Gompertz.ipynb

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  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nicoavilan/Programas-Videos/blob/main/Gompertz.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e8opldWv7cV0"
      },
      "source": [
        "Código usado en el video:\r\n",
        "\r\n",
        "[Modelos de poblaciones: Exponencial, Logístico y Gompertz (+COVID19 + Python)](https://www.youtube.com/watch?v=lGvtzgauxPE)\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "[Más videos del mismo canal](https://www.youtube.com/channel/UCaOCO-2LP3Kwlnxtt17SB4g)\r\n",
        "\r\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZFfCWdLcFMKp"
      },
      "source": [
        "## Modelo de Gompertz  $\\qquad\\frac{dP}{dt}=ke^{-ct}P$\r\n",
        "\r\n",
        "$P(t)=ae^{-be^{-ct}}$\r\n",
        "\r\n",
        "$\\frac{dP}{dt}=abce^{-ct}e^{-be^{-ct}}$\r\n",
        "\r\n",
        "\r\n"
      ]
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        "id": "-Kovtw3LhMsw",
        "outputId": "249db382-7a68-4bcc-db05-ea31e90f094b"
      },
      "source": [
        "from ipywidgets import interactive\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "import numpy as np\r\n",
        "\r\n",
        "def P(a,b,c,t):\r\n",
        "  return a*np.exp(-b*np.exp(-c*t))\r\n",
        "\r\n",
        "def dP(a,b,c,t):\r\n",
        "  return a*b*c*np.exp(-c*t)*np.exp(-b*np.exp(-c*t))\r\n",
        "\r\n",
        "def f(a,b,c):\r\n",
        "  N=300\r\n",
        "  t=np.linspace(0,50,N)\r\n",
        "\r\n",
        "  plt.figure(figsize=(10,4))\r\n",
        "\r\n",
        "  plt.subplot(1,2,1)\r\n",
        "  plt.plot(t,P(a,b,c,t))\r\n",
        "  plt.title(\"Población\")\r\n",
        "\r\n",
        "  plt.subplot(1,2,2)\r\n",
        "  plt.plot(t,dP(a,b,c,t))\r\n",
        "  plt.title(\"Derivada\")\r\n",
        "  plt.ylim(0,70)\r\n",
        "  plt.show()\r\n",
        "\r\n",
        "interactive(f, a=(0,100),b=(10,500),c=(0.,2.))"
      ],
      "execution_count": 4,
      "outputs": [
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              "interactive(children=(IntSlider(value=50, description='a'), IntSlider(value=255, description='b', max=500, min…"
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}