SARS-CoV-2.ipynb

sars-cov-2.ipynb

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        "<a href=\"https://colab.research.google.com/gist/jckantor/1801fb42544810cf8975f8ae072c42fe/sars-cov-2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "# Modeling the coronavirus SARS-CoV-2 (COVID-19) outbreak\n",
        "\n",
        "The purpose of this notebook is to demostrate the modeling of infectious epidemic using the latest available data for SARS-Cov-2. The models and data used in this notebook have been extracted from a rapidly emerging and changing literature."
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        "## The SARS-CoV-2 (COVID-19) coronavirus\n",
        "\n",
        "Human coronaviruses were first identified in the 1960's. There are currently four coronaviruses endemic to human populations around the world:\n",
        "\n",
        "* 229E (alpha coronavirus)\n",
        "* NL63 (alpha coronavirus)\n",
        "* OC43 (beta coronavirus)\n",
        "* HKU1 (beta coronavirus)\n",
        "\n",
        "These four common coronaviruses typically cause an upper respiratory disease which, in a minority of cases, progresses to pneumonia. Most people will suffer from at least one of coronaviruses during their lifetimes which cause about a quarter of all common colds.\n",
        "\n",
        "In recent decades, three coronaviruses that normally infect animals have evolved to infect humans. These include:\n",
        "\n",
        "* MERS-CoV (the beta coronavirus that causes Middle East Respiratory Syndrome, or MERS)\n",
        "* SARS-CoV (the beta coronavirus that causes severe acute respiratory syndrome, or SARS)\n",
        "* SARS-CoV-2 (the novel coronavirus that causes coronavirus disease 2019, or COVID-19)\n",
        "\n",
        "The last of these, now called SARS-CoV-2, first appeared in December, 2019, at a seafood market in Wuhan (Hubei, China). The rapid spread of SARS-CoV-2 in Wuhan, and appearance in other locations around the globe, has resulted in the World Health Organization (WHO) declaring a global health emergency. Countries around the globe are mobilizing to track the virus and control new outbreaks. \n",
        "\n",
        "At this stage, it is too early to know if these efforts will be successful in preventing SARS-CoV-2 from becoming a pandemic, and later an endemic disease with a global footprint. You can find the most recent data on the current outbreak at [Coronavirus COVID-19 Global Cases by Johns Hopkins CSSE](https://gisanddata.maps.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6).\n"
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      "source": [
        "## References\n",
        "\n",
        "Keeling, Matt J., and Pejman Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2008. JSTOR, www.jstor.org/stable/j.ctvcm4gk0. Accessed 25 Feb. 2020.\n",
        "\n",
        "Boldog, Péter, et al. \"Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China.\" Journal of Clinical Medicine 9.2 (2020): 571. https://www.mdpi.com/2077-0383/9/2/571"
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        "## Model 1. Basic SEIR model for infectious diseases.\n",
        "\n",
        "The SEIR model commonly used compartment model for epidemiology. In the SEIR model for an infectious disease, a community is broken in to four sub-groups corresponding to stages of the disease:\n",
        "\n",
        "* **Susceptible.** The subpopulation susceptible to acquire the disease. For SARS-CoV-2, the assumption is that everyone who has not previously acquired the disease is susceptible to infection.\n",
        "* **Exposed.** The subpopulation that has been exposed to the disease but not yet infective. \n",
        "* **Infectious.** The subpopulation that has become infective.\n",
        "* **Recovered.** The subpopulation that has recovered from infection, and presumed to be no longer susceiptible to the disease.\n",
        "\n",
        "Neglecting demographic processes of birth and death from other causes, and assuming a negligible death rate due to infectious disease at issue, the progression of an epidemic can be modeled by rate processesl\n",
        "\n",
        "$$\\text{Susceptible}\n",
        "\\xrightarrow{(1-u)\\frac{\\beta S I}{N}} \n",
        "\\text{Exposed} \n",
        "\\xrightarrow{\\alpha E} \n",
        "\\text{Infectious} \n",
        "\\xrightarrow{\\gamma I} \n",
        "\\text{Recovered} $$\n",
        "\n",
        "The rate processes are modeled as follows.\n",
        "\n",
        "* $(1-u)\\frac{\\beta S I}{N}$ is the rate at which susecptible population encounters the infected population resulting in trasmission of the disease. $S$ is the size of the susceptible population. $\\beta$ is a the model parameters with units of 1/day. $u$ describes the effectiveness on any public health interventions to control transmission of the disease. $u=0$ means no effective public health interventions, $u=1$ means total elimination of disease transmission.\n",
        "* $\\alpha E$ is the rate at which exposed population becomes infective, where $E$ is the size of the exposed population. The average period of time in the exposed state is the incubation period of the disease, and equal to $\\frac{1}{\\alpha}$.\n",
        "* $\\gamma I$ is the rate at which infected population recovers and becomes resistent to further infection. $I$ is the size of the infective population.\n",
        "\n",
        "\n",
        "An elementary model for the spread of an infectious disease in a uniform population is given by the deterministic SEIR equations\n",
        "\n",
        "\\begin{align*}\n",
        "\\frac{dS}{dt} & = -(1-u)\\frac{\\beta S I}{N} \\\\\n",
        "\\frac{dE}{dt} & = (1-u)\\frac{\\beta S I}{N} - \\alpha E \\\\\n",
        "\\frac{dI}{dt} & = \\alpha E - \\gamma I \\\\\n",
        "\\frac{dR}{dt} & = \\gamma I\n",
        "\\end{align*} \n",
        "\n",
        "The model becomes somewhat more transparent by working with fraction of the population in the susceptible, exposed, infective, and recovered states rather than actual population counts. To this end, define\n",
        "\n",
        "$$\n",
        "s = \\frac{S}{N}, \\quad \n",
        "e = \\frac{S}{N}, \\quad\n",
        "i = \\frac{I}{N}, \\quad\n",
        "r = \\frac{R}{N}\n",
        "$$ \n",
        "\n",
        "After substitution, this results in a system of four equations.\n",
        "\n",
        "\\begin{align*}\n",
        "\\frac{ds}{dt} & = -(1-u)\\beta s i \\\\\n",
        "\\frac{de}{dt} & = (1-u)\\beta s i - \\alpha e \\\\\n",
        "\\frac{di}{dt} & = \\alpha e  - \\gamma i \\\\\n",
        "\\frac{dr}{dt} & = \\gamma i\n",
        "\\end{align*} \n",
        "\n",
        "where $s + e + i + r = 1$ is an invariant."
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        "## Parameter values\n",
        "\n",
        "Table taken from Boldog, et al., 2020.\n",
        "\n",
        "| $R_0$ | Incubation Period | Infective Period | Method of Estimation |\n",
        "|:---:|:---:|---|---|\n",
        "| 2.6 (1.5–3.5) | - | | Epidemic Simulations \n",
        "| 2.2 (1.4–3.8) | - | | Stochastic Simulations\n",
        "| 2.9 (2.3–3.6) | 4.8 days | | Exp. Growth, Max. Likelihood Est.\n",
        "| 2.56 (2.49–2.63) | - | | Exp. Growth, Max. Likelihood Est.\n",
        "| 3.11 (2.3–4.1) | - | | SEIR\n",
        "| 2.5 (2.0–3.1) | - | | Incidence Decay and Exponential Adjustment model\n",
        "| 2.2 (1.4–3.9) | 5.2 days (4.1–7.0) | | Renewal Equations\n",
        "| - (1.4–4.0) | - | | SEIR\n",
        "| 4.71 (4.5–4.9) | 5.0 days (4.9–5.1) | | . Dec. 2019, SEIJR, MCMC\n",
        "| 2.08 (1.9–2.2) | - | | Jan. 2020, SEIJR, MCMC\n",
        "| 2.68 (2.4–2.9) | - | | . SEIR, MCMC\n",
        "| - | 5.8 days (4.6–7.9) | | . Weibull\n",
        "| - | 4.6 days (3.3–5.8) | | . Weibull incl. Wuhan\n",
        "| - | 5.0 days (4.0–5.8) | | Weibull excl. Wuhan\n",
        "| - | 5.1 days (4.4–6.1) | | LogNormal\n",
        "| 2.6 | 5.1 | 3.3 | Boldog, et al."
      ]
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      "source": [
        "## Simulation"
      ]
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        "#@title Basic SEIR model { run: \"auto\" }\n",
        "R0 = 2.4 #@param {type:\"slider\", min:0, max:5, step:0.02}\n",
        "t_incubation = 5.1 #@param {type:\"slider\", min:0.1, max:10, step:0.1}\n",
        "t_infective = 3.3 #@param {type:\"slider\", min:0.1, max:10, step:0.1}\n",
        "u_control = 0 #@param {type:\"slider\", min:0, max:1, step:0.01}\n",
        "e_initial = 0.000001 #@param [\"0.001\", \"0.000001\", \"0.000000001\"] {type:\"raw\"}\n",
        "\n",
        "import numpy as np\n",
        "from scipy.integrate import odeint\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# initial number of infected and recovered individuals\n",
        "i_initial = 0.00\n",
        "r_initial = 0.00\n",
        "s_initial = 1 - e_initial - i_initial - r_initial\n",
        "\n",
        "# convert to model parameters\n",
        "alpha = 1/t_incubation\n",
        "gamma = 1/t_infective\n",
        "beta = R0*gamma\n",
        "u = u_control\n",
        "\n",
        "# SIR model differential equations.\n",
        "def deriv(x, t, alpha, beta, gamma):\n",
        "    s, e, i, r = x\n",
        "    dsdt = -(1-u)*beta * s * i\n",
        "    dedt =  (1-u)*beta * s * i - alpha * e\n",
        "    didt = alpha * e - gamma * i\n",
        "    drdt =  gamma * i\n",
        "    return [dsdt, dedt, didt, drdt]\n",
        "\n",
        "t = np.linspace(0, 160, 160)\n",
        "x_initial = s_initial, e_initial, i_initial, r_initial\n",
        "soln = odeint(deriv, x_initial, t, args=(alpha, beta, gamma))\n",
        "s, e, i, r = soln.T\n",
        "\n",
        "# plot the data\n",
        "fig, ax = plt.subplots(2,1, figsize=(10,6))\n",
        "\n",
        "ax[0].plot(t, s, 'b', alpha=0.5, lw=3, label='Susceptible')\n",
        "ax[0].plot(t, r, 'k', alpha=0.5, lw=3, label='Recovered')\n",
        "ax[0].set_ylim(0, 1.1)\n",
        "\n",
        "ax[1].plot(t, e, 'g', alpha=0.5, lw=3, label='Exposed')\n",
        "ax[1].plot(t, i, 'r', alpha=0.5, lw=3, label='Infective')\n",
        "\n",
        "for a in ax:\n",
        "    a.set_facecolor(\"#dddddd\")\n",
        "    a.legend().get_frame().set_alpha(0.5)\n",
        "    a.set_xlabel('Time /days')\n",
        "    a.set_ylabel('Fraction')\n",
        "    a.yaxis.set_tick_params(length=0)\n",
        "    a.xaxis.set_tick_params(length=0)\n",
        "    a.grid(b=True, which='major', c='w', lw=1, ls='-')\n",
        "    for spine in ('top', 'right', 'bottom', 'left'):\n",
        "        a.spines[spine].set_visible(False)"
      ],
      "execution_count": 54,
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BZIc/+jTG2I0xGcaYdGOMIzjfuHyhIO040K/Zct9gWqN04GrgfRE5hDXo+3Jt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\nmZlZRTlQMzMzM6soB2pmZmZmFfUfDRByTGPeOh0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LKWrWGk9vDce",
        "colab_type": "text"
      },
      "source": [
        "## SEIR model for SARS-CoV-2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pxIDB4-EvDcf",
        "colab_type": "code",
        "outputId": "7b4bc1e4-6e5d-4d04-956d-b633335794f9",
        "colab": {}
      },
      "source": [
        "from scipy.integrate import odeint\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "u = 0.3\n",
        "mu = 0\n",
        "alpha = 1/5.1   # incubation period\n",
        "R0 = 2.4\n",
        "gamma = 3.3\n",
        "beta = R0*gamma\n",
        "\n",
        "N = 331000000\n",
        "\n",
        "def SEIR(x, t):\n",
        "    S, E1, E2, I1, I2, I3, R = x\n",
        "    dS = -(1-u)*beta*S*(I1 + I2 + I3)/N\n",
        "    dE1 = -dS - 2*alpha*E1\n",
        "    dE2 = 2*alpha*E1 - 2*alpha*E2\n",
        "    dI1 = 2*alpha*E2 - 3*gamma*I1 - mu*I1\n",
        "    dI2 = 3*gamma*I1 - 3*gamma*I2 - mu*I2\n",
        "    dI3 = 3*gamma*I2 - 3*gamma*I3 - mu*I3\n",
        "    dR = 3*gamma*I3\n",
        "    return [dS, dE1, dE2, dI1, dI2, dI3, dR]\n",
        "\n",
        "\n",
        "IC = [N, 1, 0, 0, 0, 0, 0]\n",
        "t = np.linspace(0, 180, 1000)\n",
        "\n",
        "\n",
        "soln = odeint(SEIR, IC, t)\n",
        "\n",
        "S = soln[:, 0]\n",
        "E = soln[:, 1] + soln[:, 2]\n",
        "I = soln[:, 3] + soln[:, 4] + soln[:, 5]\n",
        "R = soln[:, 6]\n",
        "\n",
        "plt.plot(t, S, label = 'Susceptable')\n",
        "plt.plot(t, E, label = 'Exposed')\n",
        "plt.plot(t, I, label = 'Infectious')\n",
        "plt.plot(t, R, label = 'Recovered')\n",
        "plt.ylim([1, 1.2*N])\n",
        "\n",
        "plt.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x122845990>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wo/TS3CS6oYgsE5HtIrJVRMYW0UZEZJqI7BGRTSLSqXziKqVUxRIRHu3Vkv0pGXyx/pDVcS6qNEfoduCvxpg2QFdgtIi0LdSmH9DC9RgJvOvWlEopZaEb29QhOjKMaT/uJsfuuUfpJRZ0Y8wRY8x61/QZYDvQoFCzgcDHxulXoIaI1Hd7WqWUssC5o/Skk5n8e12S1XGKVaY+dBGJAjoCawotagAcLPA6iQuLPiIyUkTiRSQ+ObnyDiKvlKp6ureKILZhDaYv20O2Pc/qOEUqdUEXkRBgITDOGHO68OIi3nLBmfjGmPeNMXHGmLiIiIiyJVVKKQuJCI/d1JJDpzJZEO+ZR+mlKugi4oezmM8zxnxeRJMkoGGB15GA55/jo5RSZXBdi3DiGtdk+o97yMr1vKP00pzlIsBHwHZjzGvFNFsE3OM626UrkGaMqTwDICilVCmcO0o/ejqLf/663+o4FyjNEXo34G6gp4gkuB43i8iDIvKgq823wF5gD/ABMKp84iqllLWuaR7OdS3CeXvZHtIyc62Ocx7fkhoYY36i6D7ygm0MMNpdoZRSypM92a81/d/6iXeXJ/Jkv9ZWx8mnV4oqpVQZtbsijD/GNmDWz79z+FSm1XHyaUFXSqlL8NfeLTEGXvthl9VR8mlBV0qpSxBZM4hh1zRm4fokdhwtfCa3NbSgK6XUJRrdozmh/r68/N0Oq6MAWtCVUuqS1QiqxugezVm2M5mfdp+wOo4WdKWUuhzDromiUa0gJn291fLhdbWgK6XUZQjwszGxf1v2HE9nzup9lmbRgq6UUpfpxjZ16N4qgjeX7Ob4mSzLcmhBV0qpyyQiTOzflix7Hi9/t9OyHFrQlVLKDZpGhHDftU1ZuD6JdftPWpJBC7pSSrnJIz2bU7e6P09/sdmSL0i1oCullJsE+/syeWB7dhw9w/sr91b49rWgK6WUG/VpV4+bO9TjzaW7SUxOr9Bta0FXSik3mzSgHYF+Np5cuAmH44Kbt5UbLehKKeVmdUID+L9b2vDbvpPMW1NxN8LQgq6UUuVgUOdIrm8ZwQvfbq+wrhct6EopVQ5EhCmDogn0szFufgI59vI/60ULulJKlZO61QN48bZoNh9K4/UlznHTc/btwzjKp7hrQVdKqXLUt309hl7ZkBkrEvllQyL7hgzl2Isvlcu2SizoIjJTRI6LyJZilncXkbQCN5Ce6P6YSilVeT3Tvy1Nw4NZN/FF8tLTqTFoULlspzRH6LOBviW0WWWMiXU9Jl9+LKWU8h7B/r682yWYHrtXs7pDD3yaNS+X7ZRY0I0xK4HUctm6UkpVAcbhoNrbr+IIC+PVBjcwdXH5DODl66b1XC0iG4HDwHhjzNaiGonISGAkQKNGjdy0aaWU8mxpixaRuXEjDV98kXG1O9CzdZ1y2Y47Cvp6oLExJl1Ebga+BFoU1dAY8z7wPkBcXFzFXT6llFIWcWRkkPz6GwRERxM2cAAjfcrvXJTLXrMx5rQxJt01/S3gJyLhl51MKaW8QMqsWdiPHaPuk08g5VjMwQ0FXUTqiYi4pru41plyuetVSqnKLvfYcVI+/IjQPn0I6tSp3LdXYpeLiPwL6A6Ei0gS8CzgB2CMmQEMAh4SETuQCQw1xmh3ilKqykue9ibGbqfOXx+rkO2VWNCNMXeUsPxt4G23JVJKKS+QtWMHaZ9/Qa1hw6hWQSeB6JWiSinlZsYYjr38Mrbq1Ql/6MEK264WdKWUcrOzK1eS8cuvhI8ejS0srMK2qwVdKaXcyDgcHH/9DfwaNqTm0CEVum0t6Eop5Uanv/uO7B07iBjzCFKtWoVuWwu6Ukq5icnNJXnaNPxbtqT6LbdU+Pbddem/UkpVeae++ILc/QeIfGd6uV9EVBQ9QldKKTdwZGVxYvo7BMbGEtKjhyUZtKArpZQbnPzXfOzHjhHx6KO4Lp6vcB7V5ZKbm0tSUhJZWVlWR6mSAgICiIyMxM/Pz+ooSlUqeenppLz3HsHXXEPwVV0sy+FRBT0pKYnQ0FCioqIs+w1XVRljSElJISkpiSZNmlgdR6lKJXXWbPJOnSLi0UctzeFRXS5ZWVnUrl1bi7kFRITatWvrX0dKlZH95ElSZ80i9KabCOzQ3tIsHlXQAS3mFtJ9r1TZpbz3Po6sLCLGjbU6iucVdKWUqixyjx7l5CefEDZwIP7NmlkdRwt6UV544QXatWtHdHQ0sbGxrFmzxpIcCQkJfPvttyW2mz17Ng8//HCRy0JCQtwdSynlcmL6OxhjCB892uoogId9KeoJfvnlF7755hvWr1+Pv78/J06cICcnx5IsCQkJxMfHc/PNN1uyfaVU8XL27ePU559T8447qBbZwOo4gAcX9Oe+3sq2w6fdus62V1Tn2T+0u2ibI0eOEB4ejr+/PwDh4c676UVFRREfH094eDjx8fGMHz+e5cuXs2LFCsaOdfadiQgrV64kNDSUV155hblz5+Lj40O/fv146aWXSExMZPTo0SQnJxMUFMQHH3xA69atGT58OAEBAWzdupVjx47x2muv0bt3byZOnEhmZiY//fQTEyZMoEmTJowbN47MzEwCAwOZNWsWrVq1AuDgwYP07duX33//nTvvvJNnn332gp9typQpLFiwgOzsbG699Vaee+45d+5epaqU5GlvIdWqEf7gA1ZHyeexBd0qvXv3ZvLkybRs2ZJevXoxZMgQbrjhhmLbT506lenTp9OtWzfS09MJCAjgu+++48svv2TNmjUEBQWRmpoKwMiRI5kxYwYtWrRgzZo1jBo1ih9//BGAffv2sWLFChITE+nRowd79uxh8uTJxMfH8/bbzvuHnD59mpUrV+Lr68uSJUt46qmnWLhwIQBr165ly5YtBAUFceWVV3LLLbcQFxeXn3Px4sXs3r2btWvXYoxhwIABrFy5kuuvv768dqVSXitrxw5Of/sttUeOxDfcc26h7LEFvaQj6fISEhLCunXrWLVqFcuWLWPIkCG89NJLxbbv1q0bjz32GHfddRe33XYbkZGRLFmyhBEjRhAUFARArVq1SE9PZ/Xq1QwePDj/vdnZ2fnTf/rTn/Dx8aFFixY0bdqUHTt2XLCttLQ0hg0bxu7duxERcnNz85fddNNN1K5dG4DbbruNn3766YKCvnjxYjp27AhAeno6u3fv1oKu1CVIfuNNfKpXp/Z991od5TyluafoTKA/cNwYc8FJlq4bRL8J3AxkAMONMevdHbQi2Ww2unfvTvfu3enQoQNz5szB19cXh8MBcN652k8++SS33HIL3377LV27dmXJkiUYYy44BdDhcFCjRg0SEhKK3Gbh9kWdQvjMM8/Qo0cPvvjiC/bt20f37t1L/X5jDBMmTOCBBzznz0OlKqOM9RtIX76ciEcfrdCbV5RGac5ymQ30vcjyfkAL12Mk8O7lx7LOzp072b17d/7rhIQEGjduTFRUFOvWrQPI7+YASExMpEOHDjzxxBPExcWxY8cOevfuzcyZM8nIyAAgNTWV6tWr06RJEz777DPAWWA3btyYv57PPvsMh8NBYmIie/fupVWrVoSGhnLmzJn8NmlpaTRo4PzyZfbs2efl/uGHH0hNTSUzM5Mvv/ySbt26nbe8T58+zJw5k/T0dAAOHTrE8ePHL3d3KVWlGGNIfv11bOHh1Lr7z1bHuUCJBd0YsxJIvUiTgcDHxulXoIaI1HdXwIqWnp7OsGHDaNu2LdHR0Wzbto1Jkybx7LPPMnbsWK677jpsNlt++zfeeIP27dsTExNDYGAg/fr1o2/fvgwYMIC4uDhiY2OZOnUqAPPmzeOjjz4iJiaGdu3a8dVXX+Wvp1WrVtxwww3069ePGTNmEBAQQI8ePdi2bRuxsbF8+umnPP7440yYMIFu3bqRl5d3Xu5rr72Wu+++m9jYWG6//fbzulvA+d3AnXfeydVXX02HDh0YNGjQeb8slFIlO/vzajJ++43wBx/Ex9Wl6knEGFNyI5Eo4Jtiuly+AV4yxvzker0UeMIYE19E25E4j+Jp1KhR5/3795+3fPv27bRp06bsP0UlN3z4cPr378+gQYOsjlJlPwOlSmKMYd+gweSdPEnT/36HTwXfjegcEVlnjIkrapk7Liwq6nrxIn9LGGPeN8bEGWPiIiIi3LBppZSqGGd++IGsrVsJf/hhy4p5SdxxlksS0LDA60jgsBvWW2UU7g9XSnkWk5dH8pvTqNa0KWED/mB1nGK54wh9EXCPOHUF0owxR9ywXqWU8ghpi74mJzGRiDFjEF+PPdu7VKct/gvoDoSLSBLwLOAHYIyZAXyL85TFPThPWxxRXmGVUqqiOXJyOPHWWwS0bUto75usjnNRJRZ0Y8wdJSw3gGeMTKOUUm52asFn5B4+TL3nJlly4+ey8Ox0SillobwzZzgxfTpBXboQfO21VscpkRb0Qmw2G7GxsfmPi132X9G6d+9OfPwFZ4MqpcpJygcfknfyJHUef7xS3ADGc3v3LRIYGFjs5flKqaoj98gRUufMofof/kBge2vGliorzy3o3z0JRze7d531OkC/sh9xp6Wl0aVLFxYtWkSrVq2444476NmzJ/fffz8hISE88MADLFu2jJo1azJ//nwiIiJISEjgwQcfJCMjg2bNmjFz5kxq1qzJtGnTmDFjBr6+vrRt25b58+dz9uxZHnnkETZv3ozdbmfSpEkMHDiQzMxMRowYwbZt22jTpg2ZmZnu3R9KqWIlv/EmGEMdD7i1XGlpl0shmZmZ53W5fPrpp4SFhfH2228zfPhw5s+fz8mTJ7n//vsBOHv2LJ06dWL9+vXccMMN+WOM33PPPbz88sts2rSJDh065M9/6aWX2LBhA5s2bWLGjBmA8w5JPXv25LfffmPZsmX87W9/4+zZs7z77rsEBQWxadMmnn766fyxZJRS5Str+3bSFi2i5t1/xq+BZ9y8olSMMZY8OnfubArbtm3bBfMqWnBwcLHL7r//flOrVi1z8ODB/Hk+Pj4mNzfXGGNMYmKiiYmJMadOnTINGzbMb7Nnzx7TsWNHY4wxffr0MbfffruZO3euOXPmjDHGmM6dO5t27dqZmJgYExMTYxo2bGi2bdtmBg4caJYuXZq/no4dO5rffvvNrT9vYZ7wGShlJYfDYfaPGGF2drnK2NPSrI5zASDeFFNX9Qi9lBwOB9u3bycwMDD/hhVFKemLk//85z+MHj2adevW0blzZ+x2O8YYFi5cSEJCAgkJCRw4cCB/PJXK8EWMUt7k7KpVnF39C+GjR2GrXt3qOGWiBb2UXn/9ddq0acO//vUv7r333vybSzgcDv79738D8Mknn3DttdcSFhZGzZo1WbVqFQBz587lhhtuwOFwcPDgQXr06MErr7zCqVOnSE9Pp0+fPrz11lsY10BpGzZsAOD6669n3rx5AGzZsoVNmzZV9I+tVJVicnI49o8Xqda4MTWHDrU6Tpl57peiFjnXh35O3759uffee/nwww9Zu3YtoaGhXH/99Tz//PM899xzBAcHs3XrVjp37kxYWBiffvopAHPmzMn/UrRp06bMmjWLvLw8/vznP5OWloYxhkcffZQaNWrwzDPPMG7cOKKjozHGEBUVxTfffMNDDz3EiBEjiI6OJjY2li5duli1W5SqElI//picffto+P57iIcOwHUxpRo+tzzExcWZwudUV8ahW0NCQvJvGuENKuNnoJQ75B47xt5+NxPUtSsN35ludZxilffwuUopVekdnzIVY7dTd8KTVke5ZFrQL5M3HZ0rVVVlxMdz+ptvqP2X+6jWsGHJb/BQWtCVUlWayc3l6OS/43tFfWq7ri+prPRLUaVUlZby0Uyyd+0i8p3p+AQGWh3nsugRulKqysre+zsn3nmH0L59Ce3Z0+o4l00LulKqSjIOB0cnTkQCAqj39FNWx3ELLeiFhISElNhm1apVtGvXjtjY2DIPmPXll1+ybdu2/NcTJ05kyZIlZc6plLo8pz77Nxnx8dR94nF8veSm9VrQL8G8efMYP348CQkJBJaxz61wQZ88eTK9evVyd0Sl1EXkJCVx/JVXCLrqKsJuu83qOG5Tqi9FRaQv8CZgAz40xrxUaPlwYApwyDXrbWPMh5cT7OW1L7MjdcflrOICrYf1EEAAABMfSURBVGu15okuT5Sq7fLly5k0aRLh4eFs2bKFzp07889//pOPPvqIBQsW8P3337NkyRLmzZvHlClTWLBgAdnZ2dx66635Iyt+/PHHTJ06FREhOjqahx56iEWLFrFixQqef/55Fi5cyN///nf69+/PoEGDWLp0KePHj8dut3PllVfy7rvv4u/vT1RUFPHx8YSHhxMfH8/48eNZvnw5K1asYOxY59CeIsLKlSsJDQ116z5TytuYvDwOP+E81/yKf7zgVeMlleYm0TZgOnATkAT8JiKLjDHbCjX91BjzcDlktMyGDRvYunUrV1xxBd26dePnn3/mL3/5Cz/99FN+EV68eDG7d+9m7dq1GGMYMGAAK1eupHbt2rzwwgv8/PPPhIeHk5qaSq1atRgwYED+ewvKyspi+PDhLF26lJYtW3LPPffw7rvvMm7cuGLzTZ06lenTp9OtWzfS09MJCAgo712iVKWX8tFMMteto/5LL1auoXFLoTRH6F2APcaYvQAiMh8YCBQu6G5V2iPp8tSlSxciIyMBiI2NZd++fVxb6L6CixcvZvHixXTs2BFwXmi0e/duNm7cyKBBgwgPDwegVq1aF93Wzp07adKkCS1btgRg2LBhTJ8+/aIFvVu3bjz22GPcdddd3HbbbflZlVJFy9q2jeS33iK0Tx/CBg60Oo7blaYPvQFwsMDrJNe8wm4XkU0i8m8RKfJSKxEZKSLxIhKfnJx8CXErlr+/f/60zWbDbrdf0MYYw4QJE/KHvt2zZw/33Xcfxpgy/Sl3sTF1fH19cTgcgPNI/pwnn3ySDz/8kMzMTLp27cqOHe7tolLKm+SdOUPSo4/iW7Mm9SY961VdLeeUpqAX9VMXrj5fA1HGmGhgCTCnqBUZY943xsQZY+IivORb5T59+jBz5sz8IQAOHTrE8ePHufHGG1mwYAEpKSkA+WOoh4aGcubMmQvW07p1a/bt28eePXuA/w25CxAVFZV/t6KFCxfmvycxMZEOHTrwxBNPEBcXpwVdqWIYYzjy1NPkJh2iwWuv4luzptWRykVpCnoSUPCIOxI4XLCBMSbFGJPtevkB0Nk98Txf7969ufPOO7n66qvp0KEDgwYN4syZM7Rr146nn36aG264gZiYGB577DEAhg4dypQpU+jYsSOJiYn56wkICGDWrFkMHjyYDh064OPjw4MPPgjAs88+y9ixY7nuuuuw2Wz573njjTdo3749MTExBAYG0q9fv4r94ZWqJFJnz+HMDz9Q569/JSiuyIEKvUKJw+eKiC+wC7gR51ksvwF3GmO2FmhT3xhzxDV9K/CEMabrxdbrLcPnehv9DJS3Obt2LQdG3Etozx40mDat0ne1XGz43BK/FDXG2EXkYeB7nKctzjTGbBWRyTjvbbcIGCMiAwA7kAoMd1t6pZS6RNm//07SI2Oo1rgx9f/xj0pfzEtSqvPQjTHfAt8WmjexwPQEYIJ7oyml1KWznzxJ0oMPIT4+NHxvBrYqcI2GjraolPI6juxsDj0yhtwjR2g0e3alHuO8LLSgK6W8isnJ4dCYsWSsW8cVU6cQ1Kmj1ZEqjI7lopTyGsZu59DfHid9xQrqPfssYbfcYnWkCqUFXSnlFUxuLocnPMWZ77+nzpNPUHPoEKsjVTjtcinEZrPRoUMH7HY7TZo0Ye7cudSoUcPqWGXWvXt3pk6dSpwXn3Or1DmOrCwOPfoY6cuWEfHoo9QePvzyV5qVBkc3w8l9kJYEZ45AbhbkuS658a8OAWEQWh9qN4fazaBmE/Cx7jhZC3ohgYGBJCQkAP8bT+Xpp5+2OJWT3W7H11c/MqUKyjtzhqSHRpGxbh31np1IzTvuuLQVpSfD3mWQ+CMcXAOpe89fHhwBfoFgcw0Jkn0aMk/9r8AD+IdBwyuh4VXQtDs06Aw+NiqKx1aHo//4B9nb3Xspu3+b1tR7qvR3Jrn66qvZtGlT/uvSDpM7d+5c9u/fz7333ktycjIRERHMmjWLsLAwYmJi2Lt3Lz4+PmRkZNCqVSv27t3LgQMHGD16NMnJyQQFBfHBBx/QunVrhg8fTq1atdiwYQOdOnVi8uTJPPLII2zevBm73c6kSZMYOHAgmZmZjBgxgm3bttGmTZsy33hDqcooZ98+Do5+mJz9+7liyhTC+pexzzz7DGz9AtbPhaS1znmBtaDxNRB7J9Tv6Dzyrn4F+Ppf+H5jICMVUvbAiV1wKB4OroVl/4BlL0BQOLToDa1vgRY3Fb0ON/LYgm61vLw8li5dyn333QdQpmFyAR5++GHuuecehg0bxsyZMxkzZgxffvklMTExrFixgh49evD111/Tp08f/Pz8GDlyJDNmzKBFixasWbOGUaNG8eOPPwKwa9culixZgs1m46mnnqJnz57MnDmTU6dO0aVLF3r16sV7771HUFAQmzZtYtOmTXTq1MmyfadURUhftYpDfx2P+PjQ6MMPCO560YvT/8cYSPoN1n8MWz6H3LMQ0Rp6/h80uxHqx5a+20QEgms7H42ugk53O+dnpDqP9Hf9F3Z+Cxs/cXbPtB0IHf4EjbuVS9eMxxb0shxJu1NmZmb+ULmdO3fmpptuAso+TO4vv/zC559/DsDdd9/N448/DsCQIUP49NNP6dGjB/Pnz2fUqFGkp6ezevVqBg8enJ8jO/t/f8YNHjw4fwyXxYsXs2jRIqZOnQo4R188cOAAK1euZMyYMQBER0cTHR1dbvtIKSuZ3FyS33mHlPfex79FCyKnv0210gwdffYEbJwPG+ZC8g7wC4b2t0GneyDySmdxdpegWtBhkPORZ4ffl8Omz5y/QNZ/DF0egJtfcd/2XDy2oFvlXB96Wloa/fv3Z/r06YwZMyZ/mNwHHnjgvPbTSjk2xLk2AwYMYMKECaSmprJu3Tp69uzJ2bNnqVGjRn7ffWHBwcH508YYFi5cSKtWrYrdhlLeKvv33zn8+BNkbd5M2B//SL2Jz+ATFFT8Gxx5zn7x9XNhx3/Akess3n+Y5izm/hVw9ajNF5r3cj5yMpxH7LWblcum9LTFYoSFhTFt2jSmTp1Kbm5umYfJveaaa5g/fz7gvAfpuRtjhISE0KVLF8aOHUv//v2x2WxUr16dJk2a8NlnnwHOor1x48Yic/Xp04e33norf/z0DRs2AHD99dczb948ALZs2XJe379SlZ3JyeHEe+/z+623kXPgAA3eeIMrXnqx+GJ+6gAsexHejIF/3g6/r4QuI2HUr/CXJdB5WMUU88KqBTmP2q8on4ud9Aj9Ijp27EhMTAzz58/n7rvvZvv27Vx99dWAszD/85//PG+YXJvNRseOHZk9ezbTpk3j3nvvZcqUKflfip4zZMgQBg8ezPLly/PnzZs3j4ceeojnn3+e3Nxchg4dSkxMzAWZnnnmGcaNG0d0dDTGGKKiovjmm2946KGHGDFiBNHR0cTGxtKlS5dy3z9KVYSzq1dz9PkXyNm7l9CbbqLu/z2NX926Fza0ZzuPftfPdfZfAzTrATdNdn4pWc5fSHqCEofPLS86fK5n0s9AeYrMhASOv/EmGb/+il9kJPWe+T9CXDd9yWcMHN0ECZ/A5s8gIwWqR0LHuyD2LqjZ2Jrw5eiyhs9VSqmKYowh49dfSZk9m7MrVmKrVYu6T02gxpAh+BS4JSTpx50FPOETOLYFbNWg1c3Q8c/QrGeFnvvtSbSgK6Usl3f6NKe/+y8n580je9cubLVrEzFuHLXu/jM+504KOH0EdnwD276C/T+DcTgv3Ll5KrS/3XlmSRXncQW9rDdXVu5jVfebqpoc2dmcXb2atEWLSF/6IyYnB/9Wraj/wgtU738LPn5+zu6U9T/Cru+dV29inOeMXzfeWcTrtLb6x/AoHlXQAwICSElJoXbt2lrUK5gxhpSUFAICAqyOorxY7tGjpK9aRfryFZxdvRqTmYmtZk1q/OlPhA34AwH1/JGktfD1KOfphhnOs8eo1wF6PAVtBmgRvwiPKuiRkZEkJSWRnJxsdZQqKSAggMjSXKChVCmY3Fyy9+4lM2EjmevXkbFuPblJSQD41q9PjZtvIqT9FQTXyUSOroPvPoDMk843B9eB5jc5+8ObdofQIs5qURfwqILu5+dHkyZNrI6hlCoDR2YmuUlJ5BxMImffPrJ37iRr506yExMhNxcAW1gIQS3qUatTa4JqpeFv9iDZ62AnzkdEa2jdHxp2gcguEN7S0lELKyuPKuhKKc9gjMFkZJCXnk5eair2EyewJ59wPh8/Tl7yUXKPHCb30GHsKafOe69vqB/+4T6EtMnGPyiNgFo5VAs9jMgu52iEEW2g7u1Qp63zUbcdBFa+Iao9kRZ0BcYU/4Wow3GR9xWzrIj35K+/mPeY4tZVYNkFGQttx1BgebHbMVDsd78O53nNRS763/rO386F7fOXF7fvjKPYCMbhgDwHJs/ums7D5DnAkYex28GeC7k5OPKcz9jtGHsu5NkxubmQl+tsm5uLyczC5GRjsrMx2TmuRzYmOwuTnY0jKxuTk4PJzMKRke18ZOZgsnJxZNmhmPji68AW6MAWmEe1sDyCGuThG2LHNyQPW3gwttqhEBIBYZFQoxFZ1RuSERZJXlgDHIE1cGDIM3nkOfLIM3k4slPIyzqOwzicrx3O5zyTd8E8h3FgN3bnfEcedmPPX4/dYT9vvede2x32Ypdd7H3n1m93lLyNc20dxoFNbM6Hj/PZ18cXH/HB5mPDV5zTA5sP5I7WlzjM70VUuoL+81sPEfT+8iKXFfs16kVO3nDrewC5hBNFinvPRb8WLuY9+keqKkm2L+T6Qo7rObMaZPhDZqBwtoZzOiNAyPAXMvzhdBCcChZOBUNaMGRXK6lsZAIHIO0ApK2uiB+pRD7ik19cfcU3v9ieK7IFi29R8/19/f/33ou8T0TyfwmdK/oFi/256QBb+Zx8YNmVoiKSDOy/xLeHAyfcGKc8VZasmtP9KktWzele5Z2zsTEmoqgFlhX0yyEi8cVd+uppKktWzel+lSWr5nQvK3PqX+hKKeUltKArpZSXqKwF/X2rA5RBZcmqOd2vsmTVnO5lWc5K2YeulFLqQpX1CF0ppVQhWtCVUspLVLqCLiJ9RWSniOwRkSetznOOiDQUkWUisl1EtorIWNf8SSJySEQSXI+bPSDrPhHZ7MoT75pXS0R+EJHdrueaHpCzVYH9liAip0VknCfsUxGZKSLHRWRLgXlF7kNxmub6N7tJRDpZnHOKiOxwZflCRGq45keJSGaB/TqjonJeJGuxn7WITHDt050i0sfinJ8WyLhPRBJc8yt2nxrXZd+V4QHYgESgKVAN2Ai0tTqXK1t9oJNrOhTYBbQFJgHjrc5XKOs+ILzQvFeAJ13TTwIvW52ziM/+KNDYE/YpcD3QCdhS0j4Ebga+w3nxb1dgjcU5ewO+rumXC+SMKtjOQ/ZpkZ+16//WRsAfaOKqCzarchZa/iow0Yp9WtmO0LsAe4wxe40xOcB8YKDFmQAwxhwxxqx3TZ8BtgMNrE1VJgOBOa7pOcAfLcxSlBuBRGPMpV5d7FbGmJVAaqHZxe3DgcDHxulXoIaI1LcqpzFmsTHG7nr5K+ARYyYXs0+LMxCYb4zJNsb8DuzBWR/K3cVyivNGDn8C/lURWQqrbAW9AXCwwOskPLBoikgU0BFY45r1sOvP25me0JWBcySYxSKyTkRGuubVNcYcAecvJ6COZemKNpTz/5N42j6F4vehJ/+7vRfnXw/nNBGRDSKyQkSusypUIUV91p66T68DjhljdheYV2H7tLIV9KLGq/Ko8y5FJARYCIwzxpwG3gWaAbHAEZx/jlmtmzGmE9APGC0i11sd6GJEpBowAPjMNcsT9+nFeOS/WxF5GrAD81yzjgCNjDEdgceAT0SkulX5XIr7rD1ynwJ3cP6BR4Xu08pW0JOAhgVeRwKHLcpyARHxw1nM5xljPgcwxhwzxuQZ5xiwH1BBfxZejDHmsOv5OPAFzkzHznUDuJ6PW5fwAv2A9caYY+CZ+9SluH3ocf9uRWQY0B+4y7g6e13dFymu6XU4+6VbWpfyop+1J+5TX+A24NNz8yp6n1a2gv4b0EJEmriO2oYCiyzOBOT3nX0EbDfGvFZgfsG+0luBLYXfW5FEJFhEQs9N4/yCbAvO/TjM1WwY8JU1CYt03lGPp+3TAorbh4uAe1xnu3QF0s51zVhBRPoCTwADjDEZBeZHiIjNNd0UaAHstSZlfqbiPutFwFAR8ReRJjizrq3ofIX0AnYYY5LOzajwfVpR376664HzjIFdOH/TPW11ngK5rsX5J98mIMH1uBmYC2x2zV8E1Lc4Z1OcZwdsBLae24dAbWApsNv1XMvqferKFQSkAGEF5lm+T3H+gjkC5OI8WryvuH2Is3tguuvf7GYgzuKce3D2P5/7dzrD1fZ217+JjcB64A8esE+L/ayBp137dCfQz8qcrvmzgQcLta3QfaqX/iullJeobF0uSimliqEFXSmlvIQWdKWU8hJa0JVSyktoQVdKKS+hBV0ppbyEFnSllPIS/w9piz2zPWMdqgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CgNk2uN7vDci",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}