais:\n",
        "\n",
        "Aqui temos uma tentativa de estimar a progressão atual da doença no estado, alterando os parâmetros iniciais de infectados, recuperados e mortos, e avaliar como se dá esse comportamento, foi usado o r0 padrão do brasil pela falta de dados especificos"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "# População de Pernambuco\n",
        "N = 9616621\n",
        "\n",
        "# Valores iniciais\n",
        "I0 = 166540\n",
        "E0 = 0\n",
        "R0 = 147843\n",
        "D0 = 8740\n",
        "S0 = N - (I0 + R0 + D0 + E0)\n",
        "\n",
        "r0 = 1.4\n",
        "sigma = 1/5.2\n",
        "gamma = 1/2.9\n",
        "mu = 0.034\n",
        "beta = r0 * gamma\n",
        "\n",
        "days = 200\n",
        "\n",
        "t = np.linspace(0,days,days)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "y0 = S0, E0, I0, R0, D0\n",
        "ret = odeint(deriv, y0, t, args=(N, beta, sigma, gamma, mu))\n",
        "S, E, I, R, D = ret.T"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {}
        }
      ],
      "source": [
        "fig = plt.figure(facecolor = 'w')\n",
        "ax = fig.add_subplot(111, facecolor = '#dddddd', axisbelow = True)\n",
        "\n",
        "ax.plot(t, S/N, 'blue', alpha = 0.5, lw = 2, label = 'Suscetíveis')\n",
        "ax.plot(t, E/N, 'brown', alpha = 0.5, lw = 2, label = 'Expostos')\n",
        "ax.plot(t, I/N, 'red', alpha = 0.5, lw = 2, label = 'Infectados')\n",
        "ax.plot(t, R/N, 'green', alpha = 0.5, lw = 2, label = 'Recuperados')\n",
        "ax.plot(t, D/N, 'black', alpha = 0.5, lw = 2, label = 'Mortos')\n",
        "\n",
        "ax.set_xlabel('Tempo/Dias')\n",
        "ax.set_ylabel(f'Numero ({N})')\n",
        "# ax.set_ylim(0,1.2)\n",
        "ax.yaxis.set_tick_params(length = 0)\n",
        "ax.xaxis.set_tick_params(length = 0)\n",
        "ax.grid(b = True, which = 'major', c = 'w', lw = 2, ls = '-')\n",
        "legend = ax.legend()\n",
        "legend.get_frame().set_alpha(0.5)\n",
        "for spine in ('top', 'right', 'bottom', 'left'):\n",
        "  ax.spines[spine].set_visible(False)\n",
        "plt.savefig('sir.pdf')\n",
        "plt.show()"
      ]
    },
    {
      "source": [
        "### Progressão Sergipe\n",
        "\n",
        "Aproveitando o projeto decidi incluir dados para simulação no meu estado natal, segue os resultados e um gráfico da progressão no estado"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "# População de Sergipe\n",
        "N = 2318822\n",
        "\n",
        "# Valores iniciais\n",
        "I0 = 85477\n",
        "E0 = 0\n",
        "R0 = 78248\n",
        "D0 = 2244\n",
        "S0 = N - (I0 + R0 + D0 + E0)\n",
        "\n",
        "r0 = 1.4\n",
        "sigma = 1/5.2\n",
        "gamma = 1/2.9\n",
        "mu = 0.034\n",
        "beta = r0 * gamma\n",
        "\n",
        "days = 200\n",
        "\n",
        "t = np.linspace(0,days,days)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "y0 = S0, E0, I0, R0, D0\n",
        "ret = odeint(deriv, y0, t, args=(N, beta, sigma, gamma, mu))\n",
        "S, E, I, R, D = ret.T"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig = plt.figure(facecolor = 'w')\n",
        "ax = fig.add_subplot(111, facecolor = '#dddddd', axisbelow = True)\n",
        "\n",
        "ax.plot(t, S/N, 'blue', alpha = 0.5, lw = 2, label = 'Suscetíveis')\n",
        "ax.plot(t, E/N, 'brown', alpha = 0.5, lw = 2, label = 'Expostos')\n",
        "ax.plot(t, I/N, 'red', alpha = 0.5, lw = 2, label = 'Infectados')\n",
        "ax.plot(t, R/N, 'green', alpha = 0.5, lw = 2, label = 'Recuperados')\n",
        "ax.plot(t, D/N, 'black', alpha = 0.5, lw = 2, label = 'Mortos')\n",
        "\n",
        "ax.set_xlabel('Tempo /Dias')\n",
        "ax.set_ylabel(f'Numero ({N})')\n",
        "# ax.set_ylim(0,1.2)\n",
        "ax.yaxis.set_tick_params(length = 0)\n",
        "ax.xaxis.set_tick_params(length = 0)\n",
        "ax.grid(b = True, which = 'major', c = 'w', lw = 2, ls = '-')\n",
        "legend = ax.legend()\n",
        "legend.get_frame().set_alpha(0.5)\n",
        "for spine in ('top', 'right', 'bottom', 'left'):\n",
        "  ax.spines[spine].set_visible(False)\n",
        "plt.savefig('sir.pdf')\n",
        "plt.show()"
      ]
    },
    {
      "source": [
        "*** Referências: ***\n",
        "\n",
        "1. Taxa de transmissão da Covid-19 no Brasil mantém estabilidade, mas apresenta leve oscilação para cima. G1. <https://g1.globo.com/bemestar/coronavirus/noticia/2020/08/25/taxa-de-transmissao-da-covid-19-no-brasil-sobe-levemente-uma-semana-depois-de-indicar-queda-aponta-imperial-college.ghtml>.\n",
        "\n",
        "2. Pernambuco | Cidades e Estados | IBGE. Ibge.gov.br. Disponível em: <https://www.ibge.gov.br/cidades-e-estados/pe.html>.\n",
        "\n",
        "3. Casal do Recife são primeiros casos de coronavírus em Pernambuco. <https://www.folhape.com.br/noticias/casal-do-recife-sao-primeiros-casos-de-coronavirus-em-pernambuco/133219/>.\n",
        "\n",
        "4. Estimativas de R(t) por Estados do Brasil. covid19. Disponível em: <https://flaviovdf.github.io/covid19/>.\n",
        "\n",
        "5. FENTRANSPORTE. A evolução epidêmica do COVID-19 – Modelo SIR. GDISPEN. Disponível em: <https://wp.ufpel.edu.br/fentransporte/2020/04/09/a-evolucao-epidemica-do-covid-19-modelo-sir/>.\n",
        "\n",
        "6. Sergipe | Cidades e Estados | IBGE. Ibge.gov.br. Disponível em: <https://www.ibge.gov.br/cidades-e-estados/se.html>.\n",
        "\n",
        "7. Governo de Sergipe. Todos contra o Corona | Governo de Sergipe. Disponível em: <https://todoscontraocorona.net.br/>.\n",
        "\n",
        "8. Simulating Compartmental Models in Epidemiology using Python & Jupyter Widgets. Medium. Disponível em: <https://towardsdatascience.com/simulating-compartmental-models-in-epidemiology-using-python-jupyter-widgets-8d76bdaff5c2>.\n",
        "\n",
        "‌"
      ],
      "cell_type": "markdown",
      "metadata": {}
    }
  ]
}