community_models_table_28.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import cobra\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.optimize import linprog\n",
    "import scipy\n",
    "import mip\n",
    "from copy import deepcopy\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import json\n",
    "def save_dict(data, name):\n",
    "    with open(name, 'w' ) as file:\n",
    "        json.dump( data, file )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Community modeling\n",
    "\n",
    "In this notebook we will implement a method to create community models of two or more species specific metabolic models using cobrapy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Growth:  0.2823653925322476\n",
      "Growth:  2.558694612613393\n"
     ]
    }
   ],
   "source": [
    "model_DP = cobra.io.read_sbml_model(\"models/consistent_DP_SNM.xml\")\n",
    "model_SA = cobra.io.read_sbml_model(\"models/consistent_iYS854_SNM.xml\")\n",
    "print(\"Growth: \", model_DP.slim_optimize())\n",
    "print(\"Growth: \", model_SA.slim_optimize())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "for rec in model_SA.reactions:\n",
    "    rec.lower_bound = max(rec.lower_bound, -1000)\n",
    "    rec.upper_bound = min(rec.upper_bound, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "compm_SA = json.loads(open(\"compm_SA.json\").read())\n",
    "compm_DP = json.loads(open(\"compm_DP.json\").read())\n",
    "compm = compm_SA.copy()\n",
    "for key in compm_DP:\n",
    "    if not key in compm:\n",
    "        compm[key] = compm_DP[key]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "BIOMASS_DP = \"Growth\" \n",
    "BIOMASS_SA = \"BIOMASS_iYS_wild_type\"\n",
    "models = [model_DP.copy(), model_SA.copy()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Community model growths on SNM3 medium\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "from community_models import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1 = Model(model_DP, BIOMASS_DP)\n",
    "model2 = Model(model_SA, BIOMASS_SA)\n",
    "shuttle_community_model = MIP_community_model(model1, model2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<community_models.MIP_community_model object at 0x7fa99e600460>\n"
     ]
    }
   ],
   "source": [
    "print(shuttle_community_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.set_medium(compm)\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COMPM_max_plot_RM.pdf\", bbox_inches='tight', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "shuttle_community_model.reset_model()\n",
    "shuttle_community_model.weights = [0.85,0.15]\n",
    "shuttle_community_model.set_medium(compm)\n",
    "COOPM = shuttle_community_model.compute_coopm(enforce_survival=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.set_medium(COOPM)\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COOPM_precomputed_0.85_0.15_RM.pdf\", bbox_inches='tight', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "shuttle_community_model.reset_model()\n",
    "shuttle_community_model.weights = [0.85,0.15]\n",
    "shuttle_community_model.set_medium(compm)\n",
    "COOPM = shuttle_community_model.compute_coopm(enforce_survival=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.set_medium(COOPM)\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COOPM_precomputed_0.85_0.15_enforce_survival_RM.pdf\", bbox_inches='tight', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "shuttle_community_model.reset_model()\n",
    "shuttle_community_model.weights = [1,1]\n",
    "shuttle_community_model.set_medium(compm)\n",
    "COOPM = shuttle_community_model.compute_coopm(enforce_survival=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.set_medium(COOPM)\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COOPM_precomputed_1_1_enforce_survival_RM.pdf\", bbox_inches='tight', dpi=1000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "shuttle_community_model.reset_model()\n",
    "shuttle_community_model.weights = [10,1]\n",
    "shuttle_community_model.set_medium(compm)\n",
    "COOPM = shuttle_community_model.compute_coopm(enforce_survival=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.set_medium(COOPM)\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COOPM_precomputed_10_1_enforce_survival_RM.pdf\", bbox_inches='tight', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "shuttle_community_model.reset_model()\n",
    "shuttle_community_model.weights = [100,1]\n",
    "shuttle_community_model.set_medium(compm)\n",
    "COOPM = shuttle_community_model.compute_coopm(enforce_survival=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.set_medium(COOPM)\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COOPM_precomputed_100_1_RM.pdf\", bbox_inches='tight', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.linspace(0,1,101)\n",
    "growths_DP = []\n",
    "growths_SA = []\n",
    "for alpha in alphas:\n",
    "    shuttle_community_model.reset_model()\n",
    "    shuttle_community_model.weights = [alpha,1-alpha]\n",
    "    shuttle_community_model.set_medium(compm)\n",
    "    try:\n",
    "        COOPM = shuttle_community_model.compute_coopm(enforce_survival=False)\n",
    "    except:\n",
    "        growths_DP.append(growths_DP[-1])\n",
    "        growths_SA.append(growths_SA[-1])\n",
    "        continue\n",
    "    shuttle_community_model.set_medium(COOPM)\n",
    "    shuttle_community_model.optimize()\n",
    "    growths_DP.append(shuttle_community_model.x1[shuttle_community_model.obj1])\n",
    "    growths_SA.append(shuttle_community_model.x2[shuttle_community_model.obj2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.savefig(\"COOPM_online_RM.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fV43WU0nXAJcDm4DX3H05gJllAwUpjE1EpEuqrgjqPceOMUSqx+DuH7n7F4Fcdz89Ztd04Pl4T2Rmd5vZFjNb08x+M7NbzWy9mRWb2eR4jy0i0plUV0b8qaRa7l7T4P0z4VhDvO4BZrSw/zRgRPg1D/h/CRxbRKTTqK6MeI8hWdz9BWB7C01mAvd64EWgt5kNTk90IiLRUV1vHkPtU0nRGmNIlyHAxpj3peG2RsxsnpmtNLOVKt8pIp1NVfhUUla9JTEitOy2mV3b0v6wPkNauftCYCFAUVFR+soaiYikQXXlXiwjm4zMnJjVVdPXY4inHkOP8L+jgM8Bi8L3XwZeTmIsmwiK/9QqDLeJiHQptdXbgGgW6nH3/wQwsxeAye6+O3x/A/BkEmNZBFxlZg8BU4Fd7v5hEo8vItIhVFeWkZUd4cQQ4yCgIuZ9RbgtLmb2IMFs6f5mVgpcD2QDuPuvCcqFng6sB/YCX0sgNhGRTqO6siymxxAMPqdzraREEsO9wMtm9qfw/dkEj6DGxd1nt7Lfgf+VQDwiIp1SVUUZmR2hx+DuPzKzp4DPh5u+5u6vpyYsEZGuq+kxhmgNPtdx99eA11IUi4iIEDyVlJsf3KmPdI/BzHKBc4FhsZ9z9wXJD0tEpOuqrthDZp/hQExiSOOy24n0GJ4AdgGvAvtSE46IiFRX7iUzO1ijNJIT3GIUuntLax2JiEgSVFWWkZndHdj/VFJU10pabmbjUxaJiIgAtYPPQY9h/8znaPYYpgFzzGwDwa0kI3jKdEJKIhMR6YJqqivwmiqyGsxjiOpTSaelLAoREQGgKmZlVdg/+BzJCW7u/r6Z9SGol5AXs+v9pEclItJFVZXvAiArtxcQ/cdVLwOuJljcbhVwDLAC+EJKIhMR6YIqyrYAkJM/EGifxJDI4PPVBKurvu/u04GjgJ2pCEpEpKvatzdIDLm1icEyAItsoZ5ydy+HYLKbu/+TYCluERFJkoY9Bgh6DVEdfC41s97A48BfzGwHGl8QEUmqfXs+BiCn+4C6bUFiiOAYg7t/JXx5g5k9D/QCnk5JVCIiXVRF2Rayu/UlIzO7bltkE0Msd/9bsgMREZFgjCH2NhKkPzEkMsYgIiIpVrFnS93Ac62MjEwlBhGRrmpf2RZy8usXx7SMrLSurppQYjCz7NZbiYjIgarY27jHENmnkszsTuBMM6sCNgPFQLG7/zJVwYmIdCVVFWVUV+xp9zGGRAafTyBYervazIYAEwEtoCcikiS1cxhyG95Ksqy0rpWUyK2kl4B+AO6+yd0Xu/tPEjmZmc0wszfNbL2ZfbeJ/UPN7Hkze93Mis3s9ESOLyLSkTU1uQ2CFVajOvh8B/A3M/vfZvZ5M+uVyInMLBP4FcEqrWOA2WY2pkGz/wM87O5HAbOA2xM5h4hIR9ZwOYxaUX5c9X7gXoLbT1cSFO55J4HPTwHWu/u77l4BPATMbNDGgZ7h614EYxkiIl1C8z2GiA4+A6XuflPsBjPLTeDzQ4CNsccDpjZocwPwjJl9A8gHTmnqQGY2D5gHMHTo0ARCEBGJrqaWwwAwi+6tpFVmdnXsBnffl+R4ZgP3uHshcDpwnwVLC9bj7gvdvcjdiwYMGNDoICIiHVFTy2FAtG8lHQRcYWabzex/zOxHZnZ+Ap/fBBwS874w3BZrLvAwgLuvICgI1D+Bc4iIdFhNLYcB4eBzFCe4ufsF7j4aGA5cB7xF41tBLXkFGGFmw80sh2BweVGDNh8AJwOY2WiCxLA1gXOIiHRYFWVbGw08Q4TnMZjZSmA1UBJ+LXb338X7eXevMrOrgCVAJnC3u681swXASndfBHwbuNPMriEYiJ7j7h7/5YiIdFz79nxMr4OPbrQ9IyOL6srKtMWRyODzWQQT2iYAlwNnmNlWdx8W7wHcfTGwuMG262JevwEcn0BMIiKdRlPLYUCEewzuvpng8dGnoe5Wz3kpiktEpEuprtzb5HIYEOFF9Mzs0Nj37r4OGJn0iEREuqB9ZU1PboNg8DmdS2IkcivpQTMbCmwgGGPYCYxLRVAiIl1NRe0chgbrJEFEbyWFcwmeBH4MHA6MB/oCX05daCIiXUdzy2FAsIhe5GY+u3uNmZ3h7j8C1odfIiKSJM0thwHRnuBWbGbXNzUTWURE2qZ2jKHhchgQ0VtJob7AicB8M3uJ/YV6/piSyEREupCKPR83uRwGRDgxuPsFULdw3liCcYYpgBKDiEgbNbccBkBGmusxJNJjAOoWznst/BIRkSRobjkMiPCy22b2NsFjqquBVcBqd38vNWGJiHQtzS2HARGe4EZQwe0jYBtBFbY1ZlZiZgvMrPFNMRERiVtzy2FAhMcYgIvcfVLtGzP7NXAp8ClwC/CN5IYmItI1tLQcBgSFeqI683mXmU1w92IAd19lZie6+0Qz03iDiMgBqq3c1nyPIbqDz5cDD5jZKoIxhlHA3nBfTnLDEhHpOvbueBeAbr2HN7nfMrLAa3CvIR1TyVo9g5ndEL7sB0wnWF11APA2wdLb+cBDqQpQRKSzK9v+FgD5fUc0ud8ygr/h0/VkUjw9hiXhf68mmL+QC6wlmOB2cjjB7cbUhCci0vmVbXubrNyezY8x1CYGrwZS/6xPq4khrL2sCW4iIimyd/vbdO87AjNrcv/+HkN6xhk0wU1EpJ2VbV9Pn0OaL15plt7EkEihntPM7CUze9PMHjazY1IZmIhIV1BduZfyTzeS36/p8QUInkqCCCYG4HbgWuAYYCHwMzObnZKoRES6iLLt7wCQ3/eIZttkpHnwOZHEsMXd/+HuO9z9r8CXgO8ncjIzmxH2ONab2XebaXOBmb1hZmvN7PeJHF9EpKPZGz6R1L1v85WS0z3GkEhi2GBmN5pZ7ZyFSiDuKM0sE/gVwXIaY4DZZjamQZsRwPeA4919LPCtBOITEelwyra9DUB+38ObbRPlxFADfAXYaGbLCKq4LQ1/mcdjCrDe3d919wqCuQ8zG7T5OvArd98B4O5bEohPRKTDKdu+nryeh5CZ3b3ZNrWJIV3LYiRSj+GrUPe46jhgYvh1p5kd5u5DWznEEGBjzPtSYGqDNiPDc/wDyARucPenGx7IzOYB8wCGDm3ttCIi0VW2/e0WxxcgZvA5TSusHujjqq+GX8mWBYwATgIKgRfMbLy772wQw0KCAXCKioo8BXGIiKScu7N3+9sMHjurxXZRvpXUVpuAQ2LeF4bbYpUCi9y90t03AG8RJAoRkU6nomwLVfs+bfFRVUj/khhtSgxmNiiB5q8AI8xseDiAPQtY1KDN4wS9BcysP8GtpXfbEqOISFSVba8deG7+iSSI8AS3ZtwVb0MPbo5dRbD20jrgYXdfGxb6OStstgTYZmZvAM8D/+bu29oYo4hIJNUlhrh7DBEdY4jl7mck2H4xsLjBtutiXjvBJLpr2xKXiEhHsHfb22Rk5ZHXs7DFdpGd+WxmhWY2PlxmW0RE2qhs+9t073N4qzUWIpcYzGxYWKHtJYIxgC1m9mcza/mmmIiItKhs+/pWbyNBNJfEuBm4w92HuPvhQC/gz8BTCUxuExGRGDXVlXy2c0OzxXli1Q0+e3QSw0h3v6P2jbtXhfMI5gPXNf8xERFpzt6d7+I1VXSPJzFEcB5DkxPI3P0ZYHRywxER6Rp2bQ7mCPcaNKnVtlFMDIPMbK6ZTTWzggb7NOtYROQA7Nz0Ilm5vcjvf2SrbWsHn6O0VtINwCTgEmCcme0G1oRfiUxwExGR0M7Sl+g9ZEqrTyRBBOcxhOMJdcyskKDe8wTgbymKS0Sk06os38WerW8w6MivxNU+3UtiHMgieqUEaxo9lfxwREQ6v12bXwGc3oUNF5huWhTHGEREJIl2lr4IlkGvwUVxta9LDGladjueCW73hf+9OvXhiIh0fjs3vUSPgePIyu0RV/uMCPYYjjazg4FLzayPmfWN/Up1gCIinYnXVLNz8yv0HhLfbSRI/5IY8Ywx/Bp4FjiMoDiPxezzcLuIiMRh99Y3qK7YQ+/CY+P+TOSW3Xb3W919NHC3ux/m7sNjvpQUREQSsLN0BQB9EuoxRPSpJHefb2YTgc+Hm15w9+LUhCUi0jnt3PQSuQWDyOsVf7362sSQrgluiSy7/U3gAWBg+PWAmX0jVYGJiHRGOze9RO8hUzGz1huHIjfBLcZlwFR3LwMws5uBFcAvUxGYiEhns2/PR3y28z2GHn15Qp+LXD2GGAbE3uCqpv5AtIiItOCTDc8B0OeQ4xP6XLBshkWyx/Bb4CUz+1P4/mwSqPksItLVbXlzEXk9htBz0FEJf9YystJWjyGRwedbzGwpMC3c9DV3fz0lUYmIdDJVFWV8suGvFE6ck9D4Qi3LyIpUBbc67v5a+PjqrQeSFMxshpm9aWbrzey7LbQ718zczOKbLy4iEnGfvPsXaqrKGTjqywf0+SAxRG+MoU3MLBP4FXAaMAaYbWZjmmjXA7iaoMa0iEinsOWtP5PdrW/C4wu1OmViAKYA6939XXevAB4CZjbR7ocEdabL0xibiEjK1FRXsHX90wwccUbdukeJysjI7JSJYQiwMeZ9abitjplNBg5x9ydbOpCZzTOzlWa2cuvWrcmPVEQkiba//wJV+3YxcORZB3yMYPA5Yk8lmVkucC4wLPZz7r4gGYFY8DzWLcCc1tqGxYMWAhQVFam8qIhE2sdvPkFmTgH9hk8/4GOkc/A5kT7NE8AugoX09h3AuTYBh8S8Lwy31eoBjAOWhiP2g4BFZnaWu688gPOJiLQ7r6lmy9tPMuDwU8nMyjvg46RzjCGRxFDo7jPacK5XgBFmNpwgIcwCvlq70913Af1r34ePxv5vJQUR6ch2lC6nomwLA0ce2NNItcyyordWErDczMYf6Ik8uDl2FbAEWAc87O5rzWyBmR34jTcRkQjb+NpvyMrrzYAjTm/TcSyNg8+t9hjMrISg7kIW8DUze5fgVpIB7u4T4j2Zuy8GFjfYdl0zbU+K97giIlFUvvtDPn7zCYYWzScrJ79Nx4raraQzUx6FiEgntPH13+A11QydPK/Nx4rUzGd3f9/d3weurH0duy31IYqIdDw1Vfsoff1uBhwxg+59hrf5eFGd4PbFJradlqxAREQ6k4/++TgVe7cmvMR2czKidCvJzOYT9AwON7PYim09gH+kKjARkY7sg1d/Tfe+I+g3/AtJOZ5lZEZqgtvvgaeAm4DYhe92u/v2lEQlItKB7Sh9kV2bX+HIU/4rrKXQdpG6leTuu9z9PYLCPKcC3cIxBiUFEZEGaqorWbfkGnILBjFkwkVJO65ZZnQGn2PcBQwGfmlm75rZo2Z2dYriEhHpkN57+VZ2bylh9Km3kJXbM2nHtYz0TXBLpFDP82b2AvA5YDpwBTAW+EWKYhMR6VDKtq/nnWU3MXDUWRw0Krnzdi0jC6JWwc3MngXygRXA34HPufuWVAUmItKRuDtvPP1NMjJzGf3F/0768S0jM3o9BqAYOJpgobtdwE4zW+Hun6UkMhGRDqBq324+Wvcopat/x67NrzDmtF+S12Nw0s8TtZnPALj7NVBXYW0O8FuCFVBzUxKZiEhEVe3bzSfvPsPHby5i6/qnqa4sI7//kRz5xZ9ROPFfU3JOswguu21mVwGfJ+g1vAfcTXBLSUSkU/Oaaj79uJht7z3P9veeZ8fG5dRU7yOne38Gj72AIeMvoteQKYQlA1Iikj0GII+gkM6rnq5ZFiIiaebulO/exO6PV7Nr86vs3PwyuzavpLpiDwAFA8ZyyNHzOGjkmfQecgyWkZmWuCKZGNz9Z2Y2EbgizIp/d/fVKYtMRCSF3J19uzdTtmM9ZdveouyTf7Lnk3Xs3rKWys+2AcHcgYKB4zh43Gx6Fx5Lv0NPJLfgoHaJN5KJwcy+CcwDHgs33W9mC939lymJLMW2vP0UbyzRNAyRrqqqfCfVlXvr3mfm9KCg/5EMHHkmPQ+aQI+DJtJj4Pg2L5edLBlRqscQ4zJgqruXAZjZzQSPrnbIxJBbcBD9D2tqXUAR6QqycnrQve/h5Pc5gu79RpDXY0hKxwjaKqo1n41gWYxa1eG2DqnX4Mn0Gjy5vcMQEYmLZWRFahG9Wr8FXjKzP4XvzyZYJkNERFIscmMMFvSv/ggsBaaFm7/m7q+nKC4REYkRubWS3N3NbLG7jwdeS3FMIiLSQLC6akSW3Y7xmpl9ri0nM7MZZvamma03s+82sf9aM3vDzIrN7FkzO7Qt5xMR6SyCRfRqcK9J+bkSSQxTgRVm9k74i7ukQUW3FplZJvArgnKgY4DZZjamQbPXgSJ3nwA8AvxXAvGJiHRalhHc4EnHk0mJDD5/qY3nmgKsd/d3AczsIWAm8EZtA3d/Pqb9i0DyqlyIiHRgtTOsvaYKMrNTeq5EZj6/38ZzDQE2xrwvJeiFNGcuQUnRRsxsHsFkO4YOHdrGsEREom9/jyH14wyJzHy+tonNuwjWTlqVtIiCc10EFAEnNrXf3RcCCwGKioo8mecWEYkiszAxpKFYTyK3korCrz+H788kqNFwhZn90d1bGw/YBBwS874w3FaPmZ0CfB840d33JRCfiEinVe9WUoolMvhcCEx292+7+7cJlt8eCJxAUJ+hNa8AI8xsuJnlALOARbENzOwo4A7gLFWHExHZLyONg8+JJIaBQOxf8JXAQWEFt1b/sg+X6r4KWAKsAx5297VmtsDMaouj/hQoAP5oZqvMbFEzhxMR6VIiOcYAPECwJMYT4fsvA783s3xinixqibsvBhY32HZdzOtTEohHRKTLiGRicPcfmtlTwPHhpivcfWX4+l+SHpmIiNSpTQzpWBYjkR4DYSJY2WpDERFJqrrB5zSssJrIGIOIiLSTdN5KUmIQEekA0rkkRtyJwQIXmdl14fuhZjYldaGJiEitugluEesx3A4cC8wO3+8mWBRPRERSLJJPJRHUe55sZq8DuPuOcKKaiIikWEZExxgqw6WzHcDMBgCpXxhcREQiuyTGrcCfgIPM7EfAMuDHKYlKRETqiWQ9Bnd/wMxeBU4ON53t7utSE5aIiMSK5AQ3M8sFJgO9ws+db2a4+4JUBSciIoHgTn70Bp+fIKy/QByL5omISPLU9hiIWD2GQnefkbJIRESkWbWDz+m4lZTI4PNyMxufskhERKRZkZrHYGYlBI+oZgFfM7N3CW4lGeDuPiG1IYqISNSeSjoHqEh1ICIi0rxI9RiAP7j75JRHIiIizapLDBFZdttSHoWIiLQonUtixNNjGGBm1za3091vSWI8IiLShN2Ve/l+ZTmf/PV7ZP39JiYNmsQjFzySknPFkxgygQLUcxARaTfPfbCMYq/mtF5DKeg/isP7HJ6yc8WTGD5M1uxmM5sB/IIg2fzG3X/SYH8ucC9wNLANuNDd30vGuUVEOrJzjvwKd2dfwbSJlzBs6jdTeq60jTGEK7P+CjgNGAPMNrMxDZrNBXa4+xHAz4Gbk3FuEZGOauXmlfzlnb9gGVkMsIzIrJV0cutN4jIFWO/u7wKY2UPATOCNmDYzgRvC148At5mZubsnKYZ6bnzhRh5c82C9bTmZObx++esAfO+v32PRW4vq7e+T14dlly4D4JtPfZNnNzxbb39hz0KWXLQEgMsWXcaK0hX19o/qN4rHLnwMgNmPzqb44+J6+48adBT3n3M/AGc9eBbv7Hin3v7jDzmehV9eCMDJ957MR3s+qrf/1MNO5eczfg7AsXcdy6f7Pq23/ytHfoUbv3AjABN/PZGqBj9kF42/iO99/nvsq9rH5IWNH0abN3keVx9zNds/287nf/v5RvuvOeYaLpt8GRt3bWTGA40nyn//89/nq+O/yj8/+SfnPnxuo/0//sKPmXnkTF778DUu/tPFjfb/YsYvOOWwU1j2wTIu/5/LG+2/88t3ctwhx7Fk/RKufabx0Njvz/k9EwdN5LF1j/GD53/QaP8Ts57giL5HcN/q+/jJP37SaP9fL/4rg3sM5o6Vd3Dry7c22r/80uX0yuvFLStu4a7X72q0f9Xlq8jOzNbPnn72Gu1v7mdv06eb6NOtD29cUQLA+y/fyuY1vwegcOK/MmzKNxodq61aTQzuvj1J5xoCbIx5XwpMba6Nu1eZ2S6gH/BJbCMzmwfMAxg6dOgBBzSoYBBjBtTvtGRnZNe9PrjHwY3298zpWff6kJ6HNNo/sPvAuteH9jqUXft21dt/aK9D614P7z280f8cw3oPq3t9eJ/Dyc3KbfbzI/uOpG+3vvX2F/YsrHs9qt8oyirL6u0/uMfBda9H9x9NdYN1VwYVDALAzBpdG8DA/OD6Mi2zyf39uvUDgl9yTe2vjTcvK6/J/b3zegPQPbt7k/t75PQAID87v8n9+dn5APTM7dnk/m7Z3erO09T+3Mzcujib2p8VPhnSv3v/JvdnhssWHJR/UJP7zYIOuH729LPXUHM/e5MGTeI7x3+HbrkFHHbcv1G2/e26fTkx/+bJZCn6Y7zxiczOA2a4+2Xh+4sJqsJdFdNmTdimNHz/Ttjmk6aOCVBUVOQrV65MbfAiIp2Mmb3q7kVN7UtkraS22gQcEvO+MNzWZBsLKl/3IhiEFhGRNElnYngFGGFmw8Na0bOARQ3aLAL+NXx9HvBcqsYXRESkaYksu90m4ZjBVcASgsdV73b3tWa2AFjp7ouAu4D7zGw9sJ0geYiISBqlLTEAuPtiYHGDbdfFvC4Hzk9nTCIiUl86byWJiEgHoMQgIiL1KDGIiEg9SgwiIlJP2ia4pYqZbQXeP8CP96fBrOouQNfcNeiau4a2XPOh7j6gqR0dPjG0hZmtbG7mX2ela+4adM1dQ6quWbeSRESkHiUGERGpp6snhoXtHUA70DV3DbrmriEl19ylxxhERKSxrt5jEBGRBpQYRESkni6RGMxshpm9aWbrzey7TezPNbM/hPtfMrNh7RBmUsVxzdea2RtmVmxmz5rZoU0dpyNp7Zpj2p1rZm5mHf7Rxniu2cwuCP+t15rZ79MdY7LF8bM91MyeN7PXw5/v09sjzmQxs7vNbEtYyKyp/WZmt4bfj2Iza1wXNVHu3qm/CJb4fgc4DMgBVgNjGrS5Evh1+HoW8If2jjsN1zwd6B6+nt8Vrjls1wN4AXgRKGrvuNPw7zwCeB3oE74f2N5xp+GaFwLzw9djgPfaO+42XvMJwGRgTTP7TweeAgw4BniprefsCj2GKcB6d3/X3SuAh4CZDdrMBH4Xvn4EONlqi/N2TK1es7s/7+57w7cvElTU68ji+XcG+CFwM1CezuBSJJ5r/jrwK3ffAeDuW9IcY7LFc80O1BbI7gVsTmN8SefuLxDUp2nOTOBeD7wI9DazwW05Z1dIDEOAjTHvS8NtTbZx9ypgF9AvLdGlRjzXHGsuwV8cHVmr1xx2sQ9x9yfTGVgKxfPvPBIYaWb/MLMXzWxG2qJLjXiu+QbgIjMrJaj/8o30hNZuEv3/vVVpLdQj0WNmFwFFwIntHUsqmVkGcAswp51DSbcsgttJJxH0Cl8ws/HuvrM9g0qx2cA97v7fZnYsQVXIce5e096BdRRdocewCTgk5n1huK3JNmaWRdD93JaW6FIjnmvGzE4Bvg+c5e770hRbqrR2zT2AccBSM3uP4F7sog4+AB3Pv3MpsMjdK919A/AWQaLoqOK55rnAwwDuvgLII1hsrrOK6//3RHSFxPAKMMLMhptZDsHg8qIGbRYB/xq+Pg94zsNRnQ6q1Ws2s6OAOwiSQke/7wytXLO773L3/u4+zN2HEYyrnOXuK9sn3KSI52f7cYLeAmbWn+DW0rtpjDHZ4rnmD4CTAcxsNEFi2JrWKNNrEXBJ+HTSMcAud/+wLQfs9LeS3L3KzK4ClhA80XC3u681swXASndfBNxF0N1cTzDIM6v9Im67OK/5p0AB8MdwnP0Ddz+r3YJuozivuVOJ85qXAKea2RtANfBv7t5he8NxXvO3gTvN7BqCgeg5HfkPPTN7kCC59w/HTa4HsgHc/dcE4yinA+uBvcDX2nzODvz9EhGRFOgKt5JERCQBSgwiIlKPEoOIiNSjxCAiIvUoMYiISD1KDCIiUo8Sg4iI1KPEIJICZtbNzP5mZpnh+7hqRYRtG62/b2Y5ZvZCuGSLSEopMYgkwMy+bmavmNnKmK+mZlVfCjzm7tVhcvgVcBpBfYDZZjamhdPcA9RbBTVcYvpZ4MKkXIhIC/TXh0jIzMYCvwCGAvcBAwnWuX8l3P9tYDzwBXff3crh/gX4avi6roZAeJzaGgJvNPVBd3+hmSqCjwM3AQ/Ef1UiiVNiEAHMLA/4I3A+wSJz/wRejUkKmQS/6Ke4e3Urx8oBDnP398JNTa2XP/UAwlwDfO4APieSECUGkcApwOvuvhbqfrn/d8z+AcARwKtNFPfb7O6xdYX7AzuTHWB4W6rCzHrE0WMROWBKDCKBSQS1kTGzg4E97v6PmP1bCWoZHNNajwH4jGCp51rJXC8/l85RllQiTIPPIoEK9pdDvImg0HydMBk8BPzGzHq0dKCwvnJmeHsKWqghYGbPmllcZRjNrB/wibtXxnlNIgdEiUEk8HvgBDN7E1gNrDCz/xvbwN3/G1gOPBfHU0nPANPCz1UBtTUE1gEPhzUEMghuT9Ur9B6uv78CGGVmpWY2N9w1Hegs9aolwlSPQSQFzGwycI27X9xCm3HApe5+bZzHfAz4rru/laQwRZqkxCCSImZ2KfC7OMYk4jlWDjDL3e9te2QiLVNiEBGRejTGICIi9SgxiIhIPUoMIiJSjxKDiIjUo8QgIiL1KDGIiEg9/x9e6nr1GiBKiQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title_font = {'fontname':'Arial', 'size':'14', 'color':'black', 'weight':'normal'} \n",
    "plt.xlabel(r\"$\\alpha\\in (0,1)$\")\n",
    "plt.ylabel('The growth of $\\it{D. pigrum}$ and $\\it{S.aureus}$')\n",
    "plt.plot(alphas, growths_SA, 'darkgoldenrod')\n",
    "plt.plot(alphas, growths_DP, 'g--')\n",
    "plt.legend([\"$\\it{S.aureus}$\" , \"$\\it{D. pigrum}$\"])\n",
    "plt.savefig(\"COOPM_mix_plot_RM.pdf\", bbox_inches='tight', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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