.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_covid_estimation.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_covid_estimation.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_covid_estimation.py:


.. _l-estim-sird-theory:

Estimation des paramètres d'un modèle SIRD
==========================================

On part d'un modèle :class:`CovidSIRD <aftercovid.models.CovidSIRD>`
qu'on utilise pour simuler des données. On regarde s'il est possible
de réestimer les paramètres du modèle à partir des observations.

.. contents::
    :local:

Simulation des données
++++++++++++++++++++++

.. GENERATED FROM PYTHON SOURCE LINES 18-30

.. code-block:: default


    import warnings
    from pprint import pprint
    import numpy
    import matplotlib.pyplot as plt
    import pandas
    from aftercovid.models import EpidemicRegressor, CovidSIRD

    model = CovidSIRD()
    model







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p><b>CovidSIRD</b></p>

    <p><i>Quantities</i></p>

    <ul>
    <li><i>S</i>: personnes non contaminées</li>
    <li><i>I</i>: nombre de personnes malades ou contaminantes</li>
    <li><i>R</i>: personnes guéries (recovered)</li>
    <li><i>D</i>: personnes décédées</li>
    </ul>

    <p><i>Constants</i></p>

    <ul>
    <li><i>N</i>: population</li>
    </ul>

    <p><i>Parameters</i></p>

    <ul>
    <li><i>beta</i>: taux de transmission dans la population</li>
    <li><i>mu</i>: 1/. : durée moyenne jusque la guérison</li>
    <li><i>nu</i>: 1/. : durée moyenne jusqu'au décès</li>
    </ul>

    <p><i>Equations</i></p>

    <ul>
    <li>\begin{equation}\mathtt{\text{\textbackslashfrac\{dD\}\{dt\} = I \textbackslashnu}}\end{equation}</li>
    <li>\begin{equation}\mathtt{\text{\textbackslashfrac\{dI\}\{dt\} = - I \textbackslashmu - I \textbackslashnu + \textbackslashfrac\{I S \textbackslashbeta\}\{N\}}}\end{equation}</li>
    <li>\begin{equation}\mathtt{\text{\textbackslashfrac\{dR\}\{dt\} = I \textbackslashmu}}\end{equation}</li>
    <li>\begin{equation}\mathtt{\text{\textbackslashfrac\{dS\}\{dt\} = - \textbackslashfrac\{I S \textbackslashbeta\}\{N\}}}\end{equation}</li>
    </ul>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 31-32

Mise à jour des coefficients.

.. GENERATED FROM PYTHON SOURCE LINES 32-38

.. code-block:: default


    model['beta'] = 0.4
    model["mu"] = 0.06
    model["nu"] = 0.04
    pprint(model.P)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [('beta', 0.4, 'taux de transmission dans la population'),
     ('mu', 0.06, '1/. : durée moyenne jusque la guérison'),
     ('nu', 0.04, "1/. : durée moyenne jusqu'au décès")]




.. GENERATED FROM PYTHON SOURCE LINES 39-40

Point de départ

.. GENERATED FROM PYTHON SOURCE LINES 40-43

.. code-block:: default

    pprint(model.Q)






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [('S', 9990.0, 'personnes non contaminées'),
     ('I', 10.0, 'nombre de personnes malades ou contaminantes'),
     ('R', 0.0, 'personnes guéries (recovered)'),
     ('D', 0.0, 'personnes décédées')]




.. GENERATED FROM PYTHON SOURCE LINES 44-45

Simulation

.. GENERATED FROM PYTHON SOURCE LINES 45-52

.. code-block:: default


    X, y = model.iterate2array(50, derivatives=True)
    data = {_[0]: x for _, x in zip(model.Q, X.T)}
    data.update({('d' + _[0]): c for _, c in zip(model.Q, y.T)})
    df = pandas.DataFrame(data)
    df.tail()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>S</th>
          <th>I</th>
          <th>R</th>
          <th>D</th>
          <th>dS</th>
          <th>dI</th>
          <th>dR</th>
          <th>dD</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>45</th>
          <td>306.649109</td>
          <td>1543.747681</td>
          <td>4889.761719</td>
          <td>3259.841309</td>
          <td>-18.935555</td>
          <td>-135.439209</td>
          <td>92.624863</td>
          <td>61.749905</td>
        </tr>
        <tr>
          <th>46</th>
          <td>287.713562</td>
          <td>1408.308472</td>
          <td>4982.386719</td>
          <td>3321.591309</td>
          <td>-16.207579</td>
          <td>-124.623268</td>
          <td>84.498505</td>
          <td>56.332336</td>
        </tr>
        <tr>
          <th>47</th>
          <td>271.505981</td>
          <td>1283.685181</td>
          <td>5066.885254</td>
          <td>3377.923584</td>
          <td>-13.941129</td>
          <td>-114.427391</td>
          <td>77.021111</td>
          <td>51.347408</td>
        </tr>
        <tr>
          <th>48</th>
          <td>257.564850</td>
          <td>1169.257812</td>
          <td>5143.906250</td>
          <td>3429.270996</td>
          <td>-12.046389</td>
          <td>-104.879387</td>
          <td>70.155464</td>
          <td>46.770313</td>
        </tr>
        <tr>
          <th>49</th>
          <td>245.518478</td>
          <td>1064.378418</td>
          <td>5214.062012</td>
          <td>3476.041260</td>
          <td>-10.452982</td>
          <td>-95.984856</td>
          <td>63.862705</td>
          <td>42.575134</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 53-54

Visualisation

.. GENERATED FROM PYTHON SOURCE LINES 54-58

.. code-block:: default


    df.plot(title="Simulation SIRD")





.. image-sg:: /auto_examples/images/sphx_glr_plot_covid_estimation_001.png
   :alt: Simulation SIRD
   :srcset: /auto_examples/images/sphx_glr_plot_covid_estimation_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 59-65

Estimation
++++++++++

Le module implémente la class :class:`EpidemicRegressor
<aftercovid.models.EpidemicRegressor>` qui réplique
l'API de :epkg:`scikit-learn`.

.. GENERATED FROM PYTHON SOURCE LINES 65-73

.. code-block:: default



    m = EpidemicRegressor('SIRD', verbose=True, learning_rate_init=1e-3,
                          max_iter=10, early_th=1)
    m.fit(X, y)
    pprint(m.model_.P)






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    0/10: loss: 1.897e+07 lr=1e-09
    1/10: loss: 4.662e+04 lr=1e-09
    2/10: loss: 2720 lr=1e-09
    3/10: loss: 74.86 lr=1e-09
    4/10: loss: 1.046 lr=1e-09
    5/10: loss: 0.1211 lr=1e-09
    6/10: loss: 0.0005634 lr=1e-09
    7/10: loss: 1.639e-05 lr=1e-09
    8/10: loss: 5.455e-06 lr=1e-09
    9/10: loss: 2.392e-07 lr=1e-09
    9/10: loss: 2.392e-07 lr=1e-09 losses: [0.12111801038239137, 0.0005633756116252936, 1.6390378310729972e-05, 5.45491596350498e-06, 2.3921170805405355e-07]
    [('beta', 0.40000004594317967, 'taux de transmission dans la population'),
     ('mu', 0.06000001116898102, '1/. : durée moyenne jusque la guérison'),
     ('nu', 0.04000001126358509, "1/. : durée moyenne jusqu'au décès")]




.. GENERATED FROM PYTHON SOURCE LINES 74-79

La réaction de la population n'est pas constante
tout au long de l'épidémie. Il est possible qu'elle
change de comportement tout au long de la propagation.
On estime alors les coefficients du modèle sur une
fenêtre glissante.

.. GENERATED FROM PYTHON SOURCE LINES 79-102

.. code-block:: default



    def find_best_model(Xt, yt, lrs, th):
        best_est, best_loss = None, None
        for lr in lrs:
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", RuntimeWarning)
                m = EpidemicRegressor(
                    'SIRD',
                    learning_rate_init=lr,
                    max_iter=500,
                    early_th=1)
                m.fit(Xt, yt)
                loss = m.score(Xt, yt)
                if numpy.isnan(loss):
                    continue
            if best_est is None or best_loss > loss:
                best_est = m
                best_loss = loss
            if best_loss < th:
                return best_est, best_loss
        return best_est, best_loss








.. GENERATED FROM PYTHON SOURCE LINES 103-105

On estime les coefficients du modèle tous les 2 jours
sur les 10 derniers jours.

.. GENERATED FROM PYTHON SOURCE LINES 105-118

.. code-block:: default



    coefs = []
    for k in range(0, X.shape[0] - 9, 2):
        end = min(k + 10, X.shape[0])
        Xt, yt = X[k:end], y[k:end]
        m, loss = find_best_model(Xt, yt, [1e-2, 1e-3], 10)
        loss = m.score(Xt, yt)
        print(f"k={k} iter={m.iter_} loss={loss:1.3f} coef={m.model_._val_p}")
        obs = dict(k=k, loss=loss, it=m.iter_, R0=m.model_.R0())
        obs.update({k: v for k, v in zip(m.model_.param_names, m.model_._val_p)})
        coefs.append(obs)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    k=0 iter=357 loss=2.239 coef=[0.42057372 0.05974595 0.06041957]
    k=2 iter=115 loss=0.681 coef=[0.40770366 0.06206369 0.04530839]
    k=4 iter=69 loss=0.195 coef=[0.40257024 0.06134319 0.04109677]
    k=6 iter=51 loss=0.048 coef=[0.40066258 0.06065819 0.03994949]
    k=8 iter=15 loss=0.003 coef=[0.40007427 0.06004131 0.04009177]
    k=10 iter=18 loss=0.000 coef=[0.4000037  0.05998615 0.03999451]
    k=12 iter=16 loss=0.004 coef=[0.40001642 0.05996604 0.03999531]
    k=14 iter=17 loss=0.001 coef=[0.39998623 0.06000873 0.04000317]
    k=16 iter=21 loss=0.003 coef=[0.4000189  0.05999387 0.03999535]
    k=18 iter=23 loss=0.004 coef=[0.39999899 0.05999656 0.04001737]
    k=20 iter=22 loss=0.004 coef=[0.39998931 0.05998449 0.04001077]
    k=22 iter=12 loss=4.303 coef=[0.40006285 0.05980054 0.03974741]
    k=24 iter=18 loss=0.003 coef=[0.40000538 0.06000393 0.04000789]
    k=26 iter=21 loss=0.008 coef=[0.4000625  0.06000895 0.04001048]
    k=28 iter=19 loss=0.013 coef=[0.40000717 0.05998938 0.03998689]
    k=30 iter=28 loss=0.004 coef=[0.40001303 0.06000733 0.04000734]
    k=32 iter=20 loss=0.005 coef=[0.40001409 0.06001034 0.04000935]
    k=34 iter=41 loss=0.028 coef=[0.4006094  0.06000335 0.04000336]
    k=36 iter=57 loss=0.537 coef=[0.39626394 0.06000206 0.04000206]
    k=38 iter=117 loss=3.544 coef=[0.41466743 0.06041745 0.04041745]
    k=40 iter=61 loss=13.908 coef=[0.4478056  0.06034639 0.04034639]




.. GENERATED FROM PYTHON SOURCE LINES 119-120

Résumé

.. GENERATED FROM PYTHON SOURCE LINES 120-124

.. code-block:: default


    dfcoef = pandas.DataFrame(coefs).set_index('k')
    dfcoef






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>loss</th>
          <th>it</th>
          <th>R0</th>
          <th>beta</th>
          <th>mu</th>
          <th>nu</th>
        </tr>
        <tr>
          <th>k</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>2.239422</td>
          <td>357</td>
          <td>3.499954</td>
          <td>0.420574</td>
          <td>0.059746</td>
          <td>0.060420</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.680529</td>
          <td>115</td>
          <td>3.797111</td>
          <td>0.407704</td>
          <td>0.062064</td>
          <td>0.045308</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.195148</td>
          <td>69</td>
          <td>3.929816</td>
          <td>0.402570</td>
          <td>0.061343</td>
          <td>0.041097</td>
        </tr>
        <tr>
          <th>6</th>
          <td>0.048300</td>
          <td>51</td>
          <td>3.982425</td>
          <td>0.400663</td>
          <td>0.060658</td>
          <td>0.039949</td>
        </tr>
        <tr>
          <th>8</th>
          <td>0.002934</td>
          <td>15</td>
          <td>3.995426</td>
          <td>0.400074</td>
          <td>0.060041</td>
          <td>0.040092</td>
        </tr>
        <tr>
          <th>10</th>
          <td>0.000293</td>
          <td>18</td>
          <td>4.000811</td>
          <td>0.400004</td>
          <td>0.059986</td>
          <td>0.039995</td>
        </tr>
        <tr>
          <th>12</th>
          <td>0.003838</td>
          <td>16</td>
          <td>4.001711</td>
          <td>0.400016</td>
          <td>0.059966</td>
          <td>0.039995</td>
        </tr>
        <tr>
          <th>14</th>
          <td>0.001382</td>
          <td>17</td>
          <td>3.999386</td>
          <td>0.399986</td>
          <td>0.060009</td>
          <td>0.040003</td>
        </tr>
        <tr>
          <th>16</th>
          <td>0.002898</td>
          <td>21</td>
          <td>4.000620</td>
          <td>0.400019</td>
          <td>0.059994</td>
          <td>0.039995</td>
        </tr>
        <tr>
          <th>18</th>
          <td>0.003569</td>
          <td>23</td>
          <td>3.999433</td>
          <td>0.399999</td>
          <td>0.059997</td>
          <td>0.040017</td>
        </tr>
        <tr>
          <th>20</th>
          <td>0.003859</td>
          <td>22</td>
          <td>4.000083</td>
          <td>0.399989</td>
          <td>0.059984</td>
          <td>0.040011</td>
        </tr>
        <tr>
          <th>22</th>
          <td>4.302730</td>
          <td>12</td>
          <td>4.018795</td>
          <td>0.400063</td>
          <td>0.059801</td>
          <td>0.039747</td>
        </tr>
        <tr>
          <th>24</th>
          <td>0.002820</td>
          <td>18</td>
          <td>3.999581</td>
          <td>0.400005</td>
          <td>0.060004</td>
          <td>0.040008</td>
        </tr>
        <tr>
          <th>26</th>
          <td>0.007914</td>
          <td>21</td>
          <td>3.999848</td>
          <td>0.400062</td>
          <td>0.060009</td>
          <td>0.040010</td>
        </tr>
        <tr>
          <th>28</th>
          <td>0.013450</td>
          <td>19</td>
          <td>4.001021</td>
          <td>0.400007</td>
          <td>0.059989</td>
          <td>0.039987</td>
        </tr>
        <tr>
          <th>30</th>
          <td>0.003588</td>
          <td>28</td>
          <td>3.999544</td>
          <td>0.400013</td>
          <td>0.060007</td>
          <td>0.040007</td>
        </tr>
        <tr>
          <th>32</th>
          <td>0.005492</td>
          <td>20</td>
          <td>3.999354</td>
          <td>0.400014</td>
          <td>0.060010</td>
          <td>0.040009</td>
        </tr>
        <tr>
          <th>34</th>
          <td>0.028213</td>
          <td>41</td>
          <td>4.005825</td>
          <td>0.400609</td>
          <td>0.060003</td>
          <td>0.040003</td>
        </tr>
        <tr>
          <th>36</th>
          <td>0.536538</td>
          <td>57</td>
          <td>3.962476</td>
          <td>0.396264</td>
          <td>0.060002</td>
          <td>0.040002</td>
        </tr>
        <tr>
          <th>38</th>
          <td>3.543706</td>
          <td>117</td>
          <td>4.112340</td>
          <td>0.414667</td>
          <td>0.060417</td>
          <td>0.040417</td>
        </tr>
        <tr>
          <th>40</th>
          <td>13.907977</td>
          <td>61</td>
          <td>4.447246</td>
          <td>0.447806</td>
          <td>0.060346</td>
          <td>0.040346</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 125-126

On visualise.

.. GENERATED FROM PYTHON SOURCE LINES 126-138

.. code-block:: default



    with warnings.catch_warnings():
        warnings.simplefilter("ignore", DeprecationWarning)
        fig, ax = plt.subplots(2, 3, figsize=(14, 6))
        dfcoef[["mu", "nu"]].plot(ax=ax[0, 0], logy=True)
        dfcoef[["beta"]].plot(ax=ax[0, 1], logy=True)
        dfcoef[["loss"]].plot(ax=ax[1, 0], logy=True)
        dfcoef[["R0"]].plot(ax=ax[0, 2])
        df.plot(ax=ax[1, 1], logy=True)
        fig.suptitle('Estimation de R0 tout au long de la simulation', fontsize=12)




.. image-sg:: /auto_examples/images/sphx_glr_plot_covid_estimation_002.png
   :alt: Estimation de R0 tout au long de la simulation
   :srcset: /auto_examples/images/sphx_glr_plot_covid_estimation_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 139-142

L'estimation des coefficients est plus compliquée
au début et à la fin de l'expérience. Il faudrait sans
doute changer de stratégie.

.. GENERATED FROM PYTHON SOURCE LINES 144-151

Différentes tailles d'estimation
++++++++++++++++++++++++++++++++

Le paramètre `beta` a été estimé sur une période de 10 jours.
Est-ce que cela change sur une période plus courte ou plus longue ?
Sur des données parfaites (sans bruit), cela ne devrait pas changer
grand chose.

.. GENERATED FROM PYTHON SOURCE LINES 151-168

.. code-block:: default


    coefs = []
    for delay in [4, 5, 6, 7, 8, 9, 10]:
        print('delay', delay)
        for k in range(0, X.shape[0] - delay, 4):
            end = min(k + delay, X.shape[0])
            Xt, yt = X[k:end], y[k:end]
            m, loss = find_best_model(Xt, yt, [1e-3, 1e-4], 10)
            loss = m.score(Xt, yt)
            if k == 0:
                print(f"k={k} iter={m.iter_} loss={loss:1.3f} "
                      f"coef={m.model_._val_p}")
            obs = dict(k=k, loss=loss, it=m.iter_, R0=m.model_.R0(), delay=delay)
            obs.update({k: v for k, v in zip(
                m.model_.param_names, m.model_._val_p)})
            coefs.append(obs)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    delay 4
    k=0 iter=5 loss=32.115 coef=[5.89156835e-01 1.20006673e-04 1.18947234e-04]
    delay 5
    k=0 iter=4 loss=16.496 coef=[0.39504264 0.08779759 0.17077553]
    delay 6
    k=0 iter=5 loss=14.249 coef=[4.40837922e-01 1.05767498e-04 1.05238477e-04]
    delay 7
    k=0 iter=5 loss=15.962 coef=[4.21134510e-01 1.07538389e-04 1.06717846e-04]
    delay 8
    k=0 iter=5 loss=25.134 coef=[4.75745677e-01 1.73788137e-04 1.46194751e-01]
    delay 9
    k=0 iter=500 loss=43.955 coef=[0.50007395 0.13988022 0.11442095]
    delay 10
    k=0 iter=500 loss=39.518 coef=[0.49275428 0.08739554 0.11358189]




.. GENERATED FROM PYTHON SOURCE LINES 169-170

Résumé

.. GENERATED FROM PYTHON SOURCE LINES 170-174

.. code-block:: default


    dfcoef = pandas.DataFrame(coefs)
    dfcoef






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>k</th>
          <th>loss</th>
          <th>it</th>
          <th>R0</th>
          <th>delay</th>
          <th>beta</th>
          <th>mu</th>
          <th>nu</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0</td>
          <td>32.115005</td>
          <td>5</td>
          <td>2465.566861</td>
          <td>4</td>
          <td>0.589157</td>
          <td>0.000120</td>
          <td>0.000119</td>
        </tr>
        <tr>
          <th>1</th>
          <td>4</td>
          <td>17.668781</td>
          <td>4</td>
          <td>3.451088</td>
          <td>4</td>
          <td>0.475600</td>
          <td>0.060345</td>
          <td>0.077467</td>
        </tr>
        <tr>
          <th>2</th>
          <td>8</td>
          <td>244.497803</td>
          <td>500</td>
          <td>10.317793</td>
          <td>4</td>
          <td>0.445306</td>
          <td>0.011301</td>
          <td>0.031858</td>
        </tr>
        <tr>
          <th>3</th>
          <td>12</td>
          <td>2.906889</td>
          <td>383</td>
          <td>3.914762</td>
          <td>4</td>
          <td>0.403306</td>
          <td>0.059440</td>
          <td>0.043582</td>
        </tr>
        <tr>
          <th>4</th>
          <td>16</td>
          <td>0.300177</td>
          <td>87</td>
          <td>3.987971</td>
          <td>4</td>
          <td>0.400577</td>
          <td>0.060186</td>
          <td>0.040260</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>73</th>
          <td>20</td>
          <td>0.000865</td>
          <td>17</td>
          <td>3.999909</td>
          <td>10</td>
          <td>0.399984</td>
          <td>0.060000</td>
          <td>0.039998</td>
        </tr>
        <tr>
          <th>74</th>
          <td>24</td>
          <td>0.001418</td>
          <td>17</td>
          <td>4.000166</td>
          <td>10</td>
          <td>0.400021</td>
          <td>0.060004</td>
          <td>0.039998</td>
        </tr>
        <tr>
          <th>75</th>
          <td>28</td>
          <td>0.036788</td>
          <td>32</td>
          <td>4.001374</td>
          <td>10</td>
          <td>0.400220</td>
          <td>0.060010</td>
          <td>0.040010</td>
        </tr>
        <tr>
          <th>76</th>
          <td>32</td>
          <td>0.691616</td>
          <td>118</td>
          <td>4.017990</td>
          <td>10</td>
          <td>0.402106</td>
          <td>0.060038</td>
          <td>0.040038</td>
        </tr>
        <tr>
          <th>77</th>
          <td>36</td>
          <td>0.309956</td>
          <td>43</td>
          <td>4.026976</td>
          <td>10</td>
          <td>0.403149</td>
          <td>0.060123</td>
          <td>0.039989</td>
        </tr>
      </tbody>
    </table>
    <p>78 rows × 8 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 175-176

Graphes

.. GENERATED FROM PYTHON SOURCE LINES 176-198

.. code-block:: default


    with warnings.catch_warnings():
        warnings.simplefilter("ignore", DeprecationWarning)
        fig, ax = plt.subplots(2, 3, figsize=(14, 6))
        for delay in sorted(set(dfcoef['delay'])):
            dfcoef.pivot(index='k', columns='delay', values='mu').plot(
                ax=ax[0, 0], logy=True, legend=False).set_title('mu')
            dfcoef.pivot(index='k', columns='delay', values='nu').plot(
                ax=ax[0, 1], logy=True, legend=False).set_title('nu')
            dfcoef.pivot(index='k', columns='delay', values='beta').plot(
                ax=ax[0, 2], logy=True, legend=False).set_title('beta')
            dfcoef.pivot(index='k', columns='delay', values='R0').plot(
                ax=ax[1, 2], logy=True, legend=False).set_title('R0')
            ax[1, 2].plot([dfcoef.index[0], dfcoef.index[-1]], [1, 1], '--',
                          label="R0=1")
            ax[1, 2].set_ylim(0, 5)
            dfcoef.pivot(index='k', columns='delay', values='loss').plot(
                ax=ax[1, 0], logy=True, legend=False).set_title('loss')
        df.plot(ax=ax[1, 1], logy=True)
        fig.suptitle('Estimation de R0 tout au long de la simulation '
                     'avec différentes tailles de fenêtre', fontsize=12)




.. image-sg:: /auto_examples/images/sphx_glr_plot_covid_estimation_003.png
   :alt: Estimation de R0 tout au long de la simulation avec différentes tailles de fenêtre, mu, nu, beta, loss, R0
   :srcset: /auto_examples/images/sphx_glr_plot_covid_estimation_003.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)
    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)
    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)
    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)
    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)
    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)
    somewhereaftercovid_39_std/aftercovid/examples/plot_covid_estimation.py:191: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
      ax[1, 2].set_ylim(0, 5)




.. GENERATED FROM PYTHON SOURCE LINES 199-201

Le graphique manque de légende.
Ce sera pour plus tard.

.. GENERATED FROM PYTHON SOURCE LINES 203-208

Données bruitées
++++++++++++++++

L'idée est de voir si l'estimation se comporte
aussi bien sur des données bruitées.

.. GENERATED FROM PYTHON SOURCE LINES 208-212

.. code-block:: default


    Xeps = CovidSIRD.add_noise(X, epsilon=1.)
    yeps = numpy.vstack([Xeps[1:] - Xeps[:-1], y[-1:]])








.. GENERATED FROM PYTHON SOURCE LINES 213-214

On recommence.

.. GENERATED FROM PYTHON SOURCE LINES 214-231

.. code-block:: default


    coefs = []
    for k in range(0, X.shape[0] - 9, 2):
        end = min(k + 10, X.shape[0])
        Xt, yt = Xeps[k:end], yeps[k:end]
        m, loss = find_best_model(Xt, yt, [1e-2, 1e-3, 1e-4], 10)
        loss = m.score(Xt, yt)
        print(
            f"k={k} iter={m.iter_} loss={loss:1.3f} coef={m.model_._val_p}")
        obs = dict(k=k, loss=loss, it=m.iter_, R0=m.model_.R0())
        obs.update({k: v for k, v in zip(
            m.model_.param_names, m.model_._val_p)})
        coefs.append(obs)

    dfcoef = pandas.DataFrame(coefs).set_index('k')
    dfcoef





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    k=0 iter=201 loss=5.780 coef=[0.41070068 0.07811434 0.03368654]
    k=2 iter=171 loss=5.510 coef=[0.39800853 0.0557951  0.05416556]
    k=4 iter=63 loss=8.261 coef=[0.39728681 0.05390793 0.05341388]
    k=6 iter=43 loss=32.931 coef=[0.40389781 0.060203   0.04468495]
    k=8 iter=25 loss=77.128 coef=[0.40437958 0.05255752 0.05316681]
    k=10 iter=140 loss=276.834 coef=[0.40840096 0.06288563 0.04039822]
    k=12 iter=75 loss=354.680 coef=[0.40832869 0.05782803 0.04400978]
    k=14 iter=94 loss=669.593 coef=[0.40700254 0.06373109 0.03444199]
    k=16 iter=180 loss=1321.086 coef=[0.40099517 0.06574307 0.03145952]
    k=18 iter=168 loss=2374.709 coef=[0.39844081 0.06222821 0.03607916]
    k=20 iter=500 loss=3829.429 coef=[0.39937998 0.05792383 0.04200519]
    k=22 iter=500 loss=4414.055 coef=[0.40180435 0.06051216 0.04185968]
    k=24 iter=500 loss=5441.578 coef=[0.39643104 0.05729299 0.04295057]
    k=26 iter=500 loss=7944.976 coef=[0.39229949 0.06049477 0.03897823]
    k=28 iter=500 loss=7648.453 coef=[0.4018207  0.06159118 0.03969054]
    k=30 iter=500 loss=6708.459 coef=[0.40640136 0.06537355 0.03655733]
    k=32 iter=500 loss=4764.194 coef=[0.39701808 0.06753454 0.02698842]
    k=34 iter=304 loss=3876.961 coef=[0.34095509 0.06808465 0.02529795]
    k=36 iter=500 loss=2729.641 coef=[0.36837205 0.06342619 0.03656187]
    k=38 iter=500 loss=2287.201 coef=[0.2733339  0.06438263 0.03290926]
    k=40 iter=500 loss=1338.684 coef=[0.27098555 0.05502118 0.03603045]


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>loss</th>
          <th>it</th>
          <th>R0</th>
          <th>beta</th>
          <th>mu</th>
          <th>nu</th>
        </tr>
        <tr>
          <th>k</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>5.780362</td>
          <td>201</td>
          <td>3.673501</td>
          <td>0.410701</td>
          <td>0.078114</td>
          <td>0.033687</td>
        </tr>
        <tr>
          <th>2</th>
          <td>5.510491</td>
          <td>171</td>
          <td>3.619554</td>
          <td>0.398009</td>
          <td>0.055795</td>
          <td>0.054166</td>
        </tr>
        <tr>
          <th>4</th>
          <td>8.260594</td>
          <td>63</td>
          <td>3.701827</td>
          <td>0.397287</td>
          <td>0.053908</td>
          <td>0.053414</td>
        </tr>
        <tr>
          <th>6</th>
          <td>32.931207</td>
          <td>43</td>
          <td>3.850755</td>
          <td>0.403898</td>
          <td>0.060203</td>
          <td>0.044685</td>
        </tr>
        <tr>
          <th>8</th>
          <td>77.127833</td>
          <td>25</td>
          <td>3.824849</td>
          <td>0.404380</td>
          <td>0.052558</td>
          <td>0.053167</td>
        </tr>
        <tr>
          <th>10</th>
          <td>276.833655</td>
          <td>140</td>
          <td>3.954161</td>
          <td>0.408401</td>
          <td>0.062886</td>
          <td>0.040398</td>
        </tr>
        <tr>
          <th>12</th>
          <td>354.680126</td>
          <td>75</td>
          <td>4.009598</td>
          <td>0.408329</td>
          <td>0.057828</td>
          <td>0.044010</td>
        </tr>
        <tr>
          <th>14</th>
          <td>669.593050</td>
          <td>94</td>
          <td>4.145765</td>
          <td>0.407003</td>
          <td>0.063731</td>
          <td>0.034442</td>
        </tr>
        <tr>
          <th>16</th>
          <td>1321.086311</td>
          <td>180</td>
          <td>4.125355</td>
          <td>0.400995</td>
          <td>0.065743</td>
          <td>0.031460</td>
        </tr>
        <tr>
          <th>18</th>
          <td>2374.708531</td>
          <td>168</td>
          <td>4.053010</td>
          <td>0.398441</td>
          <td>0.062228</td>
          <td>0.036079</td>
        </tr>
        <tr>
          <th>20</th>
          <td>3829.428959</td>
          <td>500</td>
          <td>3.996637</td>
          <td>0.399380</td>
          <td>0.057924</td>
          <td>0.042005</td>
        </tr>
        <tr>
          <th>22</th>
          <td>4414.055046</td>
          <td>500</td>
          <td>3.924950</td>
          <td>0.401804</td>
          <td>0.060512</td>
          <td>0.041860</td>
        </tr>
        <tr>
          <th>24</th>
          <td>5441.577641</td>
          <td>500</td>
          <td>3.954678</td>
          <td>0.396431</td>
          <td>0.057293</td>
          <td>0.042951</td>
        </tr>
        <tr>
          <th>26</th>
          <td>7944.976071</td>
          <td>500</td>
          <td>3.943779</td>
          <td>0.392299</td>
          <td>0.060495</td>
          <td>0.038978</td>
        </tr>
        <tr>
          <th>28</th>
          <td>7648.453448</td>
          <td>500</td>
          <td>3.967356</td>
          <td>0.401821</td>
          <td>0.061591</td>
          <td>0.039691</td>
        </tr>
        <tr>
          <th>30</th>
          <td>6708.459303</td>
          <td>500</td>
          <td>3.987029</td>
          <td>0.406401</td>
          <td>0.065374</td>
          <td>0.036557</td>
        </tr>
        <tr>
          <th>32</th>
          <td>4764.193786</td>
          <td>500</td>
          <td>4.200229</td>
          <td>0.397018</td>
          <td>0.067535</td>
          <td>0.026988</td>
        </tr>
        <tr>
          <th>34</th>
          <td>3876.960692</td>
          <td>304</td>
          <td>3.651163</td>
          <td>0.340955</td>
          <td>0.068085</td>
          <td>0.025298</td>
        </tr>
        <tr>
          <th>36</th>
          <td>2729.641058</td>
          <td>500</td>
          <td>3.684160</td>
          <td>0.368372</td>
          <td>0.063426</td>
          <td>0.036562</td>
        </tr>
        <tr>
          <th>38</th>
          <td>2287.200571</td>
          <td>500</td>
          <td>2.809421</td>
          <td>0.273334</td>
          <td>0.064383</td>
          <td>0.032909</td>
        </tr>
        <tr>
          <th>40</th>
          <td>1338.683917</td>
          <td>500</td>
          <td>2.976175</td>
          <td>0.270986</td>
          <td>0.055021</td>
          <td>0.036030</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 232-233

Graphes.

.. GENERATED FROM PYTHON SOURCE LINES 233-247

.. code-block:: default


    dfeps = pandas.DataFrame({_[0]: x for _, x in zip(model.Q, Xeps.T)})

    with warnings.catch_warnings():
        warnings.simplefilter("ignore", DeprecationWarning)
        fig, ax = plt.subplots(2, 3, figsize=(14, 6))
        dfcoef[["mu", "nu"]].plot(ax=ax[0, 0], logy=True)
        dfcoef[["beta"]].plot(ax=ax[0, 1], logy=True)
        dfcoef[["loss"]].plot(ax=ax[1, 0], logy=True)
        dfcoef[["R0"]].plot(ax=ax[0, 2])
        dfeps.plot(ax=ax[1, 1])
        fig.suptitle(
            'Estimation de R0 tout au long de la simulation sur '
            'des données bruitées', fontsize=12)



.. image-sg:: /auto_examples/images/sphx_glr_plot_covid_estimation_004.png
   :alt: Estimation de R0 tout au long de la simulation sur des données bruitées
   :srcset: /auto_examples/images/sphx_glr_plot_covid_estimation_004.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 4 minutes  10.134 seconds)


.. _sphx_glr_download_auto_examples_plot_covid_estimation.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example




    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_covid_estimation.py <plot_covid_estimation.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_covid_estimation.ipynb <plot_covid_estimation.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_