{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def make_system():\n",
    "    \"\"\"Make a system object for the HIV model.\n",
    "    \n",
    "    \n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    gamma=1.36\n",
    "    tau=0.2\n",
    "    mu=1.36e-3\n",
    "    beta=0.00027\n",
    "    ro=0.1\n",
    "    alpha=3.6e-2\n",
    "    delta=0.33\n",
    "    pi=100\n",
    "    sigma=2\n",
    "    t_0 = 0\n",
    "\n",
    "    t_end = 120\n",
    "    dT=0.06\n",
    "\n",
    "\n",
    "\n",
    "    return System(gamm=gamma, tau=tau, mu=mu,\n",
    "                  beta=beta, ro=ro, alpha=alpha,delta=delta, pi=pi, sigma=sigma,t_0=t_0,t_end=t_end,dT=dT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def update(state, time, system):\n",
    "    R, L, E, V = state\n",
    "    gamma, tau, mu, beta, ro, alpha, delta, pi, sigma, t_0, t_end, dT = system\n",
    "    \n",
    "    dRdT = gamma * tau - mu * R - beta * R * V\n",
    "    dLdT = ro * beta * R * V - mu * L - alpha * L\n",
    "    dEdT = (1 - ro) * beta * R * V + alpha * L - delta * E\n",
    "    dVdT = pi * E - sigma * V\n",
    "    R += dRdT * dT\n",
    "    L += dLdT * dT\n",
    "    E += dEdT * dT\n",
    "    V += dVdT * dT\n",
    "\n",
    "    return (State(R=R, L=L, E=E, V=V))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def run_simulation(system, update_func):\n",
    "    \"\"\"Runs a simulation of the system.\n",
    "    \n",
    "    Add a TimeFrame to the System: results\n",
    "    \n",
    "    system: System object\n",
    "    update_func: function that updates state\n",
    "    \"\"\"\n",
    "    init = State(R=200, L=0, E=0, V=4e-7)\n",
    "    gamma, tau, mu, beta, ro, alpha, delta, pi, sigma, t_0, t_end, dT = system\n",
    "    \n",
    "    frame = TimeFrame(columns=init.index)\n",
    "    frame.row[t_0] = init\n",
    "    ts = linrange(t_0, t_end, dT)\n",
    "    \n",
    "    for t in ts:\n",
    "        frame.row[t+dT] = update_func(frame.row[t], t, system)\n",
    "    \n",
    "    return frame\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R</th>\n",
       "      <th>L</th>\n",
       "      <th>E</th>\n",
       "      <th>V</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0.00</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>4.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.06</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>1.296000e-10</td>\n",
       "      <td>1.166400e-09</td>\n",
       "      <td>3.520000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.12</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>2.433575e-10</td>\n",
       "      <td>2.170017e-09</td>\n",
       "      <td>3.167584e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.18</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>3.454417e-10</td>\n",
       "      <td>3.051244e-09</td>\n",
       "      <td>2.917675e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.24</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>4.392000e-10</td>\n",
       "      <td>3.842370e-09</td>\n",
       "      <td>2.750629e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>119.76</td>\n",
       "      <td>17.993435</td>\n",
       "      <td>6.626104e-01</td>\n",
       "      <td>2.389403e-01</td>\n",
       "      <td>1.201070e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>119.82</td>\n",
       "      <td>18.004785</td>\n",
       "      <td>6.614752e-01</td>\n",
       "      <td>2.387915e-01</td>\n",
       "      <td>1.200306e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>119.88</td>\n",
       "      <td>18.016135</td>\n",
       "      <td>6.603425e-01</td>\n",
       "      <td>2.386431e-01</td>\n",
       "      <td>1.199544e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>119.94</td>\n",
       "      <td>18.027484</td>\n",
       "      <td>6.592124e-01</td>\n",
       "      <td>2.384952e-01</td>\n",
       "      <td>1.198784e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>120.00</td>\n",
       "      <td>18.038832</td>\n",
       "      <td>6.580848e-01</td>\n",
       "      <td>2.383478e-01</td>\n",
       "      <td>1.198027e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2001 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 R             L             E             V\n",
       "0.00    200.000000  0.000000e+00  0.000000e+00  4.000000e-07\n",
       "0.06    200.000000  1.296000e-10  1.166400e-09  3.520000e-07\n",
       "0.12    200.000000  2.433575e-10  2.170017e-09  3.167584e-07\n",
       "0.18    200.000000  3.454417e-10  3.051244e-09  2.917675e-07\n",
       "0.24    200.000000  4.392000e-10  3.842370e-09  2.750629e-07\n",
       "...            ...           ...           ...           ...\n",
       "119.76   17.993435  6.626104e-01  2.389403e-01  1.201070e+01\n",
       "119.82   18.004785  6.614752e-01  2.387915e-01  1.200306e+01\n",
       "119.88   18.016135  6.603425e-01  2.386431e-01  1.199544e+01\n",
       "119.94   18.027484  6.592124e-01  2.384952e-01  1.198784e+01\n",
       "120.00   18.038832  6.580848e-01  2.383478e-01  1.198027e+01\n",
       "\n",
       "[2001 rows x 4 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys = make_system()\n",
    "frame = run_simulation(sys, update)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x720 with 4 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot(frame[\"V\"])\n",
    "# plot(frame[\"R\"])\n",
    "# plot(frame[\"L\"])\n",
    "# plot(frame[\"E\"])\n",
    "fig = plt.figure(figsize=(8, 10))\n",
    "\n",
    "ax = fig.add_subplot(2, 2, 1)\n",
    "line = ax.plot(frame[\"V\"],label='V')\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim([0.1,10e3])\n",
    "legend()\n",
    "ax = fig.add_subplot(2, 2, 2)\n",
    "line = ax.plot(frame[\"R\"],label='R')\n",
    "legend()\n",
    "ax = fig.add_subplot(2, 2, 3)\n",
    "line = ax.plot(frame[\"L\"],label='L')\n",
    "legend()\n",
    "ax = fig.add_subplot(2, 2, 4)\n",
    "line = ax.plot(frame[\"E\"],label='E')\n",
    "title\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "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": 0
}