New Spatial Measles Model (variable susceptibility).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": 1,
   "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",
    "import pdb\n",
    "\n",
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   "cell_type": "code",
   "execution_count": 2,
   "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": 3,
   "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": 4,
   "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": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sp_pop = pd.read_csv(data_dir+'sp_pop.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {
    "collapsed": false
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   "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": 7,
     "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": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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     "execution_count": 8,
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     "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 0x10e819da0>"
      ]
     },
     "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": 9,
   "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": 10,
   "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": 10,
     "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": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d480438>"
      ]
     },
     "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": [
    "## Stochastic Disease 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 SIR disease model, which will be fit using MCMC.\n",
    "\n",
    "This model fits the series of 2-week infection totals in each district $i$ as a set of Poisson models:\n",
    "\n",
    "\\\\[Pr(I(t)_{i} | \\lambda(t)_i) = \\text{Poisson}(\\lambda(t)_i) \\\\]\n",
    "\n",
    "Where the outbreak intensity is modeled as:\n",
    "\n",
    "\\\\[\\lambda(t)_i = \\beta [I^{(w)}(t-1)_i]^{\\alpha} S(t-1)_i\\\\]\n",
    "\n",
    "\\\\[\\alpha \\sim \\text{Exp}(1)\\\\]\n",
    "\n",
    "We will assume here that the transmission rate is constant over time (and across districts):\n",
    "\n",
    "\\\\[\\beta \\sim \\text{Gamma}(1, 0.1)\\\\]\n",
    "\n",
    "To account for the influence of infected individuals from neighboring districts on new infections, the outbreak intensity was modeled using a spatial-weighted average of infecteds across districts, where populations were weighted as an exponential function of the distance between district centroids:\n",
    "\n",
    "\\\\[w_{d} = \\text{exp}(-\\theta d)\\\\]\n",
    "\n",
    "\\\\[\\theta \\sim \\text{Exp}(1)\\\\]\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": 12,
   "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=['YEAR_AGE'], inplace=True)\n",
    "measles_data['YEAR_AGE'] = measles_data.YEAR_AGE.astype(int)\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": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "CONFIRMED = measles_data.CONCLUSION == 'CONFIRMED'\n",
    "CLINICAL = measles_data.CONCLUSION == 'CLINICAL'\n",
    "DISCARDED = measles_data.CONCLUSION == 'DISCARDED'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract confirmed and clinical subset, with no missing county information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lab_subset = measles_data[(CONFIRMED | CLINICAL) & measles_data.COUNTY.notnull()].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "age = lab_subset.YEAR_AGE.values\n",
    "ages = lab_subset.YEAR_AGE.unique()\n",
    "counties = lab_subset.COUNTY.unique()\n",
    "y = (lab_subset.CONCLUSION=='CONFIRMED').values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "SaqEgU6SlCepg9ph7U5bsENhZcnxwKK2HbOFSl6NiEM6aOtWYFhEtF84pb2jgBfbLXTyBPCxiNg2\n",
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       "pZS6W8VSkqRe4widJEmSJOWU36GTJEmSpJwy0EmSJElSThnoJEmSJCmnDHSSJEmSlFMGOkmSJEnK\n",
       "KQOdJEmSJOXU/w8BaP5/T89mfQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eda5a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_lab_subset = lab_subset.replace({\"CONCLUSION\": {\"CLINICAL\": \"UNCONFIRMED\"}})\n",
    "by_conclusion = _lab_subset.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), grid=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(39982, 16)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lab_subset.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22097"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proportion of lab-confirmed cases older than 20 years"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.60257048468117846"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(measles_data[CONFIRMED].YEAR_AGE>20).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Extract cases by age and time.\n",
    "\n",
    "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": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['[0, 5)', '[5, 10)', '[10, 15)', '[15, 20)', '[20, 25)', '[25, 30)',\n",
       "       '[30, 35)', '[35, 40)', '[40, 45)', '[45, 50)', '[50, 55)', '[55, 60)',\n",
       "       '[60, 65)', '[65, 70)', '[70, 75)', '[75, 100)'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_group.categories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "unique_districts = measles_data.DISTRICT.dropna().unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "excludes = ['BOM RETIRO']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = sp_pop.ix[unique_districts, 'Total'].dropna()\n",
    "N = N.drop(excludes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "92"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_districts = N.index.values\n",
    "len(sp_districts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile bi-weekly confirmed and unconfirmed data by Sao Paulo district"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "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 = lab_subset[lab_subset.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": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "92"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sum over ages for susceptibles\n",
    "sp_cases_2w = [dist.sum(1) for dist in all_district_data]\n",
    "len(sp_cases_2w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "46"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I_obs.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16640"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I_obs.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['[20, 25)', '[5, 10)', '[25, 30)', '[0, 5)', '[35, 40)', '[30, 35)',\n",
       "       '[50, 55)', '[15, 20)', '[10, 15)', '[40, 45)', '[45, 50)',\n",
       "       '[75, 100)', '[65, 70)', '[55, 60)', '[70, 75)', '[60, 65)'], dtype=object)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_groups = measles_data['AGE_GROUP'].unique()\n",
    "age_groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check shape of data frame\n",
    "\n",
    "- 92 districts, 28 bi-monthly intervals, 15 age groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert I_obs.shape == (92, 28, 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Spatial distance between districts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "district_names = N.index.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sp_shp = shp[shp.NAME_2=='São Paulo'].set_index('district_name')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "centroids = sp_shp.geometry.centroid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert (distance_matrix.index == centroids.index).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "distance_matrix = distance_matrix.ix[sp_districts, sp_districts]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert not distance_matrix.isnull().values.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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": 44,
   "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": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.  ,  0.04,  0.  ,  1.  ,  0.01,  0.  ,  0.27,  0.05,  0.  ,\n",
       "        0.13,  0.  ,  0.  ,  0.  ,  0.  ,  1.  ,  0.  ,  0.01,  0.23,\n",
       "        0.  ,  0.  ,  0.1 ,  0.  ,  0.  ,  0.  ,  0.  ,  1.  ,  0.  ,\n",
       "        0.06,  0.  ,  0.01,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.01,\n",
       "        0.02,  0.  ,  0.01,  0.  ,  0.  ,  0.03,  1.  ,  0.48,  0.  ,\n",
       "        0.  ,  0.05,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,\n",
       "        0.01,  0.  ,  0.02,  0.02,  0.8 ,  0.09,  0.01,  0.28,  0.  ,\n",
       "        0.  ,  0.  ,  0.11,  0.03,  0.  ,  0.  ,  0.2 ,  0.26,  0.  ,\n",
       "        0.  ,  0.  ,  0.  ,  0.01,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,\n",
       "        0.  ,  0.  ,  0.  ,  0.01,  0.31,  0.02,  0.  ,  0.  ,  0.  ,\n",
       "        0.  ,  1.  ])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_beta = -100\n",
    "np.exp(_beta*distance_matrix).values.round(2)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specifying a neighborhood, based on shared borders. This can be used to develop a conditional autoregressive (CAR) model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "neighbors = np.array([sp_shp.geometry.touches(v).values for i, v in sp_shp.geometry.iteritems()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Prior distribution on susceptible proportion:\n",
    "\n",
    "$$p_s \\sim \\text{Beta}(2, 100)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  3.12300000e+03,   3.52900000e+03,   1.94100000e+03,\n",
       "          8.50000000e+02,   3.50000000e+02,   1.40000000e+02,\n",
       "          5.20000000e+01,   1.10000000e+01,   3.00000000e+00,\n",
       "          1.00000000e+00]),\n",
       " array([ 0.00024003,  0.01133855,  0.02243708,  0.0335356 ,  0.04463413,\n",
       "         0.05573266,  0.06683118,  0.07792971,  0.08902823,  0.10012676,\n",
       "         0.11122528]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "gIUgSWosBEkSAP8Lh8v32j0o6WkAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3dd7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymc import rbeta\n",
    "plt.hist(rbeta(2, 100, 10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "infected_by_age = I_obs.sum(0).sum(0)\n",
    "infected_dist = infected_by_age/float(infected_by_age.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pymc import MCMC, Matplot\n",
    "from pymc import (Uniform, DiscreteUniform, Beta, Lambda, Binomial, Normal, \n",
    "                  Poisson, NegativeBinomial, observed, negative_binomial_like, poisson_like,\n",
    "                  Lognormal, Exponential, binomial_like, stochastic, potential, \n",
    "                  invlogit, TruncatedNormal, Binomial, Gamma, HalfCauchy, normal_like,\n",
    "                  deterministic, MvNormalCov, Bernoulli, potential, Uninformative, \n",
    "                  Multinomial, rmultinomial, rbinomial, AdaptiveMetropolis,\n",
    "                  Dirichlet, multinomial_like)\n",
    "\n",
    "def measles_model(obs_date, confirmation=True, all_traces=False):\n",
    "    \n",
    "    n_districts, n_periods, n_age_groups = I_obs.shape\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",
    "        # Build variance-covariance matrix with first-order correlation \n",
    "        # 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",
    "        # Age-specific probabilities of confirmation as multivariate normal \n",
    "        # random variables\n",
    "        beta_age = MvNormalCov(\"beta_age\", mu=mu, C=Sigma, \n",
    "                        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, \n",
    "                                observed=True)\n",
    "\n",
    "\n",
    "    '''\n",
    "    Truncate data at observation period\n",
    "    '''\n",
    "    obs_index = all_district_data[0].index <= obs_date\n",
    "    I_obs_t = np.array([I_dist[obs_index] for I_dist in I_obs])  \n",
    "                        \n",
    "\n",
    "    # Index for observation date, used to index out values of interest \n",
    "    # from the model.\n",
    "    t_obs = obs_index.sum() - 1\n",
    "    \n",
    "    ### Chain binomial model for disease dynamics\n",
    "\n",
    "    if confirmation:\n",
    "        \n",
    "        @deterministic(trace=all_traces, dtype=int)\n",
    "        def I_age(n=I_obs_t, p=p_age):\n",
    "            # Binomial confirmation process: confirm by age\n",
    "            return np.array([[rbinomial(n_period, p) for n_period in n_dist] for n_dist in n])\n",
    "        \n",
    "        # Aggregate by age\n",
    "        I = Lambda('I_age', lambda I=I_age: I.sum(2))\n",
    "        \n",
    "    else:\n",
    "        \n",
    "        # No confirmation\n",
    "        I_age = I_obs_t\n",
    "        I = I_age.sum(2)\n",
    "    \n",
    "    # Estimage age distribution from observed distribution of infecteds to date\n",
    "    age_dist = Dirichlet('age_dist', np.ones(n_age_groups))\n",
    "    @potential\n",
    "    def I_age_like(x=I_age, p=age_dist):\n",
    "        return multinomial_like(np.sum(x, (0,1)), n=x.sum(), p=np.append(p, 1-p.sum()))\n",
    "\n",
    "    # Weakly-informative prior on proportion susceptible being \n",
    "    # between 0 and 0.07\n",
    "    p_susceptible = Beta('p_susceptible', 2, 100, size=n_districts)\n",
    "    \n",
    "    # Estimated total susceptibles by district\n",
    "    S_0 = Binomial('S_0', n=N.values.astype(int), p=p_susceptible)\n",
    "\n",
    "    @deterministic(trace=all_traces)\n",
    "    def S(I=I, S_0=S_0):\n",
    "        # Calculate susceptibles from total number of infections\n",
    "        return np.array([S_0[d] - I[d].cumsum() for d in range(n_districts)])\n",
    "    \n",
    "    # Susceptibles at time t, by age\n",
    "    @deterministic\n",
    "    def S_age(S=S, p=age_dist):\n",
    "        return np.array([rmultinomial(S_dist[-1], np.append(p, 1-p.sum())) for S_dist in S]) \n",
    "    \n",
    "    # Transmission parameter\n",
    "    β = Gamma('β', 1, 0.1, value=0.001) \n",
    "    \n",
    "    θ = Exponential('θ', 1, value=1)\n",
    "    @deterministic\n",
    "    def Iw(I=I, θ=θ): \n",
    "        # Distance-weighted infecteds\n",
    "        return np.transpose([np.exp(-θ*distance_matrix.values).dot(It) for It in I.T])\n",
    "    \n",
    "    α = Exponential('α', 1, value=1)\n",
    "    \n",
    "    # Force of infection\n",
    "    @deterministic\n",
    "    def λ(β=β, I=Iw, S=S, α=α): \n",
    "        return np.array([β*(I_d[:-1]**α)*S_d[:-1] for I_d, S_d in zip(I,S)])\n",
    "    \n",
    "    # FOI in observation period\n",
    "    λ_t = Lambda('λ_t', lambda λ=λ: λ[:, -1])\n",
    "    \n",
    "    # Poisson likelihood for observed cases\n",
    "    @potential\n",
    "    def new_cases(I=I, λ=λ): \n",
    "        return poisson_like(I[:,1:], λ)\n",
    "    \n",
    "    \n",
    "    '''\n",
    "    Vaccination targets\n",
    "    '''\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.sum(0), p)\n",
    "    \n",
    "    # Proportion of susceptibles vaccinated\n",
    "    pct_5 = Lambda('pct_5', \n",
    "                lambda V=vacc_5, S=S_age: float(V.sum())/S.sum())\n",
    "\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.sum(0), p)\n",
    "    \n",
    "    # Proportion of susceptibles vaccinated\n",
    "    pct_15 = Lambda('pct_15', \n",
    "            lambda V=vacc_15, S=S_age: float(V.sum())/S.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.sum(0), p)\n",
    "    \n",
    "    # Proportion of 30 and under susceptibles vaccinated\n",
    "    pct_30 = Lambda('pct_30', \n",
    "            lambda V=vacc_30, S=S_age: float(V.sum())/S.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.sum(0), p)\n",
    "    \n",
    "    # Proportion of adults under 30 (and young kids)\n",
    "    pct_adult = Lambda('pct_adult', \n",
    "            lambda V=vacc_adult, S=S_age: float(V.sum())/S.sum())\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": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "db = 'ram'\n",
    "n_iterations = 50000\n",
    "n_burn = 40000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "June 15, with lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = measles_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_june = MCMC(model('1997-06-15'), db=db, dbname='model_june')\n",
    "# model_june.use_step_method(AdaptiveMetropolis, model_june.S_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 2186.6 sec"
     ]
    }
   ],
   "source": [
    "model_june.sample(n_iterations, n_burn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 3026.9 sec"
     ]
    }
   ],
   "source": [
    "model_june.sample(n_iterations, n_burn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "July 15, with lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_july = MCMC(model('1997-07-15'), db=db, dbname='model_july')\n",
    "# model_july.use_step_method(AdaptiveMetropolis, model_july.S_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 2498.9 sec"
     ]
    }
   ],
   "source": [
    "model_july.sample(n_iterations, n_burn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "June 15, no lab confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_june_noconf = MCMC(model('1997-06-15', \n",
    "                                       confirmation=False), \n",
    "                         db=db, dbname='model_june_noconf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 231.9 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": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_july_noconf = MCMC(model('1997-07-15', \n",
    "                                       confirmation=False), \n",
    "                         db=db, dbname='model_july_noconf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 50000 of 50000 complete in 258.5 sec"
     ]
    }
   ],
   "source": [
    "model_july_noconf.sample(50000, 40000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary of model output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting β\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ab473860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.plot(model_june.β)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lab confirmation rates, June model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10eca3a90>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "+/8fo8jSTslFDQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea18898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sb\n",
    "\n",
    "p_age = pd.DataFrame(model_june.p_age.trace(), columns=age_groups)\n",
    "\n",
    "f, axes = plt.subplots(figsize=(14,6))\n",
    "sb.boxplot(data=p_age, linewidth=0.3, fliersize=0, ax=axes,\n",
    "          color=sb.color_palette(\"coolwarm\", 5)[0])\n",
    "axes.set_ylabel('Confirmation rate')\n",
    "axes.set_xlabel('Age group')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proportion of population susceptible, June model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "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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       "RU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bc8fb208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.summary_plot(model_june.p_susceptible)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proportion of population susceptible, June model with no confirmation correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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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       "TkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111ab0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.summary_plot(model_june_noconf.p_susceptible)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "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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       "KZ/bwc8Z/++d5eL8bNuKxXXGiur+/f14yTD8apVkL8lZVZ1nTMU96u7XZWPxB2YFbLjuvqmqg6p6\n",
       "yNi6Oulu321zXSa5qqrbjFs8q+5+WTjTt8wKAQCm2bYzFgDAP1IsAIBpFAsAYBrFAgCYRrEAAKZR\n",
       "LACAaRQLAGCaN3LNWOGCI3NUAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110fef048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.summary_plot(model_june.λ_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "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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       "fAscq1xPlzYDb0v6F/iVmfu4UewEbgd2SXqNMhV5K6XnaPkO6vVFYH/QfI9Tzk2nKZ9DW4DvgImA\n",
       "2c7udSvlFz8Hg2abs0JSSiml1J5RuxWSUkoppQ7lwiKllFJKrcmFRUoppZRakwuLlFJKKbUmFxYp\n",
       "pZRSak0uLFJKKaXUmlxYpJRSSqk11wC1kkCI+0ctkgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111272e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.summary_plot(model_july.λ_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Epidemic intensity for lab- versus clinical-confirmation models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a86c4c18>"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "TkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a8663a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam_june = model_june.λ.stats()\n",
    "\n",
    "fig, axes = plt.subplots(2, 1, sharey=True)\n",
    "\n",
    "axes[0].plot(lam_june['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "axes[0].set_ylabel('Epidemic intensity')\n",
    "axes[0].set_xlabel('time (2-week periods)')\n",
    "axes[0].set_title('Lab confirmation')\n",
    "\n",
    "lam_june_noconf = model_june_noconf.λ.stats()\n",
    "\n",
    "axes[1].plot(lam_june_noconf['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "axes[1].set_ylabel('Epidemic intensity')\n",
    "axes[1].set_xlabel('time (2-week periods)')\n",
    "axes[1].set_title('Clinical confirmation')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S_age_june = pd.DataFrame(model_june.S_age.trace()[:, -1], columns=age_groups).unstack().reset_index()\n",
    "S_age_june.columns = 'Age', 'Iteration', 'S'\n",
    "S_age_june['Confirmation'] = 'Lab'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S_age_june = pd.DataFrame(model_june.S_age.trace()[:, -1], columns=age_groups).unstack().reset_index()\n",
    "S_age_june.columns = 'Age', 'Iteration', 'S'\n",
    "S_age_june['Confirmation'] = 'Lab'\n",
    "\n",
    "S_age_june_noconf = pd.DataFrame(model_june_noconf.S_age.trace()[:, -1], columns=age_groups).unstack().reset_index()\n",
    "S_age_june_noconf.columns = 'Age', 'Iteration', 'S'\n",
    "S_age_june_noconf['Confirmation'] = 'Clinical'\n",
    "\n",
    "S_age_june = pd.concat([S_age_june, S_age_june_noconf], ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S_age_july = pd.DataFrame(model_july.S_age.trace()[:, -1], columns=age_groups).unstack().reset_index()\n",
    "S_age_july.columns = 'Age', 'Iteration', 'S'\n",
    "S_age_july['Confirmation'] = 'Lab'\n",
    "\n",
    "S_age_july_noconf = pd.DataFrame(model_july_noconf.S_age.trace()[:, -1], columns=age_groups).unstack().reset_index()\n",
    "S_age_july_noconf.columns = 'Age', 'Iteration', 'S'\n",
    "S_age_july_noconf['Confirmation'] = 'Clinical'\n",
    "\n",
    "S_age_july = pd.concat([S_age_july, S_age_july_noconf], ignore_index=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numbers of suscepibles in each age group, under lab vs clinical confirmation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "72uRJKlv/ASNJGkluQp8mGSM7n3Qw30LqI3/EEuSdAeOpEqSJEmSesN3UiVJkiRJvWFIlSRJkiT1\n",
       "hiFVkiRJktQbhlRJkiRJUm8YUiVJkiRJvWFIlSRJkiT1xr9QmdKdO8FaGAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111d067f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sb\n",
    "sb.set_context(\"talk\", font_scale=0.8)\n",
    "sb.set_style(\"white\")\n",
    "\n",
    "g = sb.factorplot(\"Age\", \"S\", \"Confirmation\", S_age_june, kind=\"box\",\n",
    "                   palette=\"hls\", size=6, aspect=2, linewidth=0.3, fliersize=0, \n",
    "                  order=np.sort(S_age_june.Age.unique()))\n",
    "g.despine(offset=10, trim=True)\n",
    "g.set_axis_labels(\"Age Group\", \"Susceptibles\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_lam = pd.DataFrame(model_june.λ_t.trace()).unstack().reset_index()\n",
    "june_lam.columns = ('district', 'iteration', 'λ')\n",
    "june_lam['month'] = 'June'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_lam_noconf = pd.DataFrame(model_june_noconf.λ_t.trace()).unstack().reset_index()\n",
    "june_lam_noconf.columns = ('district', 'iteration', 'λ')\n",
    "june_lam_noconf['month'] = 'June'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "july_lam = pd.DataFrame(model_july.λ_t.trace()).unstack().reset_index()\n",
    "july_lam.columns = ('district', 'iteration', 'λ')\n",
    "july_lam['month'] = 'July'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_july.S.value.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "july_lam_noconf = pd.DataFrame(model_july_noconf.λ_t.trace()).unstack().reset_index()\n",
    "july_lam_noconf.columns = ('district', 'iteration', 'λ')\n",
    "july_lam_noconf['month'] = 'July'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "confirmed_lam = june_lam.append(july_lam, ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "june_means = june_lam.groupby('district')['λ'].mean()\n",
    "june_means.sort(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "july_means = july_lam.groupby('district')['λ'].mean()\n",
    "july_means.sort(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sorted_districts = june_means.index.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$R_{eff}$ by district in June and July (with lab confirmation), sorted by June means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "SUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a878e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.set_context(\"talk\", font_scale=0.8)\n",
    "\n",
    "f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)\n",
    "\n",
    "sb.boxplot('district', 'λ', data=june_lam, 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_title(r'Epidemic intensity (λ) estimates, ordered by June means')\n",
    "\n",
    "sb.boxplot('district', 'λ', data=july_lam, 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": "markdown",
   "metadata": {},
   "source": [
    "$R_{eff}$ by district in June for lab-confirmed and clinical-confirmed, sorted by lab-confirmed means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "kiRJkjSIAUuSJEmSBjFgSZIkSdIgBixJkiRJGuQXW71nuzF8DDoAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a878e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)\n",
    "\n",
    "sb.boxplot('district', 'λ', data=june_lam, ax=ax_1, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=june_means.index.values)\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_title(r'June epidemic intensity (λ) estimates, ordered by lab-confirmed means')\n",
    "\n",
    "sb.boxplot('district', 'λ', data=june_lam_noconf, ax=ax_2, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=june_means.index.values)\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": "markdown",
   "metadata": {},
   "source": [
    "$R_{eff}$ by district in July for lab-confirmed and clinical-confirmed, sorted by lab-confirmed means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "july_means = july_lam.groupby('district')['λ'].mean()\n",
    "july_means.sort(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "OUm95isJgwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1df28b518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax_1, ax_2) = plt.subplots(2, 1, figsize=(12,6), sharey=True, sharex=True)\n",
    "\n",
    "sb.boxplot('district', 'λ', data=july_lam, ax=ax_1, linewidth=0.5, \n",
    "           fliersize=0, color='r', order=july_means.index.values)\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'July epidemic intensity (λ) estimates, ordered by lab-confirmed means')\n",
    "\n",
    "sb.boxplot('district', 'λ', data=july_lam_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": 153,
   "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",
      "\t0.27             0.001            0.0              [ 0.268  0.273]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.268            0.27            0.27           0.271         0.273\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.474            0.001            0.0              [ 0.471  0.476]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.471            0.473           0.474          0.475         0.476\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.696            0.001            0.0              [ 0.693  0.698]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.693            0.695           0.696          0.696         0.698\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.419            0.001            0.0              [ 0.416  0.421]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.416            0.418           0.419          0.419         0.421\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_june.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "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']})\n",
    "june_coverage['Month'] = 'June'\n",
    "june_coverage['Confirmation'] = 'Lab'\n",
    "\n",
    "june_noconf_coverage = pd.DataFrame({name: model_june_noconf.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})\n",
    "june_noconf_coverage['Month'] = 'June'\n",
    "june_noconf_coverage['Confirmation'] = 'Clinical'\n",
    "\n",
    "july_coverage = pd.DataFrame({name: model_july.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})\n",
    "july_coverage['Month'] = 'July'\n",
    "july_coverage['Confirmation'] = 'Lab'\n",
    "\n",
    "july_noconf_coverage = pd.DataFrame({name: model_july_noconf.trace(name)[:] for name in ['pct_5', 'pct_15', 'pct_30', 'pct_adult']})\n",
    "july_noconf_coverage['Month'] = 'July'\n",
    "july_noconf_coverage['Confirmation'] = 'Clinical'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "coverage = pd.concat([june_coverage, june_noconf_coverage, july_coverage, july_noconf_coverage], \n",
    "                     ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1c0c58438>"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c0c6c400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.factorplot(row=\"Month\", col=\"Confirmation\", data=coverage, kind='box',\n",
    "              row_order=['June', 'July'],\n",
    "              order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'],\n",
    "               palette=\"YlGnBu_d\", linewidth=0.7, fliersize=0, aspect=1.25).despine(left=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1ad8f2d30>"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "xtlajrO1ec7Wijp2kC8HiIhFwHLS4bv+PG0gIraQDgt0T9POuxFxTb69Ejg01cwLTKkaTqQHGI2I\n",
       "xfn+ChZ2bYvUMiKG8webIO2Z/wOMAmdFxOn5n+PNwJ62rMXsKrX9vUwaTVtFOrewC/gKWBYRJ+V5\n",
       "+vPvP4BTIqI7Ik4ALpqgvSPUM1OrnK+tcbaW42xtnrO1oo5hviQi3gH2ARuBVcCDEbGHdChgK/AN\n",
       "sDQi1k/RzmpgQ0S8Tzov54H2LnZHKVXDBpJ+AdYBuyNihLTnua3gsneaUrV8EtiWt8dnSIe3/iYd\n",
       "JhsmnW/4raS327cqs6ZUzV4kbWd7gfOBMyX9DKwH9uXnOB4gj7oNkzoUrwBfT9DePmBXRBxXYB3n\n",
       "K+dra5yt5Thbm+dsrajjh/R6xz+wYM1zDctxLZvnmnUuvzatcf3KcS2b55o18vcgTyEi+oCnaTyB\n",
       "/FNJD8/BIs07rmE5rmXzXLPO5demNa5fOa5l8+pQs1qNIJuZmZmZTaeO5yCbmZmZmU3KHWQzMzMz\n",
       "swp3kM3MzMzMKtxBNjMzMzOrcAfZzMzMzKzCHWQzMzMzs4r/ABPkIp6VyQm4AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ab416828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.factorplot(row=\"Month\", col=\"Confirmation\", data=coverage, kind='box',\n",
    "              row_order=['June', 'July'],\n",
    "              order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'],\n",
    "               palette=\"YlGnBu_d\", linewidth=0.7, fliersize=0, aspect=1.25).despine(left=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "GBAlSZJU8v8Bav3GEECno3cAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18951c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = sb.boxplot(data=june_coverage, order=['pct_5', 'pct_15', 'pct_30', 'pct_adult'], \n",
    "                  color=sb.color_palette(\"coolwarm\", 5)[0])\n",
    "axes.set_xticklabels(['Under 5', 'Under 15', 'Under 30', 'Under 5 + 20-30'])\n",
    "axes.set_ylabel('% susceptibles vaccinated')\n",
    "sb.despine(offset=10, trim=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "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",
      "\t0.231            0.003            0.0              [ 0.225  0.236]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.225            0.229           0.231          0.233         0.236\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.596            0.006            0.001            [ 0.588  0.609]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.589            0.592           0.595          0.598         0.61\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.787            0.005            0.0              [ 0.776  0.796]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.775            0.785           0.788          0.791         0.796\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.313            0.004            0.0              [ 0.306  0.322]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.306            0.31            0.312          0.315         0.322\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_june_noconf.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "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",
      "\t0.056            0.001            0.0              [ 0.055  0.057]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.055            0.055           0.056          0.056         0.057\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.389            0.001            0.0              [ 0.386  0.392]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.386            0.388           0.389          0.39          0.392\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.643            0.001            0.0              [ 0.64   0.646]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.64             0.642           0.643          0.644         0.646\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.158            0.001            0.0              [ 0.155  0.16 ]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.156            0.157           0.158          0.158         0.16\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_july.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "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",
      "\t0.009            0.0              0.0              [ 0.008  0.009]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.008            0.009           0.009          0.009         0.009\n",
      "\t\n",
      "\n",
      "pct_15:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.468            0.005            0.0              [ 0.458  0.477]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.458            0.465           0.469          0.472         0.477\n",
      "\t\n",
      "\n",
      "pct_30:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.768            0.005            0.0              [ 0.761  0.778]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.76             0.764           0.767          0.771         0.778\n",
      "\t\n",
      "\n",
      "pct_adult:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.154            0.004            0.0              [ 0.146  0.16 ]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.146            0.151           0.154          0.156         0.161\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "model_july_noconf.summary(['pct_5', 'pct_15', 'pct_30', 'pct_adult'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lam_july = model_july.λ.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1b5eb8d30>"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "oKdSqVQqlUo1S6Wgp1KpVCqVSjVL9f8B64HvN6wl7ysAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b58d6f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lam_july['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "plt.ylabel('λ')\n",
    "plt.xlabel('time (2-week periods)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lam_june_noconf = model_june_noconf.λ.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1bf9372e8>"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "ISEhISEhIWGNIhG9hISEhISEhIQ1iv8PFDRQeDwfFxsAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bf92a2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lam_june_noconf['quantiles'][50].T, 'b-', alpha=0.4)\n",
    "plt.ylabel('λ')\n",
    "plt.xlabel('time (2-week periods)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Mapping spatial effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "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": 174,
   "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": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SP_dist['DIST_NAME'] = [trans.trans(_).upper() for _ in SP_dist.NAME_3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "λ_june = pd.Series(model_june.λ_t.stats()['mean'], index=sp_districts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BRAS                 0.062417\n",
       "BARRA FUNDA          0.324059\n",
       "FREGUESIA DO O       2.107492\n",
       "CAMBUCI              0.603248\n",
       "PENHA                0.743912\n",
       "BRAZILANDIA          2.696296\n",
       "SANTA CECILIA        0.211299\n",
       "CASA VERDE           1.952935\n",
       "CAPAO REDONDO        9.130688\n",
       "CONSOLACAO           0.544182\n",
       "JAGUARE              2.080369\n",
       "CIDADE ADEMAR        2.306163\n",
       "CIDADE TIRADENTES    1.738719\n",
       "SAPOPEMBA            0.653725\n",
       "MOOCA                0.920267\n",
       "CANGAIBA             3.490634\n",
       "SAUDE                2.662397\n",
       "SANTANA              2.445026\n",
       "JARDIM ANGELA        7.469341\n",
       "CAMPO LIMPO          8.008153\n",
       "VILA MARIANA         4.988978\n",
       "VILA CURUCA          1.266134\n",
       "CIDADE DUTRA         6.302569\n",
       "ARTUR ALVIM          2.081722\n",
       "JARDIM HELENA        0.898627\n",
       "SE                   0.967562\n",
       "LAPA                 0.608799\n",
       "JARDIM PAULISTA      2.341109\n",
       "JABAQUARA            3.355646\n",
       "PINHEIROS            3.130386\n",
       "                       ...   \n",
       "BUTANTA              1.113759\n",
       "SAO RAFAEL           1.206678\n",
       "MORUMBI              0.328959\n",
       "AGUA RASA            0.955486\n",
       "MOEMA                0.250341\n",
       "VILA ANDRADE         0.938559\n",
       "ANHANGUERA           0.039575\n",
       "VILA MARIA           2.183739\n",
       "IPIRANGA             1.990685\n",
       "SOCORRO              0.601724\n",
       "CACHOEIRINHA         2.390857\n",
       "ARICANDUVA           0.921606\n",
       "CAMPO GRANDE         2.948286\n",
       "MANDAQUI             0.338616\n",
       "ITAQUERA             2.483490\n",
       "SAO MIGUEL           1.003908\n",
       "JAGUARA              0.172167\n",
       "PARQUE DO CARMO      0.839247\n",
       "JACANA               0.603664\n",
       "CIDADE LIDER         1.134638\n",
       "CAMPO BELO           1.602751\n",
       "VILA JACUI           1.204909\n",
       "ITAIM BIBI           0.461258\n",
       "VILA GUILHERME       1.354458\n",
       "CURSINO              1.673891\n",
       "MARSILAC             0.068277\n",
       "GUAIANASES           1.118360\n",
       "VILA MATILDE         1.210700\n",
       "PONTE RASA           1.042228\n",
       "PARI                 1.261043\n",
       "dtype: float64"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ_june"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SP_dist_merged = SP_dist.merge(pd.DataFrame(λ_june, columns=['λ']), left_on='DIST_NAME', right_index=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Map of outbreak intensity by district"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1fc140ba8>"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "7tzB9evXq9/J+9n/Fl/0zW8uGVPXRVe9AUT91NEJIYQQQghpOIvExMSb/32wrjOs9wBYAMgAUMmv\n",
       "VIQQQgghROxJANDEp/75lVrPsBJCCCGEECIMaJUAQgghhBAi1KiwEkIIIYQQoUaFlRBCCCGECDUq\n",
       "rIQQQgghRKj9H/LWbEpA/KpBAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fc140128>"
      ]
     },
     "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='λ', colormap=cm.Reds, axes=map_ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "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": 180,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DISTRICT\n",
       "AGUA RASA             37\n",
       "ALTO PINHEIROS        19\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",
       "BRAS                  33\n",
       "BRAZILANDIA          186\n",
       "BUTANTA               86\n",
       "C REDONDO              1\n",
       "CACHOEIRINHA         132\n",
       "CAJAMAR                1\n",
       "CAMBUCI               26\n",
       "CAMPINAS               1\n",
       "CAMPO BELO            19\n",
       "CAMPO GRANDE          30\n",
       "CAMPO LIMPO          279\n",
       "CANGAIBA              65\n",
       "CAPAO REDONDO        342\n",
       "CAPELA DO SOCOR        1\n",
       "CAPELA SOCORRO         1\n",
       "CARRAO                34\n",
       "CASA VERDE            50\n",
       "CERQUEIRA CESAR        1\n",
       "CIDADE ADEMAR        134\n",
       "CIDADE DUTRA         104\n",
       "CIDADE LIDER          53\n",
       "                    ... \n",
       "TATUAPE               36\n",
       "TREMEMBE             117\n",
       "TUCURUVI              54\n",
       "VILA ANDRADE         107\n",
       "VILA CACHOEIRINHA      1\n",
       "VILA CURUCA           97\n",
       "VILA DALVILAA          1\n",
       "VILA FORMOSA          32\n",
       "VILA GUILHERME        24\n",
       "VILA JACUI            48\n",
       "VILA LEOPOLDINA       34\n",
       "VILA MARIA            88\n",
       "VILA MARIANA          78\n",
       "VILA MATILDE          35\n",
       "VILA MEDEIROS         45\n",
       "VILA PRUDENTE         72\n",
       "VILA SONIA           120\n",
       "VILA. FORMOSA          1\n",
       "VILA. PRUDENTE         2\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",
       "dtype: float64"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measles_onset_conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "_rates = measles_onset_conf/sp_pop.sum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "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": "markdown",
   "metadata": {},
   "source": [
    "For comparison, map of empirical incidence by district"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1fbc30eb8>"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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