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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>
module2/exo4/exercice_python_fr.org
View file @ 2bd85277
...@@ -13,6 +13,13 @@ ...@@ -13,6 +13,13 @@
* Identification du système * Identification du système
#+BEGIN_SRC shell :exports both
date "+%Y-%m-%d"
#+END_SRC
#+RESULTS:
: 2020-04-19
#+BEGIN_SRC shell :exports both #+BEGIN_SRC shell :exports both
uname -a uname -a
#+END_SRC #+END_SRC
...@@ -53,9 +60,9 @@ l'[[https://www.ecdc.europa.eu/][ECDC]] : ...@@ -53,9 +60,9 @@ l'[[https://www.ecdc.europa.eu/][ECDC]] :
#+RESULTS: #+RESULTS:
: location new_cases new_deaths total_cases total_deaths : location new_cases new_deaths total_cases total_deaths
: date : date
: 2020-04-15 Zimbabwe 0 0 17 3
: 2020-04-16 Zimbabwe 6 0 23 3 : 2020-04-16 Zimbabwe 6 0 23 3
: 2020-04-17 Zimbabwe 1 0 24 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 * Evolution comparée de l'épidémie dans quelques pays
...@@ -146,6 +153,7 @@ date ...@@ -146,6 +153,7 @@ date
2020-04-15 France 5497 762 103573 15729 2020-04-15 France 5497 762 103573 15729
2020-04-16 France 2633 1438 106206 17167 2020-04-16 France 2633 1438 106206 17167
2020-04-17 France 2641 753 108847 17920 2020-04-17 France 2641 753 108847 17920
2020-04-18 France 405 761 109252 18681
#+end_example #+end_example
#+BEGIN_SRC python :session :results output file :exports results :var pltfile="total.png" #+BEGIN_SRC python :session :results output file :exports results :var pltfile="total.png"
...@@ -222,6 +230,7 @@ date ...@@ -222,6 +230,7 @@ date
2020-04-15 France 5497 762 103573 15729 2020-04-15 France 5497 762 103573 15729
2020-04-16 France 2633 1438 106206 17167 2020-04-16 France 2633 1438 106206 17167
2020-04-17 France 2641 753 108847 17920 2020-04-17 France 2641 753 108847 17920
2020-04-18 France 405 761 109252 18681
#+end_example #+end_example
Le pic observé pour la France au 04/04 (jour 20 sur le graphique) correspond à la prise en compte Le pic observé pour la France au 04/04 (jour 20 sur le graphique) correspond à la prise en compte
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module2/exo4/total.png
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module2/exo4/total.png
module2/exo4/total.png
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