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+

Quelques chiffres autour de l'épidémie de Covid-19

+
+ + +
+

1 Identification du système

+
+
+
date "+%Y-%m-%d"
+
+
+ +
+2020-04-19
+
+
+ +
+
uname -a
+
+
+ +
+Linux aluminium 4.14.0-3-amd64 #1 SMP Debian 4.14.17-1 (2018-02-14) x86_64 GNU/Linux
+
+
+ +
+
import sys
+sys.version
+
+
+ +
+3.7.3rc1 (default, Mar 13 2019, 11:01:15)
+[GCC 8.3.0]
+
+
+
+
+ + +
+

2 Récupération des données

+
+

+On prend les données distribuées par Our World In Data, elles-mêmes issues de +l'ECDC : +

+ +
+
url = "https://covid.ourworldindata.org/data/ecdc/full_data.csv"
+data_raw = pd.read_csv(url, index_col='date')
+data_raw.tail(3)
+
+
+ +
+            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
+
+
+
+
+ + +
+

3 Evolution comparée de l'épidémie dans quelques pays

+
+

+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. +

+ +

+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. +

+ +

+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. +

+ +

+En pratique, on prend +\[ + t^c_0 = \min \left\{t ; n^c(t) > \tau \right\}. +\] +

+ +
+
# Parameters
+column    = "total_deaths"
+threshold = 100
+countries = ["Italy", "Spain", "France", "United Kingdom", "Germany", "Switzerland"]
+
+total = {}
+for country in countries:
+    total[country] = data_raw.query(f"location == '{country}' & {column} > {threshold}")
+
+total[countries[2]]
+
+
+ +
+           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
+
+ + +
+

total.png +

+
+
+
+ + +
+

4 Vers un passage du pic ?

+
+

+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. +

+ +
+
threshold = 15
+
+daily = {}
+for country in countries:
+    daily[country] = data_raw.query(f"location == '{country}' & new_deaths > {threshold}")
+
+daily[countries[2]]
+
+
+ +
+           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
+
+ +

+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 (cf. données du gouvernement) +

+ + +
+

daily.png +

+
+
+
+
+
+

Auteur: François Févotte

+

Created: 2020-04-19 Sun 00:28

+

Validate

+
+ + diff --git a/module2/exo4/exercice_python_fr.org b/module2/exo4/exercice_python_fr.org index 11dc4db..4c3f2fb 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 GIT binary patch delta 141335 zcmZU)bzD|m*DZXD(kUqo(p}Oi9n#&>-JM&Mke2T5mTnM`Zlo`|yF1Uu`+45;e&6|v zAFSqPrO2F1yl;Ghph8zqkj&>$&)7ju#fL4QQA*+*3RAe(Hh zgz11rO_xWJIjDt0_H;jDUNbU3`_Fi2pc6NnnQ7nhw1k=Z4~ZXA$VK7P`eb88L*7K( zaZ+ZwHH+dFf6oU$cZRd(o9Qx!SRCZ1ADVPG-EH*b{zRsDOjh8p zE9d#z2q2n32|U$25h9+x{c>SZye%9SgDd1eqLI2ST)w6g+GcJSHryoC=t5Zz_sl3> zgx?$T^F5VpVAj0!Iu1&^?Y)BX7mO8oZY8=huKJFJ9qYwZ-d9$+11_-|q7(6N)pYUk z(ToBFDSG_K%0h&sD)#Y<$DHbyHZ~7kvHuz$6f~%~wStoE=AJRXYhFQEjKa1#dxx^$BLqdBM 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