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+<head>
+<!-- 2020-04-19 Sun 00:28 -->
+<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
+<meta name="viewport" content="width=device-width, initial-scale=1" />
+<title>Quelques chiffres autour de l'épidémie de Covid-19</title>
+<meta name="generator" content="Org mode" />
+<meta name="author" content="François Févotte" />
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+<body>
+<div id="content">
+<h1 class="title">Quelques chiffres autour de l'épidémie de Covid-19</h1>
+<div id="table-of-contents">
+<h2>Table des matières</h2>
+<div id="text-table-of-contents">
+<ul>
+<li><a href="#org09296a4">1. Identification du système</a></li>
+<li><a href="#orga74532a">2. Récupération des données</a></li>
+<li><a href="#orgbe41bde">3. Evolution comparée de l'épidémie dans quelques pays</a></li>
+<li><a href="#org2933e83">4. Vers un passage du pic ?</a></li>
+</ul>
+</div>
+</div>
+
+
+<div id="outline-container-org09296a4" class="outline-2">
+<h2 id="org09296a4"><span class="section-number-2">1</span> Identification du système</h2>
+<div class="outline-text-2" id="text-1">
+<div class="org-src-container">
+<pre class="src src-shell">date <span style="color: #de7fa8;">"+%Y-%m-%d"</span>
+</pre>
+</div>
+
+<pre class="example">
+2020-04-19
+
+</pre>
+
+<div class="org-src-container">
+<pre class="src src-shell">uname -a
+</pre>
+</div>
+
+<pre class="example">
+Linux aluminium 4.14.0-3-amd64 #1 SMP Debian 4.14.17-1 (2018-02-14) x86_64 GNU/Linux
+
+</pre>
+
+<div class="org-src-container">
+<pre class="src src-python"><span style="color: #729fcf; font-weight: bold;">import</span> sys
+sys.version
+</pre>
+</div>
+
+<pre class="example">
+3.7.3rc1 (default, Mar 13 2019, 11:01:15)
+[GCC 8.3.0]
+
+</pre>
+</div>
+</div>
+
+
+<div id="outline-container-orga74532a" class="outline-2">
+<h2 id="orga74532a"><span class="section-number-2">2</span> Récupération des données</h2>
+<div class="outline-text-2" id="text-2">
+<p>
+On prend les données distribuées par <a href="https://ourworldindata.org">Our World In Data</a>, elles-mêmes issues de
+l'<a href="https://www.ecdc.europa.eu/">ECDC</a> :
+</p>
+
+<div class="org-src-container">
+<pre class="src src-python"><span style="color: #ff2929;">url</span> = <span style="color: #de7fa8;">"https://covid.ourworldindata.org/data/ecdc/full_data.csv"</span>
+<span style="color: #ff2929;">data_raw</span> = pd.read_csv(url, index_col=<span style="color: #de7fa8;">'date'</span>)
+data_raw.tail(3)
+</pre>
+</div>
+
+<pre class="example">
+            location  new_cases  new_deaths  total_cases  total_deaths
+date
+2020-04-16  Zimbabwe          6           0           23             3
+2020-04-17  Zimbabwe          1           0           24             3
+2020-04-18  Zimbabwe          0           0           24             3
+
+</pre>
+</div>
+</div>
+
+
+<div id="outline-container-orgbe41bde" class="outline-2">
+<h2 id="orgbe41bde"><span class="section-number-2">3</span> Evolution comparée de l'épidémie dans quelques pays</h2>
+<div class="outline-text-2" id="text-3">
+<p>
+Je préfère fonder l'analyse sur le nombre de décès, qui me semble plus fiable et
+comparable d'un pays à l'autre que, par exemple, le nombre de cas dépistés. Afin
+de recaler l'axe temporel, on positionne \(t=0\) au moment où le nombre total de
+morts dépasse 100.
+</p>
+
+<p>
+La logique est la suivante : on considère le nombre \(n^c\) (de décès ou de cas)
+dans un pays \(c\). On suppose que l'évolution de \(n^c\) en fonction du temps \(t\)
+suit une loi de croissance exponentielle (au moins dans une phase initiale). On
+s'attend ainsi à avoir une expression du type :
+\[
+  n^c(t) = n^c_0 \, e^{\lambda^c \left(t-t^c_0\right)}.
+\]
+Dans cette expression, la valeur initiale \(n^c_0 = n^c(t^c_0)\) est liée à la
+taille de la population considérée. La constante de temps \(\lambda^c\) en revanche,
+n'a pas vraiment de raison de l'être : elle reflète simplement le rythme auquel
+l'épidémie se propage.
+</p>
+
+<p>
+Si l'on se donne un seuil \(\tau\) unique, on peut fixer pour chaque pays
+l'instant initial \(t^c_0\) de sorte que
+\[
+  n^c(t^c_0) = \tau.
+\]
+En effectuant un recalage de l'instant initial, c'est à dire en effectuant le
+changement de variable temporelle \(\tilde{t}^c=t-t^c_0\), on obtient
+\[
+  n^c(\tilde{t}^c) = \tau \, e^{\lambda^c\,\tilde{t}^c},
+\]
+ce qui signifie que tous les pays deviennent comparables, indépendamment de leur
+taille : on s'est ramené à comparer les constantes de temps \(\lambda^c\) entre
+elles.
+</p>
+
+<p>
+En pratique, on prend
+\[
+  t^c_0 = \min \left\{t ; n^c(t) > \tau \right\}.
+\]
+</p>
+
+<div class="org-src-container">
+<pre class="src src-python"><span style="color: #babdb6; font-style: italic;"># </span><span style="color: #babdb6; font-style: italic;">Parameters</span>
+<span style="color: #ff2929;">column</span>    = <span style="color: #de7fa8;">"total_deaths"</span>
+<span style="color: #ff2929;">threshold</span> = 100
+<span style="color: #ff2929;">countries</span> = [<span style="color: #de7fa8;">"Italy"</span>, <span style="color: #de7fa8;">"Spain"</span>, <span style="color: #de7fa8;">"France"</span>, <span style="color: #de7fa8;">"United Kingdom"</span>, <span style="color: #de7fa8;">"Germany"</span>, <span style="color: #de7fa8;">"Switzerland"</span>]
+
+<span style="color: #ff2929;">total</span> = {}
+<span style="color: #729fcf; font-weight: bold;">for</span> country <span style="color: #729fcf; font-weight: bold;">in</span> countries:
+    <span style="color: #ff2929;">total</span>[country] = data_raw.query(f<span style="color: #de7fa8;">"location == '{country}' &amp; {column} &gt; {threshold}"</span>)
+
+total[countries[2]]
+</pre>
+</div>
+
+<pre class="example">
+           location  new_cases  new_deaths  total_cases  total_deaths
+date
+2020-03-16   France        924          36         5423           127
+2020-03-17   France       1210          21         6633           148
+2020-03-18   France       1097          27         7730           175
+2020-03-19   France       1404          69         9134           244
+2020-03-20   France       1861         128        10995           372
+2020-03-21   France       1617          78        12612           450
+2020-03-22   France       1847         112        14459           562
+2020-03-23   France       1559         112        16018           674
+2020-03-24   France       3838         186        19856           860
+2020-03-25   France       2446         240        22302          1100
+2020-03-26   France       2931         231        25233          1331
+2020-03-27   France       3922         365        29155          1696
+2020-03-28   France       3809         299        32964          1995
+2020-03-29   France       4611         319        37575          2314
+2020-03-30   France       2599         292        40174          2606
+2020-03-31   France       4376         418        44550          3024
+2020-04-01   France       7578         499        52128          3523
+2020-04-02   France       4861         509        56989          4032
+2020-04-03   France       2116         471        59105          4503
+2020-04-04   France       5233        2004        64338          6507
+2020-04-05   France       4267        1053        68605          7560
+2020-04-06   France       1873         518        70478          8078
+2020-04-07   France       3912         833        74390          8911
+2020-04-08   France       3777        1417        78167         10328
+2020-04-09   France       3881         541        82048         10869
+2020-04-10   France       4286        1341        86334         12210
+2020-04-11   France       4342         987        90676         13197
+2020-04-12   France       3114         635        93790         13832
+2020-04-13   France       1613         561        95403         14393
+2020-04-14   France       2673         574        98076         14967
+2020-04-15   France       5497         762       103573         15729
+2020-04-16   France       2633        1438       106206         17167
+2020-04-17   France       2641         753       108847         17920
+2020-04-18   France        405         761       109252         18681
+</pre>
+
+
+<div class="figure">
+<p><img src="total.png" alt="total.png" />
+</p>
+</div>
+</div>
+</div>
+
+
+<div id="outline-container-org2933e83" class="outline-2">
+<h2 id="org2933e83"><span class="section-number-2">4</span> Vers un passage du pic ?</h2>
+<div class="outline-text-2" id="text-4">
+<p>
+On s'intéresse ici à l'atteinte d'un pic du nombre de décès quotidiens liés à
+Covid-19.  Là encore, l'axe temporel est recalé afin de permettre une
+comparaison entre pays : \(t=0\) est positionné au moment où le nombre quotidien
+de morts dépasse 15.
+</p>
+
+<div class="org-src-container">
+<pre class="src src-python"><span style="color: #ff2929;">threshold</span> = 15
+
+<span style="color: #ff2929;">daily</span> = {}
+<span style="color: #729fcf; font-weight: bold;">for</span> country <span style="color: #729fcf; font-weight: bold;">in</span> countries:
+    <span style="color: #ff2929;">daily</span>[country] = data_raw.query(f<span style="color: #de7fa8;">"location == '{country}' &amp; new_deaths &gt; {threshold}"</span>)
+
+daily[countries[2]]
+</pre>
+</div>
+
+<pre class="example">
+           location  new_cases  new_deaths  total_cases  total_deaths
+date
+2020-03-14   France        785          18         3661            79
+2020-03-16   France        924          36         5423           127
+2020-03-17   France       1210          21         6633           148
+2020-03-18   France       1097          27         7730           175
+2020-03-19   France       1404          69         9134           244
+2020-03-20   France       1861         128        10995           372
+2020-03-21   France       1617          78        12612           450
+2020-03-22   France       1847         112        14459           562
+2020-03-23   France       1559         112        16018           674
+2020-03-24   France       3838         186        19856           860
+2020-03-25   France       2446         240        22302          1100
+2020-03-26   France       2931         231        25233          1331
+2020-03-27   France       3922         365        29155          1696
+2020-03-28   France       3809         299        32964          1995
+2020-03-29   France       4611         319        37575          2314
+2020-03-30   France       2599         292        40174          2606
+2020-03-31   France       4376         418        44550          3024
+2020-04-01   France       7578         499        52128          3523
+2020-04-02   France       4861         509        56989          4032
+2020-04-03   France       2116         471        59105          4503
+2020-04-04   France       5233        2004        64338          6507
+2020-04-05   France       4267        1053        68605          7560
+2020-04-06   France       1873         518        70478          8078
+2020-04-07   France       3912         833        74390          8911
+2020-04-08   France       3777        1417        78167         10328
+2020-04-09   France       3881         541        82048         10869
+2020-04-10   France       4286        1341        86334         12210
+2020-04-11   France       4342         987        90676         13197
+2020-04-12   France       3114         635        93790         13832
+2020-04-13   France       1613         561        95403         14393
+2020-04-14   France       2673         574        98076         14967
+2020-04-15   France       5497         762       103573         15729
+2020-04-16   France       2633        1438       106206         17167
+2020-04-17   France       2641         753       108847         17920
+2020-04-18   France        405         761       109252         18681
+</pre>
+
+<p>
+Le pic observé pour la France au 04/04 (jour 20 sur le graphique) correspond à la prise en compte
+instantanée de tous les décès en EHPAD, dont le décompte est disponible à partir
+du 01/02 (<i>cf.</i> <a href="https://www.gouvernement.fr/info-coronavirus/carte-et-donnees">données du gouvernement</a>)
+</p>
+
+
+<div class="figure">
+<p><img src="daily.png" alt="daily.png" />
+</p>
+</div>
+</div>
+</div>
+</div>
+<div id="postamble" class="status">
+<p class="author">Auteur: François Févotte</p>
+<p class="date">Created: 2020-04-19 Sun 00:28</p>
+<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
+</div>
+</body>
+</html>
diff --git a/module2/exo4/exercice_python_fr.org b/module2/exo4/exercice_python_fr.org
index 11dc4db5d767f08196ce6108a458e4273e7f1bc1..4c3f2fb3287395c1e0cc2d3daf829bcd02b1c586 100644
--- a/module2/exo4/exercice_python_fr.org
+++ b/module2/exo4/exercice_python_fr.org
@@ -13,6 +13,13 @@
 
 * Identification du système
 
+#+BEGIN_SRC shell :exports both
+  date "+%Y-%m-%d"
+#+END_SRC
+
+#+RESULTS:
+: 2020-04-19
+
 #+BEGIN_SRC shell :exports both
   uname -a
 #+END_SRC
@@ -53,9 +60,9 @@ l'[[https://www.ecdc.europa.eu/][ECDC]] :
 #+RESULTS:
 :             location  new_cases  new_deaths  total_cases  total_deaths
 : date                                                                  
-: 2020-04-15  Zimbabwe          0           0           17             3
 : 2020-04-16  Zimbabwe          6           0           23             3
 : 2020-04-17  Zimbabwe          1           0           24             3
+: 2020-04-18  Zimbabwe          0           0           24             3
 
 
 * Evolution comparée de l'épidémie dans quelques pays
@@ -146,6 +153,7 @@ date
 2020-04-15   France       5497         762       103573         15729
 2020-04-16   France       2633        1438       106206         17167
 2020-04-17   France       2641         753       108847         17920
+2020-04-18   France        405         761       109252         18681
 #+end_example
 
 #+BEGIN_SRC python :session :results output file :exports results :var pltfile="total.png"
@@ -222,6 +230,7 @@ date
 2020-04-15   France       5497         762       103573         15729
 2020-04-16   France       2633        1438       106206         17167
 2020-04-17   France       2641         753       108847         17920
+2020-04-18   France        405         761       109252         18681
 #+end_example
 
 Le pic observé pour la France au 04/04 (jour 20 sur le graphique) correspond à la prise en compte
diff --git a/module2/exo4/exercice_python_fr.pdf b/module2/exo4/exercice_python_fr.pdf
index b70c38e680af904bcfb0c02c72ff475f0182ba76..2cada7d022eb0e4dc5078c38df8d225066246a0a 100644
Binary files a/module2/exo4/exercice_python_fr.pdf and b/module2/exo4/exercice_python_fr.pdf differ
diff --git a/module2/exo4/total.png b/module2/exo4/total.png
index 02495911309e29870920882ff8ae8e793e8c7376..ad9fca6f28fa1f4a64a20754172a466ad1f4c628 100644
Binary files a/module2/exo4/total.png and b/module2/exo4/total.png differ
