{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2cd0caa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "\n",
    "from epimodels.continuous.models import SISLogistic\n",
    "from epimodels.fitting import (\n",
    "    Dataset,\n",
    "    DataSeries,\n",
    "    ParameterSpec,\n",
    "    ModelFitter,\n",
    "    FittingResult,\n",
    "    fit_model,\n",
    "    SumOfSquaredErrors,\n",
    "    WeightedSSE,\n",
    "    PoissonLikelihood,\n",
    "    NegativeBinomialLikelihood,\n",
    "    NormalLikelihood,\n",
    "    HuberLoss,\n",
    "    ScipyOptimizer,\n",
    "    MultiStartOptimizer,\n",
    ")\n",
    "\n",
    "np.random.seed(42)\n",
    "plt.style.use('seaborn-v0_8-whitegrid')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "be2407e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"dengue_data_logistic.csv\")\n",
    "\n",
    "df = df.sort_values(\"data_iniSE\")\n",
    "\n",
    "times = np.arange(len(df))\n",
    "\n",
    "observed_I = df[\"casos_est\"].values\n",
    "\n",
    "TOTAL_POPULATION = df[\"pop\"].iloc[0]\n",
    "INITIAL_INFECTED = observed_I[0]\n",
    "INITIAL_SUSCEPTIBLE = TOTAL_POPULATION - INITIAL_INFECTED"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ddca0af4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset valid: True\n",
      "Time range: (0.0, 103.0)\n",
      "Dataset(n_series=1, variables=['I'], time_range=(0.0, 103.0))\n"
     ]
    }
   ],
   "source": [
    "model = SISLogistic()\n",
    "dataset = Dataset(model)\n",
    "\n",
    "dataset.register(\n",
    "    name='infected',\n",
    "    values=observed_I,\n",
    "    times=times,\n",
    "    state_variable='I',\n",
    ")\n",
    "\n",
    "validation_result = dataset.validate(total_population=TOTAL_POPULATION)\n",
    "\n",
    "print(f\"Dataset valid: {validation_result.is_valid}\")\n",
    "print(f\"Time range: {dataset.time_range}\")\n",
    "print(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "65a1aa83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters to fit:\n",
      "  R0: bounds=(1.01, 5.0), initial=2.0\n",
      "  gamma: bounds=(0.01, 0.5), initial=0.3\n",
      "  r: bounds=(0.01, 0.5), initial=0.4\n",
      "  k: bounds=(1000, 20000), initial=5000\n"
     ]
    }
   ],
   "source": [
    "param_specs = [\n",
    "    ParameterSpec(\n",
    "        name='R0',\n",
    "        bounds=(1.01, 5.0),\n",
    "        initial=2.0,\n",
    "    ),\n",
    "    ParameterSpec(\n",
    "        name='gamma',\n",
    "        bounds=(0.01, 0.5),\n",
    "        initial=0.3,\n",
    "    ),\n",
    "    ParameterSpec(\n",
    "        name='r',\n",
    "        bounds=(0.01, 0.5),\n",
    "        initial=0.4,\n",
    "    ),\n",
    "    ParameterSpec(\n",
    "        name='k',\n",
    "        bounds=(1000, 20000),\n",
    "        initial=5000,\n",
    "    ),\n",
    "]\n",
    "\n",
    "print(\"Parameters to fit:\")\n",
    "for spec in param_specs:\n",
    "    print(f\"  {spec.name}: bounds={spec.bounds}, initial={spec.initial}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4e22e9b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================================================\n",
      "FITTING RESULTS\n",
      "==================================================\n",
      "Convergence: True\n",
      "Number of evaluations: 50\n",
      "Final loss: 248362.48\n",
      "\n",
      "Fitted parameters:\n",
      "  R0: 1.0100\n",
      "  gamma: 0.5000\n",
      "  r: 0.5000\n",
      "  k: 1000.0000\n"
     ]
    }
   ],
   "source": [
    "fitter = ModelFitter(\n",
    "    model=model,\n",
    "    dataset=dataset,\n",
    "    parameters_to_fit=param_specs,\n",
    "    total_population=INITIAL_SUSCEPTIBLE + INITIAL_INFECTED,\n",
    "    optimizer=ScipyOptimizer(method='L-BFGS-B', max_iterations=200),\n",
    ")\n",
    "\n",
    "result = fitter.fit()\n",
    "\n",
    "print(\"\\n\" + \"=\"*50)\n",
    "print(\"FITTING RESULTS\")\n",
    "print(\"=\"*50)\n",
    "print(f\"Convergence: {result.convergence}\")\n",
    "print(f\"Number of evaluations: {result.n_evaluations}\")\n",
    "print(f\"Final loss: {result.best_loss:.2f}\")\n",
    "\n",
    "print(\"\\nFitted parameters:\")\n",
    "\n",
    "for param, value in result.best_params.items():\n",
    "\n",
    "    print(f\"  {param}: {value:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1a8320d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fitted_model = result.fitted_model\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "ax.plot(times, observed_I, 'ro', label='Observed I', markersize=4, alpha=0.7)\n",
    "\n",
    "if fitted_model is not None and fitted_model.traces:\n",
    "    ax.plot(fitted_model.traces['time'], fitted_model.traces['I'], \n",
    "            'g--', label='Fitted', linewidth=2)\n",
    "\n",
    "ax.set_xlabel('Time (days)', fontsize=12)\n",
    "ax.set_ylabel('Number of Infected', fontsize=12)\n",
    "ax.set_title('Model Fitting Results', fontsize=14)\n",
    "ax.legend(fontsize=11)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}