Spatial Measles Model.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Disease Outbreak Response Decision-making Under Uncertainty: A retrospective analysis of measles in Sao Paulo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
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   "outputs": [
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   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import numpy.ma as ma\n",
    "from datetime import datetime\n",
    "import matplotlib.pyplot as plt\n",
    "pd.set_option('max_columns', 20)\n",
    "pd.set_option('max_rows', 25)\n",
    "\n",
    "from IPython.core.display import HTML\n",
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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "data_dir = \"data/\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import outbreak data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "measles_data = pd.read_csv(data_dir+\"measles.csv\", index_col=0)\n",
    "measles_data.NOTIFICATION = pd.to_datetime(measles_data.NOTIFICATION)\n",
    "measles_data.BIRTH = pd.to_datetime(measles_data.BIRTH)\n",
    "measles_data.ONSET = pd.to_datetime(measles_data.ONSET)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "measles_data = measles_data.replace({'DISTRICT': {'BRASILANDIA':'BRAZILANDIA'}})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sao Paulo population by district"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sp_pop = pd.read_csv(data_dir+'sp_pop.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "_names = sp_pop.index.values\n",
    "_names[_names=='BRASILANDIA'] = 'BRAZILANDIA'\n",
    "sp_pop.set_index(_names, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0 a 4 anos</th>\n",
       "      <th>5 a 9 anos</th>\n",
       "      <th>10 a 14 anos</th>\n",
       "      <th>15 a 19 anos</th>\n",
       "      <th>20 a 24 anos</th>\n",
       "      <th>25 a 29 anos</th>\n",
       "      <th>30 a 34 anos</th>\n",
       "      <th>35 a 39 anos</th>\n",
       "      <th>40 a 44 anos</th>\n",
       "      <th>45 a 49 anos</th>\n",
       "      <th>50 a 54 anos</th>\n",
       "      <th>55 a 59 anos</th>\n",
       "      <th>60 a 64 anos</th>\n",
       "      <th>65 a 69 anos</th>\n",
       "      <th>70 a 74 anos</th>\n",
       "      <th>75 anos e +</th>\n",
       "      <th>Total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AGUA RASA</th>\n",
       "      <td> 5411</td>\n",
       "      <td> 5750</td>\n",
       "      <td>  6450</td>\n",
       "      <td>  7122</td>\n",
       "      <td>  7621</td>\n",
       "      <td>  7340</td>\n",
       "      <td> 6999</td>\n",
       "      <td> 6984</td>\n",
       "      <td> 6346</td>\n",
       "      <td> 5608</td>\n",
       "      <td> 4987</td>\n",
       "      <td> 4212</td>\n",
       "      <td> 4152</td>\n",
       "      <td> 3595</td>\n",
       "      <td> 2937</td>\n",
       "      <td> 3637</td>\n",
       "      <td>  89151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ALTO DE PINHEIROS</th>\n",
       "      <td> 2070</td>\n",
       "      <td> 2369</td>\n",
       "      <td>  2953</td>\n",
       "      <td>  3661</td>\n",
       "      <td>  4612</td>\n",
       "      <td>  4190</td>\n",
       "      <td> 3539</td>\n",
       "      <td> 3633</td>\n",
       "      <td> 3448</td>\n",
       "      <td> 3289</td>\n",
       "      <td> 3040</td>\n",
       "      <td> 2533</td>\n",
       "      <td> 2298</td>\n",
       "      <td> 1732</td>\n",
       "      <td> 1305</td>\n",
       "      <td> 1823</td>\n",
       "      <td>  46495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ANHANGUERA</th>\n",
       "      <td> 3068</td>\n",
       "      <td> 3006</td>\n",
       "      <td>  2755</td>\n",
       "      <td>  2431</td>\n",
       "      <td>  2426</td>\n",
       "      <td>  2636</td>\n",
       "      <td> 2695</td>\n",
       "      <td> 2308</td>\n",
       "      <td> 1653</td>\n",
       "      <td> 1107</td>\n",
       "      <td>  753</td>\n",
       "      <td>  509</td>\n",
       "      <td>  352</td>\n",
       "      <td>  217</td>\n",
       "      <td>  162</td>\n",
       "      <td>  171</td>\n",
       "      <td>  26249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ARICANDUVA</th>\n",
       "      <td> 7732</td>\n",
       "      <td> 7730</td>\n",
       "      <td>  8373</td>\n",
       "      <td>  8956</td>\n",
       "      <td>  9182</td>\n",
       "      <td>  8531</td>\n",
       "      <td> 7813</td>\n",
       "      <td> 7365</td>\n",
       "      <td> 6551</td>\n",
       "      <td> 5554</td>\n",
       "      <td> 4887</td>\n",
       "      <td> 3858</td>\n",
       "      <td> 3320</td>\n",
       "      <td> 2449</td>\n",
       "      <td> 1611</td>\n",
       "      <td> 1723</td>\n",
       "      <td>  95635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ARTUR ALVIM</th>\n",
       "      <td> 9031</td>\n",
       "      <td> 9078</td>\n",
       "      <td> 10000</td>\n",
       "      <td> 11058</td>\n",
       "      <td> 11387</td>\n",
       "      <td> 10347</td>\n",
       "      <td> 9125</td>\n",
       "      <td> 8658</td>\n",
       "      <td> 7830</td>\n",
       "      <td> 7055</td>\n",
       "      <td> 5919</td>\n",
       "      <td> 4612</td>\n",
       "      <td> 3756</td>\n",
       "      <td> 2633</td>\n",
       "      <td> 1727</td>\n",
       "      <td> 1724</td>\n",
       "      <td> 113940</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0 a 4 anos  5 a 9 anos  10 a 14 anos  15 a 19 anos  \\\n",
       "AGUA RASA                5411        5750          6450          7122   \n",
       "ALTO DE PINHEIROS        2070        2369          2953          3661   \n",
       "ANHANGUERA               3068        3006          2755          2431   \n",
       "ARICANDUVA               7732        7730          8373          8956   \n",
       "ARTUR ALVIM              9031        9078         10000         11058   \n",
       "\n",
       "                   20 a 24 anos  25 a 29 anos  30 a 34 anos  35 a 39 anos  \\\n",
       "AGUA RASA                  7621          7340          6999          6984   \n",
       "ALTO DE PINHEIROS          4612          4190          3539          3633   \n",
       "ANHANGUERA                 2426          2636          2695          2308   \n",
       "ARICANDUVA                 9182          8531          7813          7365   \n",
       "ARTUR ALVIM               11387         10347          9125          8658   \n",
       "\n",
       "                   40 a 44 anos  45 a 49 anos  50 a 54 anos  55 a 59 anos  \\\n",
       "AGUA RASA                  6346          5608          4987          4212   \n",
       "ALTO DE PINHEIROS          3448          3289          3040          2533   \n",
       "ANHANGUERA                 1653          1107           753           509   \n",
       "ARICANDUVA                 6551          5554          4887          3858   \n",
       "ARTUR ALVIM                7830          7055          5919          4612   \n",
       "\n",
       "                   60 a 64 anos  65 a 69 anos  70 a 74 anos  75 anos e +  \\\n",
       "AGUA RASA                  4152          3595          2937         3637   \n",
       "ALTO DE PINHEIROS          2298          1732          1305         1823   \n",
       "ANHANGUERA                  352           217           162          171   \n",
       "ARICANDUVA                 3320          2449          1611         1723   \n",
       "ARTUR ALVIM                3756          2633          1727         1724   \n",
       "\n",
       "                    Total  \n",
       "AGUA RASA           89151  \n",
       "ALTO DE PINHEIROS   46495  \n",
       "ANHANGUERA          26249  \n",
       "ARICANDUVA          95635  \n",
       "ARTUR ALVIM        113940  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_pop.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot of cumulative cases by district"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
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       "cO3R6WJMzNEhVvIxDY+qDmMyCl0JICIXYEJ6bKxpE2KyQl1de2yUtKKaKvEcTCapmJi6ITbXxBwv\n",
       "3AB8TUQ+AZQxeV/hxeaZW4G/qb6J0gjeISIOZkL0Q1W9bdrnfkVEctHr70QJL2qJg0PFzClxgLKY\n",
       "mJiYBiY218TExMQ0MLGSj4mJiWlgYiUfExMT08DESj4mJiamgYmVfExMTEwDEyv5mJiYmAYmVvIx\n",
       "MTExDcz/BxiyFesc7w0iAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11114d7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "measles_onset_dist = measles_data.groupby(['DISTRICT','ONSET']).size().unstack(level=0).fillna(0)\n",
    "measles_onset_dist.cumsum().plot(legend=False, grid=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "total_district_cases = measles_onset_dist.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Top 5 districts by number of cases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DISTRICT\n",
       "GRAJAU             1074\n",
       "JARDIM ANGELA       944\n",
       "CAPAO REDONDO       849\n",
       "JARDIM SAO LUIZ     778\n",
       "CAMPO LIMPO         692\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "totals = measles_onset_dist.sum()\n",
    "totals.sort(ascending=False)\n",
    "totals[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Age distribution of cases, by confirmation status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3c78d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "by_conclusion = measles_data.groupby([\"YEAR_AGE\", \"CONCLUSION\"])\n",
    "counts_by_cause = by_conclusion.size().unstack().fillna(0)\n",
    "ax = counts_by_cause.plot(kind='bar', stacked=True, xlim=(0,50), figsize=(15,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chain Binomial Transmission Model\n",
    "\n",
    "As a baseline for comparison, we can fit a model to all the clinically-confirmed cases, regardless of lab confirmation status. For this, we will use a simple chain binomial model, which will be fit using MCMC.\n",
    "\n",
    "This model fits the series of 2-week infection totals as a set of Binomial models:\n",
    "\n",
    "\\\\[Pr(I_{t+1} | S_t, p_t) = \\text{Bin}(S_t, p_t) \\\\]\n",
    "\n",
    "Where the binomial probability is modeled as:\n",
    "\n",
    "\\\\[p_t = 1 - \\exp\\(-\\lambda_t\\)\\\\]\n",
    "\n",
    "\\\\[\\lambda_t = \\frac{\\beta_t I_t}{N}\\\\]\n",
    "\n",
    "We will assume here that the transmission rate is constant over time (and across districts):\n",
    "\n",
    "\\\\[\\beta_t = \\beta_0\\\\]\n",
    "\n",
    "which allows the effective reproductive number to be calculated as:\n",
    "\n",
    "\\\\[R_t = \\frac{\\beta S_t}{N}\\\\]\n",
    "\n",
    "### Confirmation Sub-model\n",
    "\n",
    "Rather than assume all clinical cases are true cases, we can adjust the model to account for lab confirmation probability. This is done by including a sub-model that estimates age group-specific probabilities of confirmation, and using these probabilities to estimate the number of lab-confirmed cases. These estimates are then plugged into the model in place of the clinically-confirmed cases.\n",
    "\n",
    "We specified a structured confirmation model to retrospectively determine the age group-specific probabilities of lab confirmation for measles, conditional on clinical diagnosis. Individual lab confirmation events $c_i$ were modeled as Bernoulli random variables, with the probability of confirmation being allowed to vary by age group:\n",
    "\n",
    "$$c_i \\sim \\text{Bernoulli}(p_{a(i)})$$\n",
    "\n",
    "where $a(i)$ denotes the appropriate age group for the individual indexed by i. There were 16 age groups, the first 15 of which were 5-year age intervals $[0,5), [5, 10), \\ldots , [70, 75)$, with the 16th interval including all individuals 75 years and older.\n",
    "\n",
    "Since the age interval choices were arbitrary, and the confirmation probabilities of adjacent groups likely correlated, we modeled the correlation structure directly, using a multivariate logit-normal model. Specifically, we allowed first-order autocorrelation among the age groups, whereby the variance-covariance matrix retained a tridiagonal structure. \n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\Sigma = \\left[{\n",
    "\\begin{array}{c}\n",
    "  {\\sigma^2} & {\\sigma^2 \\rho} & 0& \\ldots & {0} & {0}  \\\\\n",
    "  {\\sigma^2 \\rho} & {\\sigma^2} &  \\sigma^2 \\rho & \\ldots & {0}  & {0} \\\\\n",
    "  {0} & \\sigma^2 \\rho & {\\sigma^2} & \\ldots & {0} & {0} \\\\\n",
    "  \\vdots & \\vdots & \\vdots &  & \\vdots & \\vdots\\\\\n",
    "  {0} & {0} & 0 & \\ldots &  {\\sigma^2} & \\sigma^2 \\rho  \\\\\n",
    "{0} & {0} & 0 & \\ldots & \\sigma^2 \\rho &  {\\sigma^2} \n",
    "\\end{array}\n",
    "}\\right]\n",
    "\\end{aligned}$$\n",
    "\n",
    "From this, the confirmation probabilities were specified as multivariate normal on the inverse-logit scale.\n",
    "\n",
    "$$ \\text{logit}(p_a) = \\{a\\} \\sim N(\\mu, \\Sigma)$$\n",
    "\n",
    "Priors for the confirmation sub-model were specified by:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mu_i &\\sim N(0, 100) \\\\\n",
    "\\sigma &\\sim \\text{HalfCauchy}(25) \\\\\n",
    "\\rho &\\sim U(-1, 1)\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Age classes are defined in 5-year intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "age_classes = [0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,100]\n",
    "measles_data.dropna(subset=['AGE'], inplace=True)\n",
    "measles_data['AGE_GROUP'] = pd.cut(measles_data.AGE, age_classes, right=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lab-checked observations are extracted for use in estimating lab confirmation probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "CONFIRMED = measles_data.CONCLUSION == 'CONFIRMED'\n",
    "CLINICAL = measles_data.CONCLUSION == 'CLINICAL'\n",
    "DISCARDED = measles_data.CONCLUSION == 'DISCARDED'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lab_subset = measles_data[(CONFIRMED | DISCARDED) & measles_data.YEAR_AGE.notnull() & measles_data.COUNTY.notnull()].copy()\n",
    "lab_subset.loc[lab_subset.YEAR_AGE > 75, 'YEAR_AGE'] = 75\n",
    "age = lab_subset.YEAR_AGE.astype(int).values\n",
    "ages = lab_subset.YEAR_AGE.astype(int).unique()\n",
    "counties = lab_subset.COUNTY.unique()\n",
    "y = (lab_subset.CONCLUSION=='CONFIRMED').values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proportion of lab-confirmed cases older than 20 years"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6034981469764078"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(measles_data[CONFIRMED].AGE>20).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract cases by age and time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/pandas/core/categorical.py:462: FutureWarning: Accessing 'levels' is deprecated, use 'categories'\n",
      "  warn(\"Accessing 'levels' is deprecated, use 'categories'\", FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "age_group = pd.cut(age, age_classes, right=False)\n",
    "age_index = np.array([age_group.categories.tolist().index(i) for i in age_group])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get index from full crosstabulation to use as index for each district\n",
    "dates_index = measles_data.groupby(\n",
    "        ['ONSET', 'AGE_GROUP']).size().unstack().index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "unique_districts = measles_data.DISTRICT.dropna().unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = sp_pop.ix[unique_districts, 'Total'].dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "93"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_districts = N.index.values\n",
    "len(sp_districts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_district_data = []\n",
    "all_confirmed_cases = []\n",
    "for d in sp_districts:\n",
    "    \n",
    "    # All bi-weekly unconfirmed and confirmed cases\n",
    "    district_data = measles_data[measles_data.DISTRICT==d]\n",
    "    district_counts_2w = district_data.groupby(\n",
    "        ['ONSET', 'AGE_GROUP']).size().unstack().reindex(dates_index).fillna(0).resample('2W', how='sum')\n",
    "    all_district_data.append(district_counts_2w)\n",
    "    \n",
    "    # All confirmed cases, by district\n",
    "    confirmed_data = district_data[district_data.CONCLUSION!='CONFIRMED']\n",
    "    confirmed_counts = confirmed_data.groupby(\n",
    "        ['ONSET', 'AGE_GROUP']).size().unstack().reindex(dates_index).fillna(0).sum()\n",
    "    all_confirmed_cases.append(confirmed_counts.reindex_axis(measles_data['AGE_GROUP'].unique()).fillna(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time series of cases by district, summarized in 2-week intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Sum over ages for susceptibles\n",
    "sp_cases_2w = [dist.sum(1) for dist in all_district_data]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ensure the age groups are ordered\n",
    "I_obs = np.array([dist.reindex_axis(measles_data['AGE_GROUP'].unique(), \n",
    "                            axis=1).fillna(0).values.astype(int) for dist in all_district_data])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['[0, 5)', '[5, 10)', '[10, 15)', '[15, 20)', '[20, 25)', '[25, 30)',\n",
       "       '[30, 35)', '[35, 40)', '[40, 45)', '[45, 50)', '[50, 55)',\n",
       "       '[55, 60)', '[60, 65)', '[65, 70)', '[70, 75)', '[75, 100)'], dtype=object)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measles_data['AGE_GROUP'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check shape of data frame\n",
    "\n",
    "- 93 districts, 28 bi-monthly intervals, 16 age groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert I_obs.shape == (93, 28, 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spatial distance between districts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import geopandas as gpd\n",
    "\n",
    "shp = gpd.GeoDataFrame.from_file(\"Sao Paulo/Brazil_full/BRA_adm3.shp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "district_names = N.index.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import trans\n",
    "shp['district_name'] = shp.NAME_3.apply(\n",
    "    lambda x: trans.trans(x).upper())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sp_shp = shp[shp.NAME_2=='São Paulo'].set_index('district_name')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "centroids = sp_shp.geometry.centroid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "distance_matrix = pd.concat([sp_shp.geometry.distance(o) for o in sp_shp.geometry],\n",
    "                     axis=1)\n",
    "distance_matrix.columns = sp_shp.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "min_x, min_y = sp_shp.bounds.min()[:2]\n",
    "max_x, max_y = sp_shp.bounds.max()[2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert (distance_matrix.index == centroids.index).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "centroid_xy = np.array([[c.x, c.y] for c in sp_shp.geometry.centroid])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an arbitrary distance metric for an arbitrary district, as an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.  ,  0.  ,  0.  ,  0.01,  0.  ,  0.12,  0.  ,  0.  ,  0.  ,\n",
       "        0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.04,  0.  ,  0.  ,  0.  ,\n",
       "        1.  ,  0.  ,  0.  ,  0.  ,  0.01,  0.01,  0.  ,  0.  ,  0.  ,\n",
       "        0.01,  0.  ,  0.  ,  0.  ,  0.  ,  0.18,  0.  ,  0.  ,  0.  ,\n",
       "        0.  ,  0.04,  1.  ,  0.  ,  0.  ,  0.  ,  0.1 ,  0.01,  0.  ,\n",
       "        0.  ,  0.19,  0.  ,  0.  ,  0.  ,  0.  ,  0.04,  0.  ,  1.  ,\n",
       "        0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.11,  0.  ,  1.  ,\n",
       "        0.02,  0.  ,  1.  ,  0.  ,  1.  ,  0.  ,  0.01,  0.  ,  0.02,\n",
       "        0.03,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,\n",
       "        0.  ,  0.  ,  0.  ,  0.1 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.65,\n",
       "        0.  ,  0.01,  0.  ,  0.  ,  0.  ,  1.  ])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_beta = -100\n",
    "np.exp(_beta*distance_matrix).values.round(2)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Spatial decision model\n",
    "\n",
    "We attempt to estimate $R_t$ for a truncated subset of the data, to simulate a decision-maker's information during (rather than after) an outbreak. This essentially involves turning part of the time series into missing data, and running the model.\n",
    "\n",
    "This is an example of creating a mask for data not observed by the decision date."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        ..., \n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]],\n",
       "\n",
       "       [[False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        ..., \n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]],\n",
       "\n",
       "       [[False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        ..., \n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]],\n",
       "\n",
       "       ..., \n",
       "       [[False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        ..., \n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]],\n",
       "\n",
       "       [[False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        ..., \n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]],\n",
       "\n",
       "       [[False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        [False, False, False, ..., False, False, False],\n",
       "        ..., \n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]]], dtype=bool)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([np.resize(all_district_data[0].index > '1997-06-15', I_obs[0].T.shape).T]*len(all_district_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pymc import MCMC, Matplot\n",
    "from pymc import (Uniform, DiscreteUniform, Beta, Lambda, Binomial, Normal, Poisson, \n",
    "                  NegativeBinomial, observed, negative_binomial_like, Lognormal, Exponential, binomial_like,\n",
    "                  stochastic, potential, invlogit, TruncatedNormal, Binomial, Gamma)\n",
    "from pymc import (HalfCauchy, deterministic, MvNormalCov, Bernoulli, potential, Uninformative, Multinomial,\n",
    "                  rmultinomial, rbinomial, AdaptiveMetropolis)\n",
    "\n",
    "from pymc.gp import *\n",
    "from pymc.gp.cov_funs import matern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def measles_model(obs_date, confirmation=True, spatially_weighted=True, all_traces=False):\n",
    "    \n",
    "    ### Confirmation sub-model\n",
    "    \n",
    "    if confirmation:\n",
    "\n",
    "        # Specify priors on age-specific means\n",
    "        age_classes = np.unique(age_index)\n",
    "\n",
    "        mu = Normal(\"mu\", mu=0, tau=0.0001, value=[0]*len(age_classes))\n",
    "        sig = HalfCauchy('sig', 0, 25, value=1)\n",
    "        var = sig**2\n",
    "        cor = Uniform('cor', -1, 1, value=0)\n",
    "\n",
    "\n",
    "        # Build variance-covariance matrix with first-order correlation among age classes\n",
    "        @deterministic\n",
    "        def Sigma(var=var, cor=cor):\n",
    "            I = np.eye(len(age_classes))*var\n",
    "            E = np.diag(np.ones(len(age_classes)-1), k=-1)*var*cor\n",
    "            return I + E + E.T\n",
    "\n",
    "\n",
    "        # Age-specific probabilities of confirmation as multivariate normal random variables\n",
    "        beta_age = MvNormalCov(\"beta_age\", mu=mu, C=Sigma, value=[1]*len(age_classes))\n",
    "        p_age = Lambda('p_age', lambda t=beta_age: invlogit(t))\n",
    "\n",
    "        @deterministic(trace=False)\n",
    "        def p_confirm(beta=beta_age):\n",
    "            return invlogit(beta[age_index])\n",
    "\n",
    "\n",
    "        # Confirmation likelihood\n",
    "        lab_confirmed = Bernoulli('lab_confirmed', p=p_confirm, value=y, observed=True)\n",
    "\n",
    "\n",
    "    '''\n",
    "    Missing data sub-model \n",
    "    \n",
    "    We treat observations later than the decision date as missing data. This is \n",
    "    implemented as a `masked_array` in NumPy, which requires a boolean mask to identify missing values.\n",
    "    '''\n",
    "    missing_mask = all_district_data[0].index > obs_date\n",
    "    district_mask = np.resize(missing_mask, I_obs[0].T.shape).T\n",
    "    \n",
    "    # Index to the observation period\n",
    "    current_index = (~missing_mask).sum()-1\n",
    "\n",
    "    I_obs_masked = ma.masked_array(I_obs,\n",
    "                                   mask=np.array([district_mask]*len(all_district_data)),\n",
    "                                   fill_value=1)\n",
    "\n",
    "\n",
    "    # Index for observation date, used to index out values of interest from the model.\n",
    "    t_obs = (~missing_mask).sum() - 1\n",
    "\n",
    "\n",
    "    # Imputed infecteds\n",
    "    I_imp = DiscreteUniform('I_imp', 0, 2000, value=I_obs_masked, observed=True)\n",
    "\n",
    "    ### Chain binomial model for disease dynamics\n",
    "\n",
    "    if confirmation:\n",
    "        \n",
    "        # Confirmed cases\n",
    "        @stochastic(trace=all_traces, dtype=int)\n",
    "        def I(value=(I_imp.value*0.7).astype(int), n=I_imp, p=p_age):\n",
    "            return np.sum([np.sum([binomial_like(vj[:,i], nj[:,i], p[i]) for i in range(len(p))]).sum(0) \n",
    "                                    for vj, nj in zip(value, n)])\n",
    "\n",
    "    else:\n",
    "        \n",
    "        I = I_imp\n",
    "\n",
    "\n",
    "    # Infecteds at time $t_{obs}$\n",
    "    It = Lambda('It', lambda I=I: I.sum(0)[t_obs])\n",
    "\n",
    "\n",
    "    # Calculate susceptibles from total number of infections\n",
    "    @deterministic(trace=all_traces)\n",
    "    def S(I=I):\n",
    "        return np.array([Ij.sum() - np.array([Ij[:i].sum() for i in range(len(Ij))]) for Ij in I])\n",
    "\n",
    "\n",
    "    # Total infecteds until time t_obs, by age\n",
    "    I_total = Lambda('I_total', lambda I=I: I[:,:t_obs].sum(0).sum(0))\n",
    "    # Age distribution of infecteds\n",
    "    age_dist = Lambda('age_dist', lambda I=I_total: I/I.sum())\n",
    "    \n",
    "    # Susceptibles at time t\n",
    "    S_t = Lambda('S_t', lambda S=S: S[:, t_obs])\n",
    "    \n",
    "    # Susceptibles at time t, by age\n",
    "    @deterministic\n",
    "    def S_age(S=S_t, p=age_dist):\n",
    "        return np.array([rmultinomial(si, p) for si in S])  \n",
    "    \n",
    "    @deterministic\n",
    "    def vacc_5(S=S_age):\n",
    "        # Vaccination of 15 and under\n",
    "        p = [0.95] + [0]*15\n",
    "        return rbinomial(S[current_index], p)\n",
    "    \n",
    "    # Proportion of susceptibles vaccinated\n",
    "    pct_5 = Lambda('pct_5', lambda V=vacc_5, S=S_age: float(V.sum())/S[current_index].sum())\n",
    "    \n",
    "    @deterministic\n",
    "    def vacc_15(S=S_age):\n",
    "        # Vaccination of 15 and under\n",
    "        p = [0.95]*3 + [0]*13\n",
    "        return rbinomial(S[current_index], p)\n",
    "    \n",
    "    # Proportion of susceptibles vaccinated\n",
    "    pct_15 = Lambda('pct_15', lambda V=vacc_15, S=S_age: float(V.sum())/S[current_index].sum())\n",
    "    \n",
    "    @deterministic\n",
    "    def vacc_30(S=S_age):\n",
    "        # Vaccination of 30 and under\n",
    "        p = [0.95]*6 + [0]*10\n",
    "        return rbinomial(S[current_index], p)\n",
    "    \n",
    "    # Proportion of 30 and under susceptibles vaccinated\n",
    "    pct_30 = Lambda('pct_30', lambda V=vacc_30, S=S_age: float(V.sum())/S[current_index].sum())\n",
    "    \n",
    "    @deterministic\n",
    "    def vacc_adult(S=S_age):\n",
    "        # Vaccination of adults under 30 (and young kids)\n",
    "        p = [0.95, 0, 0, 0, 0.95, 0.95] + [0]*10\n",
    "        return rbinomial(S[current_index], p)\n",
    "    \n",
    "    # Proportion of adults under 30 (and young kids)\n",
    "    pct_adult = Lambda('pct_adult', lambda V=vacc_adult, S=S_age: float(V.sum())/S[current_index].sum())\n",
    "    \n",
    "    # Transmission parameter\n",
    "    beta = Gamma('beta', 1, 0.1, value=10) \n",
    "\n",
    "\n",
    "    '''\n",
    "    Calculation of the effective reproduction number depends on whether we believe that the districts \n",
    "    are independent or not. If not (`spatially_weighted = True`), both the number of susceptibles and the \n",
    "    denominator population are calculated as a distance-weighted average of all the districts in Sao Paulo.\n",
    "    '''\n",
    "    if spatially_weighted:\n",
    "\n",
    "        geo_mesh = np.transpose([np.linspace(min_x, max_x),\n",
    "                                np.linspace(min_y, max_y)])\n",
    "\n",
    "        # Vague prior for the overall mean\n",
    "        m = Uninformative('m', value=0)\n",
    "\n",
    "        def constant(x, val):\n",
    "            return np.zeros(x.shape[:-1],dtype=float) + val\n",
    "\n",
    "        @deterministic\n",
    "        def M(m=m):\n",
    "            return Mean(constant, val=m)\n",
    "\n",
    "        # ==================\n",
    "        # = The covariance =\n",
    "        # ==================\n",
    "\n",
    "        # Vague priors for the amplitude and scale\n",
    "        amp = Exponential('amp', 1e-5, value=1)\n",
    "        scale = Exponential('scale',1e-5, value=0.1)\n",
    "        @deterministic\n",
    "        def C(amp=amp, scale=scale):\n",
    "            return FullRankCovariance(exponential.euclidean, amp = amp, scale = scale)\n",
    "\n",
    "        # ===================\n",
    "        # = The GP submodel =\n",
    "        # ===================\n",
    "        zeta = GPSubmodel('zeta', M, C, geo_mesh)\n",
    "\n",
    "        z_eval = Lambda('z_eval', lambda z=zeta.f(centroid_xy): z)\n",
    "\n",
    "\n",
    "\n",
    "    if spatially_weighted:\n",
    "        alpha = Exponential('alpha', 1, value=0.0001)\n",
    "        Rt = Lambda('Rt', lambda B=beta, S=S, z=z_eval, a=alpha: ((B * (1 + a*z) * S.T) / N.values).T)\n",
    "    else:\n",
    "        Rt = Lambda('Rt', lambda B=beta, S=S: ((B * S).T / N.values).T)\n",
    "\n",
    "\n",
    "    # Effective reproduction number at time of observation, and implied vaccination target\n",
    "    Rt_obs = Lambda('Rt_obs', lambda r=Rt: r[:, t_obs])\n",
    "    vaccination_target = Lambda('vaccination_target', lambda r=Rt_obs: np.maximum(1-1./r, 0))\n",
    "\n",
    "\n",
    "    # Force of infection, assuming mass action transmission\n",
    "    if spatially_weighted:\n",
    "        lam = Lambda('lam', lambda B=beta, I=I, z=z_eval, a=alpha: \n",
    "                     np.array([(B * (1 + zj) * Ij) / nj for Ij,nj,zj in zip(I, N.values, a*z)]), \n",
    "                     trace=False)\n",
    "    else:\n",
    "        lam = Lambda('lam', lambda B=beta, I=I: np.array([(B * Ij) / nj for Ij,nj in zip(I, N.values)]), \n",
    "                     trace=False)\n",
    "\n",
    "\n",
    "    # 2-week infection probabilities\n",
    "    p = Lambda('p', lambda lam=lam: 1. - np.exp(-lam) + 1e-6, trace=False)\n",
    "\n",
    "\n",
    "    # Binomial likelihood for observed cases\n",
    "    @potential\n",
    "    def new_cases(p=p, I=I, S=S): \n",
    "        return np.sum([[binomial_like(i, s, pt) for pt,i,s in zip(pj[:t_obs], Ij[:t_obs], Sj[:t_obs])] \n",
    "                                                   for pj,Ij,Sj in zip(p, I, S)])\n",
    "\n",
    "    return locals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run models for June 15 and July 15 observation points, both with and without clinical confirmation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "db = 'txt'\n",
    "n_iterations = 50000\n",
    "n_burn = 40000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "June 15, with lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_june = MCMC(measles_model('1997-06-15', spatially_weighted=False), \n",
    "                         db=db, dbname='model_june')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50001 of 50000 complete in 6400.6 sec"
     ]
    }
   ],
   "source": [
    "model_june.sample(n_iterations, n_burn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "July 15, with lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model_july = MCMC(measles_model('1997-07-15', spatially_weighted=False), \n",
    "                         db=db, dbname='model_july')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 1974.3 sec"
     ]
    }
   ],
   "source": [
    "model_july.sample(n_iterations, n_burn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "June 15, no lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_june_noconf = MCMC(measles_model('1997-06-15', \n",
    "                                       spatially_weighted=False, \n",
    "                                       confirmation=False), \n",
    "                         db=db, dbname='model_june_noconf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50001 of 50000 complete in 884.4 sec"
     ]
    }
   ],
   "source": [
    "model_june_noconf.sample(n_iterations, n_burn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "July 15, no lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_july_noconf = MCMC(measles_model('1997-07-15', spatially_weighted=False, \n",
    "                                       confirmation=False), \n",
    "                         db=db, dbname='model_july_noconf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 998.2 sec"
     ]
    }
   ],
   "source": [
    "model_july_noconf.sample(50000, 40000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary of model output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Rt_june = model_june.Rt.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11307dc50>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "MlhEZBTwL1hQ//lGyxP0TlgOQSvwSSwwGwxvzgT+OhRDcxCWQxAEQdCNsByCIAiCboRyCIIgCLoR\n",
       "yiEIgiDoRiiHIAiCoBuhHIIgCIJuhHIIgiAIuvH/AyX7PaFLKhN5AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113078630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Rt_june['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "plt.ylabel('R(t)')\n",
    "plt.xlabel('time (2-week periods)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
     ]
    },
    {
     "data": {
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       "mCRJvWJhkiT1ioVJktQrFiZJUq/8fyJgdxvRq+yPAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dbe7860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.summary_plot(model_june.vacc_30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting pct_15\n"
     ]
    },
    {
     "data": {
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       "TkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dbbf438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.plot(model_june.pct_15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting pct_30\n"
     ]
    },
    {
     "data": {
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       "91C7KS0mPgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f77be80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.plot(model_june.pct_30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_Rt = pd.DataFrame(model_june.Rt_obs.trace()).unstack().reset_index()\n",
    "june_Rt.columns = ('district', 'iteration', 'Rt')\n",
    "june_Rt['month'] = 'June'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "june_Rt_noconf = pd.DataFrame(model_june_noconf.Rt_obs.trace()).unstack().reset_index()\n",
    "june_Rt_noconf.columns = ('district', 'iteration', 'Rt')\n",
    "june_Rt_noconf['month'] = 'June'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "july_Rt = pd.DataFrame(model_july.Rt_obs.trace()).unstack().reset_index()\n",
    "july_Rt.columns = ('district', 'iteration', 'Rt')\n",
    "july_Rt['month'] = 'July'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "confirmed_Rt = june_Rt.append(july_Rt, ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_means = june_Rt.groupby('district')['Rt'].mean()\n",
    "june_means.sort(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sorted_districts = june_means.index.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "JEmqmEFLkiRJkipm0JIkSZKkihm0JEmSJKliBi1JkiRJqphBS5IkSZIq9v8DLA18M4e29goAAAAA\n",
       "SUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x428d9a438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sb\n",
    "\n",
    "sb.set_context(\"talk\", font_scale=1.1)\n",
    "f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)\n",
    "\n",
    "sb.boxplot('district', 'Rt', data=june_Rt, ax=ax_1, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=sorted_districts)\n",
    "ax_1.hlines(1, xmin=0, xmax=93, linestyles='dashed', linewidth=0.2)\n",
    "ax_1.set_xticks([])\n",
    "ax_1.set_xlabel('')\n",
    "ax_1.set_ylabel('June')\n",
    "ax_1.set_ylim(0, 6)\n",
    "ax_1.set_yticks(range(7))\n",
    "ax_1.set_title(r'$R_t$ estimates, ordered by June means')\n",
    "\n",
    "sb.boxplot('district', 'Rt', data=july_Rt, ax=ax_2, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=sorted_districts)\n",
    "ax_2.hlines(1, xmin=0, xmax=93, linestyles='dashed', linewidth=0.2)\n",
    "ax_2.set_xticks([])\n",
    "ax_2.set_ylabel('July')\n",
    "\n",
    "f.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "pI79Bat4oV7Snm04AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x42be2f278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.set_context(\"talk\", font_scale=1.1)\n",
    "f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)\n",
    "\n",
    "sb.boxplot('district', 'Rt', data=june_Rt, ax=ax_1, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=sorted_districts)\n",
    "ax_1.hlines(1, xmin=0, xmax=93, linestyles='dotted', linewidth=0.75)\n",
    "ax_1.set_xticks([])\n",
    "ax_1.set_xlabel('')\n",
    "ax_1.set_ylabel('Lab')\n",
    "ax_1.set_yticks(np.arange(13, step=2))\n",
    "ax_1.set_title(r'June $R_t$ estimates, ordered by confirmed means')\n",
    "\n",
    "sb.boxplot('district', 'Rt', data=june_Rt_noconf, ax=ax_2, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=sorted_districts)\n",
    "ax_2.hlines(1, xmin=0, xmax=93, linestyles='dotted', linewidth=0.75)\n",
    "ax_2.set_xticks([])\n",
    "ax_2.set_ylabel('Clinical')\n",
    "\n",
    "f.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "pct_5:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.102            0.056            0.001                [ 0.   0.2]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.0              0.062           0.097          0.129         0.226\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.369            0.087            0.002            [ 0.219  0.556]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.194            0.312           0.37           0.424         0.548\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.922            0.047            0.001            [ 0.839  1.   ]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.815            0.893           0.926          0.963         1.0\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.593            0.09             0.003            [ 0.407  0.75 ]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.407            0.531           0.593          0.656         0.758\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_june.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_coverage = pd.DataFrame({name: model_june.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/site-packages/seaborn/categorical.py:1587: UserWarning: The boxplot API has been changed. Attempting to adjust your arguments for the new API (which might not work). Please update your code. See the version 0.6 release notes for more info.\n",
      "  warnings.warn(msg, UserWarning)\n"
     ]
    },
    {
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       "f3aMLlDiAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x434606da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = sb.boxplot(june_coverage, order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'])\n",
    "axes.set_xticklabels(['Under 5', 'Under 15', 'Under 30', 'Under 5 + 20-30'])\n",
    "plt.ylabel('% susceptibles vaccinated')\n",
    "sb.despine(offset=10, trim=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "pct_5:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.163            0.001            0.0              [ 0.162  0.165]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.161            0.163           0.163          0.164         0.165\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.464            0.001            0.0              [ 0.462  0.466]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.462            0.463           0.464          0.465         0.466\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.872            0.001            0.0              [ 0.871  0.874]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.871            0.872           0.872          0.873         0.874\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.502            0.001            0.0              [ 0.499  0.504]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.499            0.501           0.502          0.502         0.504\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_june_noconf.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "pct_5:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.11             0.05             0.001            [ 0.026  0.206]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.026            0.079           0.108          0.146         0.212\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.292            0.073            0.002            [ 0.146  0.425]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.154            0.242           0.293          0.342         0.441\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.899            0.049            0.001            [ 0.805  0.976]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.794            0.868           0.897          0.939         0.974\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.67             0.076            0.002            [ 0.526  0.818]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.514            0.618           0.667          0.727         0.816\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_july.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "pct_5:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.133            0.001            0.0              [ 0.131  0.135]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.131            0.132           0.133          0.133         0.135\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.365            0.001            0.0              [ 0.362  0.367]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.362            0.364           0.365          0.366         0.367\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.861            0.001            0.0              [ 0.859  0.863]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.859            0.86            0.861          0.862         0.863\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.568            0.001            0.0              [ 0.566  0.571]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.565            0.567           0.568          0.569         0.57\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_july_noconf.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Rt_july = model_july.Rt.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1172d5630>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "CLqAEPsgCIIuIMQ+CIKgCwixD4Ig6AL+f2850yFraWapAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11743b438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Rt_july['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "plt.ylabel('R(t)')\n",
    "plt.xlabel('time (2-week periods)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Rt_june_noconf = model_june_noconf.Rt.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x117602c88>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173a2128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Rt_june_noconf['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "plt.ylabel('R(t)')\n",
    "plt.xlabel('time (2-week periods)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
     ]
    },
    {
     "data": {
      "image/png": [
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       "v98vAy5r970YeOicm9N6nveLaE6r3gW8csbl7rSO7/WZB7SuZB31vwD4eFXdv9LjuhafJKmTunD1\n",
       "iiRJD2CDkiR1kg1KktRJNihJUifZoCRJnWSDkiR1kg1KktRJNihJUif9f1luSM/PTcsQAAAAAElF\n",
       "TkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11796aac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.summary_plot(model_june.p_age)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 16)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "june_age_dist = model_june.age_dist.trace()[:]\n",
    "june_age_dist.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_age_dist = pd.DataFrame(june_age_dist, columns=measles_data['AGE_GROUP'].unique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
     ]
    },
    {
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       "AAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x36cf97eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,12))\n",
    "Matplot.summary_plot(model_july.vaccination_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
     ]
    },
    {
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       "AAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac22128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,12))\n",
    "Matplot.summary_plot(model_july.vaccination_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting alpha\n"
     ]
    },
    {
     "data": {
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       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aae6668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.plot(model_june.alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Mapping spatial effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.basemap import Basemap\n",
    "import geopandas as gpd\n",
    "\n",
    "lllat=-24\n",
    "urlat=-23.3\n",
    "lllon=-47\n",
    "urlon=-46.3\n",
    "\n",
    "SP_base = Basemap(ax=None, lon_0=(urlon + lllon) / 2, lat_0=(urlat + lllat) / 2,\n",
    "        llcrnrlat=lllat, urcrnrlat=urlat, llcrnrlon=lllon, urcrnrlon=urlon, \n",
    "                  resolution='i',\n",
    "                 epsg='4326')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SP_dist = gpd.GeoDataFrame.from_file('Sao Paulo/Brazil_full/BRA_adm3.shp').to_crs({'proj': 'longlat', \n",
    "                                                                               'ellps': 'WGS84', \n",
    "                                                                               'datum': 'WGS84'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SP_dist['DIST_NAME'] = [trans.trans(_).upper() for _ in SP_dist.NAME_3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ENGTYPE_3</th>\n",
       "      <th>HASC_3</th>\n",
       "      <th>ID_0</th>\n",
       "      <th>ID_1</th>\n",
       "      <th>ID_2</th>\n",
       "      <th>ID_3</th>\n",
       "      <th>ISO</th>\n",
       "      <th>NAME_0</th>\n",
       "      <th>NAME_1</th>\n",
       "      <th>NAME_2</th>\n",
       "      <th>...</th>\n",
       "      <th>NL_NAME_3</th>\n",
       "      <th>REMARKS_3</th>\n",
       "      <th>Shape_Area</th>\n",
       "      <th>Shape_Leng</th>\n",
       "      <th>TYPE_3</th>\n",
       "      <th>VALIDFR_3</th>\n",
       "      <th>VALIDTO_3</th>\n",
       "      <th>VARNAME_3</th>\n",
       "      <th>geometry</th>\n",
       "      <th>DIST_NAME</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> District</td>\n",
       "      <td> None</td>\n",
       "      <td> 32</td>\n",
       "      <td> 434</td>\n",
       "      <td> 4112</td>\n",
       "      <td> 4868</td>\n",
       "      <td> BRA</td>\n",
       "      <td> Brazil</td>\n",
       "      <td> Bahia</td>\n",
       "      <td>   Piritiba</td>\n",
       "      <td>...</td>\n",
       "      <td> None</td>\n",
       "      <td> None</td>\n",
       "      <td> 0.041872</td>\n",
       "      <td> 1.033621</td>\n",
       "      <td> Distrito</td>\n",
       "      <td> Unknown</td>\n",
       "      <td> Present</td>\n",
       "      <td> None</td>\n",
       "      <td> POLYGON ((-40.38711999999998 -11.6031739999999...</td>\n",
       "      <td>    PIRITIBA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> District</td>\n",
       "      <td> None</td>\n",
       "      <td> 32</td>\n",
       "      <td> 434</td>\n",
       "      <td> 4112</td>\n",
       "      <td> 4869</td>\n",
       "      <td> BRA</td>\n",
       "      <td> Brazil</td>\n",
       "      <td> Bahia</td>\n",
       "      <td>   Piritiba</td>\n",
       "      <td>...</td>\n",
       "      <td> None</td>\n",
       "      <td> None</td>\n",
       "      <td> 0.008318</td>\n",
       "      <td> 0.375198</td>\n",
       "      <td> Distrito</td>\n",
       "      <td> Unknown</td>\n",
       "      <td> Present</td>\n",
       "      <td> None</td>\n",
       "      <td> POLYGON ((-40.62181199999998 -11.7807669999999...</td>\n",
       "      <td> PORTO FELIZ</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> District</td>\n",
       "      <td> None</td>\n",
       "      <td> 32</td>\n",
       "      <td> 434</td>\n",
       "      <td> 4113</td>\n",
       "      <td> 4870</td>\n",
       "      <td> BRA</td>\n",
       "      <td> Brazil</td>\n",
       "      <td> Bahia</td>\n",
       "      <td> Planaltino</td>\n",
       "      <td>...</td>\n",
       "      <td> None</td>\n",
       "      <td> None</td>\n",
       "      <td> 0.024796</td>\n",
       "      <td> 0.751948</td>\n",
       "      <td> Distrito</td>\n",
       "      <td> Unknown</td>\n",
       "      <td> Present</td>\n",
       "      <td> None</td>\n",
       "      <td> POLYGON ((-40.11320899999998 -13.3009799999998...</td>\n",
       "      <td>  IBITIGUIRA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> District</td>\n",
       "      <td> None</td>\n",
       "      <td> 32</td>\n",
       "      <td> 434</td>\n",
       "      <td> 4113</td>\n",
       "      <td> 4871</td>\n",
       "      <td> BRA</td>\n",
       "      <td> Brazil</td>\n",
       "      <td> Bahia</td>\n",
       "      <td> Planaltino</td>\n",
       "      <td>...</td>\n",
       "      <td> None</td>\n",
       "      <td> None</td>\n",
       "      <td> 0.027577</td>\n",
       "      <td> 0.776489</td>\n",
       "      <td> Distrito</td>\n",
       "      <td> Unknown</td>\n",
       "      <td> Present</td>\n",
       "      <td> None</td>\n",
       "      <td> POLYGON ((-40.15503999999993 -13.1252719999998...</td>\n",
       "      <td> NOVA ITAIPE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> District</td>\n",
       "      <td> None</td>\n",
       "      <td> 32</td>\n",
       "      <td> 434</td>\n",
       "      <td> 4113</td>\n",
       "      <td> 4872</td>\n",
       "      <td> BRA</td>\n",
       "      <td> Brazil</td>\n",
       "      <td> Bahia</td>\n",
       "      <td> Planaltino</td>\n",
       "      <td>...</td>\n",
       "      <td> None</td>\n",
       "      <td> None</td>\n",
       "      <td> 0.025845</td>\n",
       "      <td> 1.052880</td>\n",
       "      <td> Distrito</td>\n",
       "      <td> Unknown</td>\n",
       "      <td> Present</td>\n",
       "      <td> None</td>\n",
       "      <td> POLYGON ((-40.38104599999997 -13.2141219999999...</td>\n",
       "      <td>  PLANALTINO</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  ENGTYPE_3 HASC_3  ID_0  ID_1  ID_2  ID_3  ISO  NAME_0 NAME_1      NAME_2  \\\n",
       "0  District   None    32   434  4112  4868  BRA  Brazil  Bahia    Piritiba   \n",
       "1  District   None    32   434  4112  4869  BRA  Brazil  Bahia    Piritiba   \n",
       "2  District   None    32   434  4113  4870  BRA  Brazil  Bahia  Planaltino   \n",
       "3  District   None    32   434  4113  4871  BRA  Brazil  Bahia  Planaltino   \n",
       "4  District   None    32   434  4113  4872  BRA  Brazil  Bahia  Planaltino   \n",
       "\n",
       "      ...      NL_NAME_3 REMARKS_3 Shape_Area  Shape_Leng    TYPE_3 VALIDFR_3  \\\n",
       "0     ...           None      None   0.041872    1.033621  Distrito   Unknown   \n",
       "1     ...           None      None   0.008318    0.375198  Distrito   Unknown   \n",
       "2     ...           None      None   0.024796    0.751948  Distrito   Unknown   \n",
       "3     ...           None      None   0.027577    0.776489  Distrito   Unknown   \n",
       "4     ...           None      None   0.025845    1.052880  Distrito   Unknown   \n",
       "\n",
       "  VALIDTO_3 VARNAME_3                                           geometry  \\\n",
       "0   Present      None  POLYGON ((-40.38711999999998 -11.6031739999999...   \n",
       "1   Present      None  POLYGON ((-40.62181199999998 -11.7807669999999...   \n",
       "2   Present      None  POLYGON ((-40.11320899999998 -13.3009799999998...   \n",
       "3   Present      None  POLYGON ((-40.15503999999993 -13.1252719999998...   \n",
       "4   Present      None  POLYGON ((-40.38104599999997 -13.2141219999999...   \n",
       "\n",
       "     DIST_NAME  \n",
       "0     PIRITIBA  \n",
       "1  PORTO FELIZ  \n",
       "2   IBITIGUIRA  \n",
       "3  NOVA ITAIPE  \n",
       "4   PLANALTINO  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SP_dist.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Piritiba', 'Porto Feliz', 'Ibitiguira', ..., 'Tupiratins',\n",
       "       'Wanderlândia', 'Xambioá'], dtype=object)"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SP_dist.NAME_3.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['BRAS', 'BARRA FUNDA', 'FREGUESIA DO O', 'CAMBUCI', 'PENHA',\n",
       "       'BRAZILANDIA', 'SANTA CECILIA', 'CASA VERDE', 'CAPAO REDONDO',\n",
       "       'CONSOLACAO', 'JAGUARE', 'CIDADE ADEMAR', 'CIDADE TIRADENTES',\n",
       "       'SAPOPEMBA', 'MOOCA', 'CANGAIBA', 'SAUDE', 'SANTANA',\n",
       "       'JARDIM ANGELA', 'CAMPO LIMPO', 'VILA MARIANA', 'VILA CURUCA',\n",
       "       'CIDADE DUTRA', 'ARTUR ALVIM', 'JARDIM HELENA', 'SE', 'LAPA',\n",
       "       'JARDIM PAULISTA', 'JABAQUARA', 'PINHEIROS', 'RIO PEQUENO',\n",
       "       'GRAJAU', 'VILA SONIA', 'IGUATEMI', 'SANTO AMARO', 'LIMAO',\n",
       "       'PERDIZES', 'SAO DOMINGOS', 'SAO LUCAS', 'PIRITUBA',\n",
       "       'RAPOSO TAVARES', 'VILA FORMOSA', 'BELEM', 'REPUBLICA',\n",
       "       'SAO MATEUS', 'TREMEMBE', 'VILA PRUDENTE', 'VILA LEOPOLDINA',\n",
       "       'BOM RETIRO', 'JOSE BONIFACIO', 'PARELHEIROS', 'PERUS', 'PEDREIRA',\n",
       "       'JARAGUA', 'LAJEADO', 'SACOMA', 'ITAIM PAULISTA', 'TUCURUVI',\n",
       "       'VILA MEDEIROS', 'LIBERDADE', 'TATUAPE', 'CARRAO', 'BELA VISTA',\n",
       "       'BUTANTA', 'SAO RAFAEL', 'MORUMBI', 'AGUA RASA', 'MOEMA',\n",
       "       'VILA ANDRADE', 'ANHANGUERA', 'VILA MARIA', 'IPIRANGA', 'SOCORRO',\n",
       "       'CACHOEIRINHA', 'ARICANDUVA', 'CAMPO GRANDE', 'MANDAQUI',\n",
       "       'ITAQUERA', 'SAO MIGUEL', 'JAGUARA', 'PARQUE DO CARMO', 'JACANA',\n",
       "       'CIDADE LIDER', 'CAMPO BELO', 'VILA JACUI', 'ITAIM BIBI',\n",
       "       'VILA GUILHERME', 'CURSINO', 'MARSILAC', 'GUAIANASES',\n",
       "       'VILA MATILDE', 'PONTE RASA', 'PARI'], dtype=object)"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "district_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Rt_june = pd.Series(model_june.Rt_obs.stats()['mean'], index=sp_districts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BRAS              1.027835\n",
       "BARRA FUNDA       1.777664\n",
       "FREGUESIA DO O    0.160857\n",
       "CAMBUCI           0.897236\n",
       "PENHA             0.167268\n",
       "BRAZILANDIA       0.181805\n",
       "SANTA CECILIA     0.423634\n",
       "CASA VERDE        0.305393\n",
       "CAPAO REDONDO     0.267271\n",
       "CONSOLACAO        0.383250\n",
       "...\n",
       "CIDADE LIDER      0.216627\n",
       "CAMPO BELO        0.375009\n",
       "VILA JACUI        0.148078\n",
       "ITAIM BIBI        0.424089\n",
       "VILA GUILHERME    0.283753\n",
       "CURSINO           0.177329\n",
       "MARSILAC          3.106626\n",
       "GUAIANASES        0.316312\n",
       "VILA MATILDE      0.207121\n",
       "PONTE RASA        0.205254\n",
       "PARI              1.745154\n",
       "Length: 93, dtype: float64"
      ]
     },
     "execution_count": 308,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rt_june"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SP_dist_merged = SP_dist.merge(pd.DataFrame(Rt_june, columns=['Rt']), left_on='DIST_NAME', right_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "SP_dist_merged = SP_dist.merge(foo, left_on='DIST_NAME', right_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "measles_onset_conf = measles_data[CONFIRMED].groupby(['DISTRICT','ONSET']).size().unstack(level=0).fillna(0).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DISTRICT\n",
       "AGUA RASA         37\n",
       "ALTO PINHEIROS    19\n",
       "AMERICANOPOLIS     1\n",
       "ANHANGUERA        22\n",
       "ARICANDUVA        32\n",
       "ARTUR ALVIM       68\n",
       "BARRA FUNDA       37\n",
       "BELA VISTA        83\n",
       "BELEM             16\n",
       "BOM RETIRO        40\n",
       "...\n",
       "VILA.CARRAO         1\n",
       "VILA.JAGUARA        1\n",
       "VILA.LEOPOLDINA     1\n",
       "VILAILA ANDRADE     1\n",
       "VILAILA CURUCA      1\n",
       "VILAILA FORMOSA     1\n",
       "VILAILA MARIA       1\n",
       "VILAILA MATILDE     1\n",
       "VILAILA MEDEIROS    1\n",
       "VILAILA SONIA       3\n",
       "VILAL FORMOSA       1\n",
       "Length: 153, dtype: float64"
      ]
     },
     "execution_count": 296,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measles_onset_conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "_rates = measles_onset_conf/sp_pop.sum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "SP_dist_conf = SP_dist.merge(pd.DataFrame(_rates, columns=['rate']), left_on='DIST_NAME', right_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x4723f3be0>"
      ]
     },
     "execution_count": 320,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "rIQQQgghhK9RYSWEEEIIIXyNCishhBBCCOFr/wfFAlk1Hdzq8wAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4723f30b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import cm\n",
    "\n",
    "map_fig = plt.figure(figsize=(16,12))\n",
    "map_ax = plt.gca()\n",
    "SP_base.drawcoastlines()\n",
    "SP_base.drawrivers()\n",
    "\n",
    "SP_dist_merged.plot(column='cases', colormap=cm.Reds, axes=map_ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
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