{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "

\n", " Mathematische Modelle zur Beschreibung der COVID-19-Pandemie in Deutschland\n", "

\n", "\n", "von **Ingo Dahn (dahn@dahn-research.eu)**" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Was ist ein Jupyter Notebook?\n", "\n", "Dies ist ein Jupyter-Notebook, das vor allem für die selbständige, interaktive Arbeit gedacht ist, das aber auch gerne in der Lehre eingesetzt werden kann. Mit diesem Notebook kann der Leser die Grundlagen von drei wichtigen epidemiologischen Modellen verstehen, aber - und das macht Jupyter-Notebooks zu etwas Besonderem - er/sie kann dadurch aktiv mit den Daten zur Ausbreitung von COVID-19 arbeiten und so die Leistungsfähigkeit und die Grenzen der behandelten mathematischen Modelle erfahren.\n", "\n", "Anders als in einem Lehrbuch können Sie die durchgeführten Berechnungen ausführen, sie modifizieren und sie auf andere Daten (vielleicht für ein anderes Land?) anwenden. Sie würden manche Berechnungen anders durchführen oder würden gerne zusätzliche Analysen durchführen? Sehr gut! Tun Sie es einfach, ändern Sie die Berechnungen, fügen Sie neue Zellen hinzu - Sie können nichts kaputt machen!\n", "\n", "Zusätzlich enthält dieses Notebook einige interaktive Aufgaben, in denen Sie mit Hilfe der Modelle eigene Voraussagen treffen können, deren Gültigkeit dann automatisch bewertet wird (nur für Sie - die Bewertung wird nirgends gespeichert).\n", "\n", "Eine gute Online-Umgebung, um mit Jupyter-Notebooks wie diesem zu arbeiten, ist das [CoCalc-System](https://cocalc.com). Wenn Sie etwas Zeit haben und auf die interaktiven Aufgaben verzichten können, so können Sie auch das [Binder-System](https://mybinder.org/v2/gh/ingodahn/Corona/master?filepath=Deutschland.ipynb) verwenden. Dieses Notebook verwendet übrigens den Kernel SageMath 9.0.\n", "\n", "Schließlich können Sie mit diesem Notebook auch im [CoCalc-Player](https://dahn-research.eu/corona/Deutschland.html) interaktiv arbeiten.\n", "\n", "**Praktische Hinweise**\n", "\n", "In der ausführbaren Ansicht dieses Notebooks in CoCalc bzw. im CoCalc-Player können die Eingabezellen editiert und neu berechnet werden um die Verfahren zu prüfen oder sie auf andere Daten anzuwenden.Viele Zellen haben Schieberegler, mit denen Parameter der Berechnung angepasst werden können. Jede Neuberechnung einer Zelle ändert möglicherweise Daten oder Definitionen, die andere Zellen verwenden\n", "\n", "**Deshalb müssen die Zellen immer in der gegebenen Reihenfolge ausgeführt werden!**\n", "\n", "**Um eine Zelle auszuführen wählen Sie die Zelle aus und verwenden Sie die Tastenkombination Shift+Return.**\n", "\n", "Falls Sie Verbesserungsvorschläge, Modifikationen, Erweiterungen oder Anwendungen auf andere Daten haben oder einfach nur dieses Notebook nutzen, so würde ich mich über eine Information dazu freuen.\n", "\n", "Diese Seite wird unter der [Creative Commons Lizenz CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) veröffentlicht. Dieses Notebook ist auf [GitHub](https://github.com/ingodahn/Corona) verfügbar.\n", "\n", "Koblenz im Juli 2020\n", "\n", "Dr. Ingo Dahn\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Inhalt\n", "\n", "**_Wie gut beschreiben mathematische Modelle reale Prozesse?_** \n", "\n", "In diesem Jupyter-Notebook untersuchen wir die Passung der einfachsten Pandemie-Modelle - des exponentiellen Modells, des SI-Modells und des SIR-Modells - zu den Daten der Pandemie in Deutschland für die Zeit vom 24.2. bis zum 30.6.2020, wie sie vom Robert-Koch-Institut zur Verfügung gestellt wurden. \n", "\n", "Zunächst wird ein Überblick über die verwendeten Daten zur Entwicklung der COVID-19-Pandemie gegeben. Es werden taggenaue Daten für COVID-19-Infektionen, -Todesfälle und -Genesungen verwendet.\n", "\n", "Der Hauptteil zu den mathematischen Modellen diskutiert zunächst die Frage, wie die Qualität eines (nichtlinearen) mathematischen Modells beurteilt werden kann. Wir definieren dafür die Modell-Toleranz und die Vorhersage-Toleranz, die \n", "auf der Berechnung relativer Residuen beruhen.\n", "\n", "Danach werden für jedes der drei behandelten Modelle die Überlegungen vorgestellt, die hinter dem jeweiligen Modellansatz stehen und die zur Bestimmung der jeweils dem Modell zugrundeliegenden Differentialgleichungen führen.\n", "\n", "Danach versuchen wir, geeignete Werte der Parameter für die einzelnen Modelle zu bestimmen, so dass die Modelle den Verlauf der Pandemie - zumindest in einem gewissen Zeitabschnitt - möglichst gut beschreiben und sinnvolle Vorhersagen ermöglichen.\n", "\n", "Für das Verständnis des exponentiellen Modells sind elementare Kenntnisse über Exponentialfunktionen ausreichend, wenn die automatische Bestimmung der Parameter hingenommen wird.\n", "\n", "Das logistische Modell beruht auf der Kenntnis der logistischen Funktion, die in diesem Kapitel eingeführt wird. Auch für das logistische Modell kann die Bestimmung geeigneter Parameter automatisch erfolgen. Dabei werden wir sehen, wie das Modell laufend durch Änderungen an den Parametern angepasst werden muss bis es schließlich Anfang Mai 2020 seine Grenzen erreicht. Für das Verständnis des logistischen Modells sind elementare Kenntnisse über Differentialgleichungen hilfreich, jedoch nicht zwingend erforderlich.\n", "\n", "Die Anwendung des SIR-Modell auf die Modellierung der COVID-19-Pandemie erfordert schließlich ein gewisses Verständnis für ein System von Differentialgleichungen und dessen näherungsweise numerische Lösung mit dem Runge-Kutta-Verfahren.\n", "\n", "Ein abschließendes Fazit fasst die Ergebnisse zusammen und ein Ausblick zeigt Möglichkeiten, dieses Notebook (selbst) weiterzuentwickeln." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false }, "slideshow": { "slide_type": "slide" } }, "source": [ "# Daten\n", "\n", "Im Folgenden wird statt mit Kalender-Daten, mit Tagen seit dem 24.2.2020, dem Beginn der täglichen Datenemeldungen des Robert-Koch-Instituts gerechnet. Die folgende Tabelle ermöglicht eine Umrechnung.\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", " Tag Nr.\n", " \n", " Datum\n", "
024.2.2020
2015.3.2020
404.4.2020
6024.4.2020
8014.5.2020
1003.6.2020
12023.6.2020
14013.7.2020
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "Die Daten sind aktuell bis zum 30.06.2020." ], "text/plain": [ "Die Daten sind aktuell bis zum 30.06.2020." ] }, "execution_count": 2, "metadata": { }, "output_type": "execute_result" } ], "source": [ "infections_de=[16.0, 18.0, 21.0, 26.0, 53.0, 66.0, 117.0, 150.0, 188.0, 240.0, 400.0, 639.0, 795.0, 902.0, 1139.0, 1296.0, 1567.0, 2369.0, 3062.0, 3795.0, 4838.0, 6012.0, 7156.0, 8198.0, 10999.0, 13957.0, 16662.0, 18610.0, 22672.0, 27436.0, 31554.0, 36508.0, 42288.0, 48582.0, 52547.0, 57298.0, 61913.0, 67366.0, 73522.0, 79696.0, 85778.0, 91714.0, 95391.0, 99225.0, 103228.0, 108202.0, 113525.0, 117658.0, 120479.0, 123016.0, 125098.0, 127584.0, 130450.0, 133830.0, 137439.0, 139897.0, 141672.0, 143457.0, 145694.0, 148046.0, 150383.0, 152438.0, 154175.0, 155193.0, 156337.0, 157641.0, 159119.0, 160758.0, 161703.0, 162496.0, 163175.0, 163860.0, 164807.0, 166091.0, 167300.0, 168531.0, 169218.0, 169575.0, 170508.0, 171306.0, 172239.0, 173152.0, 173772.0, 174355.0, 174697.0, 175210.0, 176007.0, 176752.0, 177212.0, 177850.0, 178281.0, 178570.0, 179002.0, 179364.0, 179717.0, 180458.0, 181196.0, 181482.0, 181815.0, 182028.0, 182370.0, 182764.0, 182937.0, 183271.0, 183979.0, 184193.0, 184543.0, 184861.0, 185416.0, 185674.0, 186022.0, 186269.0, 186461.0, 186839.0, 187184.0, 187764.0, 188534.0, 189135.0, 189822.0, 190359.0, 190862.0, 191449.0, 192079.0, 192556.0, 193243.0, 193499.0, 193761.0, 194259.0]\n", "dataNr_de=len(infections_de)\n", "deadsAll_de=(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 12.0, 20.0, 31.0, 46.0, 55.0, 86.0, 114.0, 149.0, 198.0, 253.0, 325.0, 389.0, 455.0, 583.0, 732.0, 872.0, 1017.0, 1158.0, 1342.0, 1434.0, 1607.0, 1861.0, 2107.0, 2373.0, 2544.0, 2673.0, 2799.0, 2969.0, 3254.0, 3569.0, 3868.0, 4110.0, 4294.0, 4404.0, 4598.0, 4879.0, 5094.0, 5321.0, 5500.0, 5640.0, 5750.0, 5913.0, 6115.0, 6288.0, 6481.0, 6575.0, 6649.0, 6692.0, 6831.0, 6996.0, 7119.0, 7266.0, 7369.0, 7395.0, 7417.0, 7533.0, 7634.0, 7723.0, 7824.0, 7881.0, 7914.0, 7935.0, 8007.0, 8090.0, 8147.0, 8174.0, 8216.0, 8247.0, 8257.0, 8302.0, 8349.0, 8411.0, 8450.0, 8489.0, 8500.0, 8511.0, 8522.0, 8551.0, 8581.0, 8614.0, 8646.0, 8668.0, 8674.0, 8711.0, 8729.0, 8755.0, 8763.0, 8781.0, 8787.0, 8791.0, 8800.0, 8830.0, 8856.0, 8872.0, 8883.0, 8882.0, 8885.0, 8895.0, 8914.0, 8927.0, 8948.0, 8954.0, 8957.0, 8961.0, 8973.0)\n", "deads_de=list(deadsAll_de)[23:dataNr_de]\n", "maxDays=dataNr_de+3\n", "deadsNr_de=len(deads_de)\n", "infections_de_points=[(n,infections_de[n]) for n in range(0,dataNr_de)]\n", "recoveredAll_de=(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 13500.0, 16100.0, 18700.0, 21400.0, 23800.0, 26400.0, 28700.0, 30600.0, 33000.0, 46300.0, 49000.0, 53913.0, 57400.0, 60200.0, 64300.0, 68200.0, 72600.0, 77000.0, 81800.0, 85400.0, 88000.0, 91500.0, 95200.0, 99400.0, 103300.0, 106800.0, 109800.0, 112000.0, 114500.0, 117400.0, 120400.0, 123500.0, 126900.0, 129000.0, 130600.0, 132700.0, 135100.0, 137400.0, 139900.0, 141700.0, 143300.0, 144400.0, 145600.0, 147200.0, 148700.0, 150300.0, 151700.0, 152600.0, 153400.0, 154600.0, 155700.0, 156900.0, 158000.0, 159000.0, 159900.0, 160500.0, 161200.0, 162000.0, 162800.0, 163200.0, 164100.0, 164900.0, 165200.0, 165900.0, 166400.0, 167300.0, 167800.0, 168300.0, 168800.0, 169100.0, 169600.0, 170200.0, 170700.0, 171100.0, 171600.0, 171900.0, 172200.0, 172650.0, 173100.0, 173600.0, 174100.0, 174400.0, 174700.0, 174900.0, 175300.0, 175700.0, 176300.0, 176800.0, 177100.0, 177500.0, 177700.0, 178100.0, 179100.0)\n", "recovered_de=list(recoveredAll_de)[35:dataNr_de]\n", "recoveredNr_de=len(recovered_de)\n", "date0='240220'\n", "from IPython.display import Markdown as md\n", "from datetime import *\n", "from dateutil import *\n", "from dateutil.relativedelta import relativedelta\n", "firstDateTime_de=datetime(2020,2,24)\n", "lastDateTime_de=firstDateTime_de+relativedelta(days=int(dataNr_de-1))\n", "lastDate_de=lastDateTime_de.strftime('%d.%m.%Y')\n", "html(u\"Die Daten sind aktuell bis zum %s.\"%(lastDate_de))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "Es stehen taggenaue Meldungen des RKI zu\n", "* gemeldeten Infektionen\n", "* geschätzte Genesungen (auf volle 100 gerundet)\n", "* gemeldete Todesfälle\n", "\n", "zur Verfügung. Wir gehen davon aus, dass die absolute Zahl der der Todesfälle realistisch ist, während die Zahlen der realen Infektionen bzw. Genesungen nicht einmal von der Größenordnung her abgeschätzt werden kann, solange keine repräsentativen Querschnittsanalysen vorliegen. Die dazu gemeldeten bzw. geschätzten Zahlen erlauben lediglich das Erkennen von Tendenzen. deshalb stellen wir im Folgenden Diagramm, für eine erste Orientierung, die zur Verfügung stehenden kumulierten Daten auf ihren maximalen Wert normiert dar.\n", "\n", "Auch in den folgenden Abschnitten arbeiten wir direkt mit den gemeldeten Daten. Der Leser ist jedoch eingeladen, die Infektionszahlen mit einem Dunkelfaktor seiner Wahl zu multiplizieren (5-15 gelten als realistische Faktoren) und die Modelle neu berechnen zu lassen." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def normedPoints(data):\n", " maxData=max(data)\n", " return [(n,data[n]/maxData) for n in range(0,len(data))]\n", "infectionsNormedPoints_de=normedPoints(infections_de)\n", "deadsNormedPoints_de=normedPoints(deadsAll_de)\n", "recoveredNormedPoints_de=normedPoints(recoveredAll_de)\n", "yetInfected_de=[infections_de[n]-recoveredAll_de[n] - deadsAll_de[n] for n in range(0,dataNr_de)]\n", "yetInfectedNormedPoints_de=normedPoints(yetInfected_de)\n", "list_plot(infectionsNormedPoints_de, legend_label='Infiziert', color='blue')+list_plot(deadsNormedPoints_de,color='red',legend_label='Verstorben')+list_plot(recoveredNormedPoints_de,color='green',legend_label='Genesen')+list_plot(yetInfectedNormedPoints_de,color='pink',legend_label='Noch infiziert')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Reproduktionsrate\n", "\n", "Hauptziel der Massnahmen zur Eindämmung der Pandemie ist zunächst, eine Überlastung der Intensivpflege in den deutschen Krankenhäusern (ohne zusätzliche Ressourcen) zu verhindern. Dazu müsste die Reproduktionsrate des Virus, d.h. die Zahl der von einem Infizierten angesteckten Personen nach Einschätzung der Deutschen Gesellschaft für Epidemiologie auf 1.1-1.2 gesenkt werden.\n", "\n", "Im epidemiologischen Bulletin des RKI vom 17.4.2020 ist der folgende Weg zur Schätzung der Reproduktionsrate beschrieben. Sie beruht auf einer Schätzung der sogenannten Generationenzahl, d.i. die Zahl zwischen dem Beginn der Infektion eines Patienten und dem Beginn der Infektion eines von ihm angesteckten Patienten. Die Generationenzahl wird aufgrund des typischen Verlaufs der Infektion mit 4 Tagen angesetzt.\n", "\n", "Dann kann die Reproduktionszahl geschätzt werden als Quotient der Anzahl der Neuerkrankungen in 2 aufeinanderfolgenden Perioden von der Länge der Generationenzahl, also $R(n)=\\frac{i(n)-i(n-4)}{i(n-4)-i(n-8)}$, wobei $i(n)$ die Zahl der Infizierten am Tag $n$ ist.." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Im folgenden Diagramm kann die für die Berechnung der Reproduktionszahl verwendete Generationenzahl variiert werden. Es wird mit dem Durchschnitt der Infektionszahlen der letzten $w$ Tage gerechnet." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1cbc6fdd017d4639beb7fb0643e55475", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 2 widgets\n", " w: TransformIntSlider(value=7, descriptio…" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" } ], "source": [ "@interact\n", "def _(w=slider(1,15,step_size=1,default=7),Gz=slider(1,15,step_size=1,default=4)):\n", " Id=[(infections_de[n]+infections_de[n-w+1])/2 for n in range(w,dataNr_de)]\n", " #R=[(n,((infections_de[n]-infections_de[n-Gz])/(infections_de[n-Gz]-infections_de[n-2*Gz])).n()) for n in range(2*Gz,dataNr_de)]\n", " R=[(n,((Id[n-w-1]-Id[n-w-1-Gz])/(Id[n-w-1-Gz]-Id[n-w-1-2*Gz])).n()) for n in range(w+2*Gz,dataNr_de)]\n", " show(list_plot(R)+plot(1,(0,dataNr_de),color='black'))\n", " " ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Neuinfektionen\n", "\n", "Das folgende Diagramm zeigt für jeden Tag die Zahl der gemeldeten Neuinfektionen pro Tag, gemittelt über die letzten $w$ Tage." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "50e2551e8a264039a256d725a688ee98", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " w: TransformIntSlider(value=1, description…" ] }, "execution_count": 5, "metadata": { }, "output_type": "execute_result" } ], "source": [ "@interact\n", "def _(w=slider(1,14,step_size=1,default=1)):\n", " k_n_de = [(n,(infections_de[n]-infections_de[n-w])/w) for n in range(w,dataNr_de)]\n", " show(list_plot(k_n_de))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Todesfälle\n", "\n", "Das folgende Diagramm zeigt für jeden Tag die Zahl der gemeldeten COVID-19-Todesfälle pro Tag, gemittelt über die letzten $w$ Tage." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true }, "scrolled": true }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7fa8387d476844d9b6dffcdb14637901", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " w: TransformIntSlider(value=1, description…" ] }, "execution_count": 6, "metadata": { }, "output_type": "execute_result" } ], "source": [ "@interact\n", "def _(w=slider(1,14,step_size=1,default=1)):\n", " k_n_de = [(n,(deadsAll_de[n]-deadsAll_de[n-w])/w) for n in range(w,dataNr_de)]\n", " show(list_plot(k_n_de))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Mathematische Modelle\n", "\n", "Wir suchen mathematische Funktionen, die den Verlauf der Pandemie möglichst gut beschreiben. Wie wir sehen werden, kann man in der ersten Phase (etwa bis Ende März 2020) dafür Exponentialfunktionen verwenden. In dieser Zeit breitet sich das Virus weitgehend ungehemmt aus. Im April beginnen hemmende Faktoren zu wirken, vermutlich vor allem Kontaktbeschränkungen, die die Ausbreitungsgeschwindigkeit verlangsamen. In dieser Phase liefern logistische Funktionen brauchbare Ergebnisse für die Beschreibung der Entwicklung der Zahl der Infizierten bzw. Verstorbenen.\n", "\n", "Wie wir sehen schwanken die Daten der Neuinfektionen und Todesfälle von Tag zu Tag erheblich. Wir werden im Folgenden stets mit kumulierten Daten Arbeiten. Gegenüber diesen Daten sind die täglichen Schwankungen vergleichsweise klein, weshalb wir auf eine Mittelung zum Ausgleich der täglichen Schwankungen verzichten.\n", "\n", "Bei der Interpretation der Ergebnisse ist zu berücksichtigen, dass die Daten mit einer erheblichen Ungenauigkeit behaftet sind, da bei Weitem nicht alle Erkrankten Symptome zeigen und deshalb in dem untersuchten Zeitraum gar nicht erfasst wurden. Solange das Testregime dabei bleibt, vorwiegend Personen mit Symptomen zu testen, wie das im März und April der Fall war, können wir annehmen, dass sich die Zahl der Infizierten von der Zahl der gemeldeten um einen unbekannten Dunkelfaktor unterscheidet. Insofern sind in der folgenden Analyse weniger die absoluten Zahlen als deren relative Unterschiede und deren Entwicklung von Interesse.\n", "\n", "Wir wollen untersuchen, wie genau sich die reale Entwicklung der Zahl der mit COVID-19 Infizierten in Deutschland mit den verfügbaren mathematischen Modellen vorhersagen ließ. \n", "\n", "**Aufgabe:** Führen Sie eine ähnliche Analyse für die Zahl der Todesfälle mit COVID-19-Bezug durch. Sie können dazu die Code-Zellen in diesem Notebook so modifizieren, dass Sie statt `infections_de` die Liste `deads_de` verwenden. Vergleichen Sie die beiden Analysen!\n", "\n", "Versuchen Sie zunächst eine Vorhersage \"von Hand\":\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Qualität der Modelle\n", "\n", "Die zu erwartende Genauigkeit einer Vorhersage hängt offenbar vom Zeithorizont $zh$ der Voraussage ab - davon, über wie viele Tage im Voraus eine Aussage gemacht werden soll. Den Zeithorizont, mit dem im Folgenden gerechnet wird, können Sie mit diesem Regler festlegen." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "b69507d8abbd4b428a4f65b6856f45c5", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " zhs: TransformIntSlider(value=3, descripti…" ] }, "execution_count": 47, "metadata": { }, "output_type": "execute_result" } ], "source": [ "zh=3\n", "@interact\n", "def _(zhs=slider(1,14,step_size=1,default=3,label='zh (Tage)')):\n", " global zh\n", " zh=zhs\n", " show(html(\"Der Zeithorizont für die Vorhersagen beträgt %i Tage.\"%(zh)))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "Es ist umstritten, wie die Passung einer nichtlinearen Regressionsfunktion $f$ zu einer gegebenen Datenreihe `dataP` am Besten definiert wird. Die Datenreihe der kumulierten Infektionszahlen weist Daten mit erheblichen Größenunterschieden auf. Bei größeren absoluten Werten der Daten erscheint auch eine größere absolute Abweichung der Funktionswerte von den Daten als akzeptable. Deshalb messen wir die Qualität der Regression hier mit dem relativen Residuum `rR2(dataP,f)`, das wie folgt definiert wird. \n", "\n", "Ist $\\vec{vd}$ der Vektor der beobachteten Daten und $\\vec{vf}$ der Vektor der entsprechenden Funktionswerte der Funktion $f$, so definieren wir $rR2(\\vec{vd},f)=\\frac{\\|\\vec{vd}-\\vec{vf}\\|}{\\|\\vec{vd}\\|}$. Je geringer dieser Wert desto genauer die Approximation.\n", "\n", "Das relative Residuum ist zu einem gegebenen Zeitpunkt $x$ für zwei Bereiche von Interesse.\n", "* Für den Bereich der Trainingsdaten von $0$ bis $x$ zur Beschreibung der Passgenauigkeit des Modells und\n", "* Für den Vorhersagebereich von $x+1$ bis $x+zh$ zur Einschätzung der Vorhersagequalität.\n", "Deshalb definieren wir noch $rR3(\\vec{vd},f,x_0,x_1)=rR2(\\vec{vd}|[x_0,x_1],f|[x_0,x_1])$, d.h. wir schränken die Argumente von $rR2$ auf den Bereich $[x_0,x_1]$ ein, insbesondere für $x_0=0,x_1=x$ und $x_0=x+1,x_1=x+zh$.\n", "\n", "Damit wird die Modelltoleranz $MT(\\vec{vd},f,x)=rR3(\\vec{vd},f,0,x)$ und die Vorhersagetoleranz $VT(\\vec{vd},f,x,zh)=rR3(\\vec{vd},f,x+1,x+zh)$. Je kleiner diese Werte sind, desto besser beschreibt das Modell die Trainigsdaten bzw. desto besser ist die Vorhersage.\n", "\n", "Es sei zugegeben, dass in der Wahl dieser Definitionen eine gewisse Willkür steckt. **Der Leser wird deshalb ausdrücklich ermutigt, die Definitionen in der folgenden Zelle durch eigene zu ersetzen!**" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "Residuen sind definiert" ], "text/plain": [ "Residuen sind definiert" ] }, "execution_count": 34, "metadata": { }, "output_type": "execute_result" } ], "source": [ "# Definition Residuum\n", "def R2(dataP,f):\n", " return (vector([(p[1]-f(p[0])) for p in dataP]).norm().n())^2\n", "#Definition Residuum mit relativem Fehler\n", "def rR2(dataP,f):\n", " return vector(RR,[p[1]-f(p[0]) for p in dataP]).norm()/vector(RR,[p[1] for p in dataP]).norm()\n", "def rR3(dataP,f,x0,x1):\n", " return rR2(dataP[x0:x1+1],f)\n", "#Definition Modell-Toleranz\n", "def MT(dataP,f,x):\n", " return rR3(dataP,f,0,x)\n", "#Definition Vorhersage-Toleranz\n", "def VT(dataP,f,x,z):\n", " return rR3(dataP,f,x,x+z)\n", "html(\"Residuen sind definiert\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "## Exponentielles Modell\n", "\n", "In der ersten Phase der Epidemie, etwa bis zum 31.3.2020 (Tag 36), beschreibt ein einfaches Modell des exponentiellen Wachstums die Entwicklung der Zahl der vom Robert-Koch-Institut gemeldeten Infektionsfälle recht gut. Die realen Fallzahlen schwanken in geringem Maße um den Verlauf einer approximierenden Exponentialfunktion. Wie wir sehen werden, wird die Abweichung Ende März größer als die vorherige zufällige Schwankungsbreite - das Modell eines exponentiellen Verlaufs stößt an seine Grenzen.\n", "\n", "Das exponentielle Modell geht von der einzigen Annahme aus, dass die Zahl der Neuinfektionen in einem kleinen Zeitraum $\\Delta x$ proportional ist zur Zahl der zu Beginn Infizierten $I(x)$ und zur Länge des Zeitraums:\n", "\n", "$I(x+\\Delta x) = c\\cdot \\Delta x \\cdot I(x)$.\n", "\n", "$c$ ist dabei proportional zur Wahrscheinlichkeit, dass sich eine Person infiziert. Für $\\Delta x \\rightarrow 0$ ergibt sich daraus die Differentialgleichung $I'=c\\cdot I(x)$ mit der Lösung $I(x)=ae^{cx}$, wobei $a=I(0)$ der Anfangswert ist. $c$ bestimmt, wie steil die Exponentialfunktion ansteigt.\n", "\n", "Das exponentielle Modell beschreibt ein ungehemmtes und unbegrenztes Wachstum und vernachlässigt Genesungen - wie wir sehen werden in der Anfangsphase der Pandemie durchaus zu Recht.\n", "\n", "Für die Berechnung der passenden Parameter $a,c$ stellt uns SageMath die funktion`find_fit` zur Verfügung. Diese Funktion versucht mittels Regressionsverfahren eine Funktion zu finden, die möglichst gut zu den gegebenen Werten passt." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "### Zahl der Infektionen\n", "\n", "Das folgende Diagramm zeigt die kumulierte Zahl der Infektionen in Deutschland nach Angaben des Robert-Koch-Instituts vom 24.2.2020 (Tag 0) bis zu dem mit dem Schieberegler bestimmten Tag (grüne Linie). Die rote Kurve stellt eine Exponentialfunktion dar, die den Verlauf der Infektionszahlen bis zu diesem Tag möglichst gut approximiert und für den gewählten Zeithorizont `zh` darüber hinaus. Für diesen Tag werden Modell-Tolearanz und Vorhersage-Toleranz angezeigt." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "31e4ba1108d345c8a4d56f464a0bacf9", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " Tag: TransformIntSlider(value=20, descript…" ] }, "execution_count": 9, "metadata": { }, "output_type": "execute_result" } ], "source": [ "dataExpNr_de=37\n", "@interact\n", "def _(Tag=slider(7,36,default=20,step_size=1)):\n", " infectionsTag=infections_de_points[0:Tag+zh+1]\n", " var('x,a,c')\n", " f_exp(x)=a*e^(c*x)\n", " q=find_fit(infectionsTag[0:Tag+1], f_exp, solution_dict = True)\n", " show(f_exp(a=q[a],c=q[c]))\n", " g(x)=f_exp(x,a=q[a],c=q[c])\n", " show(\"Modell-Toleranz:\",MT(infectionsTag,g,Tag))\n", " show(\"Vorhersage-Toleranz:\",VT(infectionsTag,g,Tag+1,zh))\n", " show(list_plot(infectionsTag)+plot(f_exp(a=q[a],c=q[c]), 0, Tag+zh, color='red')+line([(Tag,0),(Tag,g(Tag))],color='green'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "Bei einer rein exponentiellen Entwicklung $a e^{cx}$ sollen sich die Logarithmen der Werte entsprechend einer linearen Funktion $cx+\\ln(a)$ entwickeln. eine solche Funktion können wir mit Hilfe der linearen Regression näherungsweise bestimmen.\n", "\n", "Sehen wir uns deshalb die Logarithmen dieser Werte an. Dazu zeichnen wir eine passende Regressionsgerade und einen Korridor um diese Gerade, der die zufälligen Schwankungen begrenzt." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0.23548969330841651*x + 3.3731000021350055" ] }, "execution_count": 10, "metadata": { }, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 10, "metadata": { }, "output_type": "execute_result" } ], "source": [ "f_lin(x)=c*x+a\n", "infectionsLnExp_de_points=[(n,ln(infections_de[n])) for n in range(1,dataExpNr_de)]\n", "q=find_fit(infectionsLnExp_de_points, f_lin, solution_dict = True)\n", "show(f_lin(a=q[a],c=q[c]))\n", "delta=0.6\n", "list_plot(infectionsLnExp_de_points)+plot(f_lin(a=q[a],c=q[c]), 0, dataExpNr_de, color='red')+plot(f_lin(a=q[a],c=q[c])+delta, 0, dataExpNr_de, color='green')+plot(f_lin(a=q[a],c=q[c])-delta, 0, dataExpNr_de, color='green')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "Wie man sieht, verlassen die Logarithmen der kumulierten Infektionszahlen um den Tag 36 (31.3.2020) den Korridor der zufälligen Schwankungen. Dieser Trend setzte sich in den folgenden Tagen fort wie man sehen kann, wenn man die Berechnungen mit `dataExpNr` > 36 wiederholt." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Sehen wir uns die Entwicklung der Modell-Toleranz und der Vorhersage-Toleranz während der exponentiellen Phase an. Wir sehen, dass eine gute Passung des Modells zu den bisher beobachteten Daten kein Garant für eine gute Vorhersage ist. Dies gilt insbesondere in der frühen Phase, als noch relativ wenige Daten vorlagen, als auch gegen Ende der exponentiellen Phase, als das Modell beginnt, seine Passgenauigkeit zu verlieren.\n", "\n", "Es könnte sein, dass eine kontinuierliche Verschlechterung der Vorhersagequalität ein Frühindikator dafür ist, dass das Modell an seine Grenzen stößt, auch wenn die bisherige Passung des Modells zu den Daten noch recht gut ist.\n", "\n", "Mit dem Schieberegler im folgenden Diagramm können Sie die Werte dadurch glätten, dass jeweils mit dem arithmetischen Mittel der kumulierten Infektionszahlen der letzten $w$ Tage gerechnet wird ($w=0\\ldots zh$)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7b75471d11a342c1b1572f492753a094", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " w: TransformIntSlider(value=1, description…" ] }, "execution_count": 11, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def infMittel(w):\n", " return [(n,mean(infections_de[n+1-w:n+1])) for n in range(w,dataNr_de)]\n", "def tres(dataP,Tag):\n", " infectionsTag=dataP[0:Tag+zh+1];\n", " f_exp(x)=a*e^(c*x)\n", " q=find_fit(infectionsTag[0:Tag+1], f_exp, solution_dict = True)\n", " g(x)=f_exp(x,a=q[a],c=q[c])\n", " return [MT(infectionsTag,g,Tag),VT(infectionsTag,g,Tag+1,zh)]\n", "@interact\n", "def _(w=slider(1,zh,step_size=1,default=1)):\n", " inf1=infMittel(w)\n", " mt=[(n,tres(inf1,n)[0]) for n in range(7,dataExpNr_de-zh)]\n", " vt=[(n,tres(inf1,n)[1]) for n in range(7,dataExpNr_de-zh)]\n", " show(list_plot(mt,color='blue',legend_label='Modell-Toleranz')+list_plot(vt,color='red',legend_label='Vorhersage-Toleranz'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### Verdopplungsrate\n", "\n", "Am 28.3.2020 [erklärte Kanzleramtschef Braun](https://www.tagesspiegel.de/politik/kanzleramtschef-erteilt-rascher-lockerung-eine-absage-bis-20-april-bleiben-alle-coronavirus-massnahmen-bestehen/25690036.html): \n", "\n", "> Wenn wir es schaffen, die Infektionsgeschwindigkeit so zu verlangsamen, dass wir zehn, zwölf oder noch mehr Tage haben bis zu einer Verdopplung, dann wissen wir, dass wir auf dem richtigen Weg sind.\n", "\n", "Wir definieren die Verdopplungsrate zu einem Zeitpunkt $x$ als die kleinste Zahl $d$, so dass die kumulierte Zahl der Infizierten zum Zeitpunkt $x-d$ höchstens halb so groß ist, wie die kumulierte Zahl der Infizierten zum Zeitpunkt $x$. Betrachten wir die Verdopplungsrate in der exponentiellen Phase im März 2020." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 12, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def d(dataP,x):\n", " xy=dataP[x]\n", " xd=x\n", " while 2*dataP[xd]>xy:\n", " xd=xd-1\n", " return x-xd\n", "double= [(x,d(infections_de,x)) for x in range(5,dataExpNr_de)]\n", "list_plot(double)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Da die Berechnungen nur taggenau erfolgen können Verzögerungen in der Meldepraxis durchaus zu Sprüngen von $\\pm 1$ Tag führen. Wie wir sehen, ist die Verdopplungsrate im März 2020 weit vom Zielwert von 10-12 entfernt, auch wenn ein Anstieg festzustellen ist.\n", "\n", "Nun hat jede Exponentialfunktion $e^{kx}$ eine konstante Verdopplungsrate von $\\frac{\\ln 2}{k}$. Eine Änderung der Verdopplungsrate zeigt also an, dass der Parameter $k$ des exponentiellen Modells angepasst werden muss - bzw. dass das exponentielle Modell an die Grenzen seiner Leistungsfähigkeit stößt.\n", "\n", "In der folgenden Aufgabe geht es um die Berechnung der Verdopplungsrate - nicht aufgrund der realen Daten sondern aufgrund des Ende März bestmöglichen exponentiellen Modells. Vergleichen Sie die Ergebnisse mit obigem Diagramm.\n", "\n", "\n", "\n", "Wie in dieser Aufgabe berechnen wir die Verdopplungsrate des zu einem Zeitpunkt besten exponentiellen Modells im Laufe des März 2020:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 13, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def dExp(dataP,Tag):\n", " infectionsTag=dataP[0:Tag]\n", " var('x,a,c')\n", " f_exp(x)=a*e^(c*x)\n", " q=find_fit(infectionsTag[0:Tag+1], f_exp, solution_dict = True)\n", " return (log(2)/q[c]).n()\n", "list_plot([(n,dExp(infections_de_points,n)) for n in range(5,dataExpNr_de)])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Wir bemerken, dass die Entwicklung der Verdopplungsrate der exponentiellen Modelle ein deutlicheres Bild von der Entwicklung der Pandemie vermittelt als die tag-genaue Bestimmung der Verdopplungsrate in den realen Daten, ohne Berücksichtigung der Modelle." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Logistisches Modell\n", "\n", "Ab Anfang April 2020, kann das Wachstum der Zahl der gemeldeten Infektionen immer schlechter durch Exponentialfunktionen beschrieben werden. Das Virus stößt - aus welchen Gründen auch immer - auf Faktoren, die seine Ausbreitung behindern (z.B. Senkung der Reproduktionsrate durch Einschränkung sozialer Kontakte, hoher Grad der Durchseuchung der Bevölkerung).\n", "\n", "Solche begrenzenden Faktoren werden im logistischen Modell ([SI-Modell](https://de.wikipedia.org/wiki/SI-Modell)) berücksichtigt. Dieses Modell nimmt an, dass es eine obere Grenze $N$ für die Zahl der Infizierten gibt. Dabei kann $N$ durchaus kleiner als die reale Gesamtbevölkerung sein, denn manche Teile der Bevölkerung kommen z.B. durch Kontaktbeschränkungen, Vorsichtsmaßnahmen oder geographische Beschränkungen nie in Kontakt mit dem Virus. Die Gruppe der für die Virusausbreitung relevanten $N$ Personen wird zu jedem Zeitpunkt $x$ unterteilt in die $I(x)$ infizierten und die $S(x)$ noch infizierbaren (Susceptibles). Damit ist für alle $x$ $S(x)+I(x)=N$ - $S(x)$ ergibt sich für festes $x$ aus $I(x)$ durch $S = N-I$.\n", "\n", "Wir bemerken, dass $\\frac{S(x)}{N}$ die Wahrscheinlichkeit dafür ist, dass eine zum Zeitpunkt $x$ zufällig ausgewählte Person infizierbar ist. Das logistische Modell nimmt an, dass der Zuwachs an Infektionen in einem kleinen Zeitraum proportional zur Länge des Zeitraums, zur Zahl der zu Beginn Infizierten und zu dieser Wahrscheinlichkeit ist: \n", "\n", "$$I(x+\\Delta x) - I(x) = c\\cdot \\Delta x\\cdot\\frac{S(x)}{N}\\cdot I(x) = c \\cdot \\Delta x\\cdot \\frac{N-I(x)}{N}\\cdot I(x)$$ \n", "\n", "Daraus ergibt sich für $\\Delta x \\rightarrow 0$ die logistische Differentialgleichung $$I' = c\\cdot\\frac{N-I}{N}\\cdot I.$$\n", "\n", "Die allgemeine [Lösung der logistischen Differentialgleichung](http://statistik.wu-wien.ac.at/~leydold/MOK/HTML/node183.html) wird durch eine logistische Funktion $$I(x)=a\\cdot \\frac{N}{a+(N-a)\\cdot e^{-c x}}$$ beschrieben. Dabei ist $a$ der Anfangswert bei $x=0$, $N$ ist eine angenommene Sättigungsgrenze, der sich die Zahl der Infizierten asymptotisch annähert (Kapazitätsgrenze) und $c$ ist ein Parameter der die Geschwindigkeit dieser Annäherung beschreibt. \n", "\n", "Das logistische Modell betrachtet alle Infizierten als infektiös, berücksichtigt also Todesfälle und Immunität nicht. Dies erfolgt im verfeinerten SIR-Modell." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### Zahl der Infektionen\n", "\n", "Versuchen Sie in der folgenden Aufgabe mit Hilfe der Schieberegler eine logistische Funktion zu finden, die möglichst genau zu den Daten passt, die den Verlauf der Epidemie in der VR China im Januar 2020 darstellen.\n", "\n", "In der Literatur werden unterschiedliche Bezeichnungen verwendet; so werden unsere Konstanten $N,c$ in der folgenden Aufgabe mit $S,k\\cdot S$ bezeichnet.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Versuchen wir nun automatisch eine logistische Funktion für die Entwicklung der COVID-19-Pandemie in Deutschland zu bestimmen, welche die Zahl der Infizierten bis Ende März (Tag 67) möglichst gut beschreibt. Als Startwerte für die Regression nehmen wir $a=400$ und $k=0.14$, was den Koeffizienten des exponentiellen Modells Ende März entspricht und $S=2 000 000$, was von der Größenordnung her plausibel erscheint.\n", "\n", "Mit den Schiebereglern können Sie die Startwerte ändern. Die Startfunktion wird grün dargestellt, das Ergebnis der logistischen Regression in rot." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f223e6eb307f4e92af425247450b35cc", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 3 widgets\n", " a0: TransformIntSlider(value=400, descrip…" ] }, "execution_count": 14, "metadata": { }, "output_type": "execute_result" } ], "source": [ "Tag=67\n", "infectionsTag67=infections_de_points[5:Tag+1]\n", "@interact\n", "def _(a0=slider(100,1000,default=400,step_size=100),N0=slider(150000,250000,default=200000,step_size=10000),c0=slider(0.1,0.2,default=0.14,step_size=0.01)):\n", " var('a,N,c,x')\n", " f_log(a,N,c,x)=a*N/(a+(N-a)*e^(-c*x))\n", " q=find_fit(infectionsTag67, f_log, variables=[x],parameters=[a,N,c],initial_guess=(a0,N0,c0),solution_dict = True)\n", " list_plot(infectionsTag67)\n", " show(list_plot(infectionsTag67)+plot(f_log(a=a0,N=N0,c=c0), 5, Tag,color='green')+plot(f_log(a=q[a],N=q[N],c=q[c]), 5, Tag,color='red'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Wie für das exponentielle Modell können nun für jeden Tag (grün) Modell- und Vorhersage-Toleranz des optimalen logistischen Modells (rot) berechnen.\n", "\n", "**Frage:** Wie verhalten sich Toleranzen des logistischen Modells und des exponentiellen Modells (s.o.) in der exponentiellen Phase (also vor Tag 36) zueinander?" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "4630df4a649e472aa994ab9d65cc8f96", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " Tag: TransformIntSlider(value=50, descript…" ] }, "execution_count": 15, "metadata": { }, "output_type": "execute_result" } ], "source": [ "dataLogNr_de=dataNr_de\n", "@interact\n", "def _(Tag=slider(7,dataLogNr_de,default=50,step_size=1)):\n", " infectionsTag=infections_de_points[0:Tag+zh+1]\n", " var('a,N,c,x')\n", " f_log(a,N,c,x)=a*N/(a+(N-a)*e^(-c*x))\n", " q=find_fit(infectionsTag67, f_log, variables=[x],parameters=[a,N,c],initial_guess=(400,200000,0.14),solution_dict = True)\n", " g(x)=f_log(a=q[a],N=q[N],c=q[c])\n", " show(\"a=\",q[a],\" N=\",q[N],\" c=\",q[c])\n", " show(\"Modell-Toleranz:\",MT(infectionsTag,g,Tag))\n", " show(\"Vorhersage-Toleranz:\",VT(infectionsTag,g,Tag+1,zh))\n", " show(list_plot(infectionsTag)+plot(g, 0, Tag+zh, color='red')+line([(Tag,0),(Tag,g(Tag))],color='green'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Das folgende Diagramm stellt die Entwicklung der Modell- und Vorhersage-Toleranz für das SI-Modell nach dem Ende der exponentiellen Phase bis Ende Juni 2020 dar. Mit dem Regler $w=0\\ldots zh$ kann bestimmt werden, ob mit den Original-Infektionszahlen ($w=1$) oder mit dem gleitenden Durchschnitt der letzten $w$ Tage gerechnet wird." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c1bb3d42a06c40648c6f1bed60144174", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " w: TransformIntSlider(value=1, description…" ] }, "execution_count": 16, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def tresLog(dataP,Tag):\n", " infectionsTag=dataP[0:Tag+zh+1];\n", " var('a,N,c,x')\n", " f_log(a,N,c,x)=a*N/(a+(N-a)*e^(-c*x))\n", " q=find_fit(infectionsTag67, f_log, variables=[x],parameters=[a,N,c],initial_guess=(400,200000,0.14),solution_dict = True)\n", " g(x)=f_log(a=q[a],N=q[N],c=q[c])\n", " return [MT(infectionsTag,g,Tag),VT(infectionsTag,g,Tag+1,zh)]\n", "@interact\n", "def _(w=slider(1,zh,step_size=1,default=1)):\n", " inf1=infMittel(w)\n", " mt=[(n,tresLog(inf1,n)[0]) for n in range(37,dataNr_de-zh-1)]\n", " vt=[(n,tresLog(inf1,n)[1]) for n in range(37,dataNr_de-zh-1)]\n", " show(list_plot(mt,color='blue',legend_label='Modell-Toleranz')+list_plot(vt,color='red',legend_label='Vorhersage-Toleranz'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Wie wir sehen, erreicht das logistische Modell um Tag 64 (28.4.2020) mit Modell- und Vorhersage-Toleranzen von etwa 3.3% seine maximale Leistungsfähigkeit bei einem 3-Tages-Horizont für die Vorhersagen. \n", "\n", "Bis zu diesem Zeitpunkt ist die Vorhersage-Toleranz sogar besser, als die Modell-Toleranz. Wir können dies dadurch erklären, dass sich das Verhalten der Pandemie von Tag zu Tag besser durch ein logistisches Modell beschreiben lässt." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### Verdopplungsraten\n", "\n", "Sehen wir uns zunächst die realen Verdopplungszahlen an, d.h. wir bestimmen für die Zeit nach der exponentiellen Phase zu jedem Tag x wie viele Tage vorher die kumulierten Infektionszahlen halb so hoch waren. Die grüne Linie zeigt die angestrebte Verdopplungsrate von 11." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 17, "metadata": { }, "output_type": "execute_result" } ], "source": [ "doubleL= [(x,d(infections_de,x)) for x in range(dataExpNr_de,dataNr_de)]\n", "list_plot(doubleL)+plot(11,x,dataExpNr_de,dataNr_de,color='green')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Die Verdopplungsrate von 11 Tagen wird am Tag 44 (8.4.2020) erreicht. Wir beobachten eine kontinuierlichere - sogar fast lineare -Entwicklung als in der exponentiellen Phase. Dies wird noch deutlicher, wenn man den Beginn des dargestellten Zeitraums `dataExpMr_de` etwa durch 5 ersetzt." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Wie für Exponentialfunktionen können wir auch für logistische Funktionen $L(x)=a \\frac{N}{a+(N-a)e^{-cx}}$ eine Verdopplungsrate berechnen. Gesucht wird dafür zu gegebenem x ein Wert $d$, so dass $L(x-d)=\\frac{1}{2}L(x)$. Dieser Wert $d$ hängt natürlich von $a,S,c$ ab.\n", "\n", "SageMath liefert uns eine Lösung für diese Gleichung und damit für die Verdopplungsrate des jeweiligen logistischen Modells:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "d(a,N,c,x)= (c*x + log((a*e^(c*x) + 2*N - 2*a)*e^(-c*x)/(N - a)))/c" ] }, "execution_count": 18, "metadata": { }, "output_type": "execute_result" } ], "source": [ "var('x,a,k,N,d,D')\n", "L(a,N,c,x)=a*N/(a+(N-a)*e^(-c*x))\n", "ss(a,N,c)=solve(L(a,N,c,x-d) == 0.5*L(a,N,c,x),d)\n", "d(a,N,c,x)=ss[0].rhs().simplify_full()\n", "show(LatexExpr(\"d(a,N,c,x)=\"),d(a,N,c,x))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Damit könnte man versuchen, die Verdopplungsrate für die Zukunft vorherzusagen. Es ist jedoch zu erwarten, dass im Falle der COVID-19-Pandemie eine einfache lineare Regression der realen Verdopplungsraten ein besseres Ergebnis liefert, als es logistische Modelle mit ihrer schließlich wachsenden Modell- und Vorhersage-Toleranz liefern könnten. Wir verzichten deshalb darauf, dies weiter zu untersuchen." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## SIR-Modell\n", "\n", "Das SIR-Modell unterscheidet sich vom exponentiellen und logistischen (SI-)Modell dadurch, dass es Genesene und Verstorbene berücksichtigt und davon ausgeht, dass diese nicht mehr infektiös sind. Wir fassen Genesene und verstorbene in der Gruppe $R$ (recovered) zusammen. Die Größe dieser Gruppe zum Zeitpunkt $x$ bezeichnen wir mit $R(x)$.\n", "\n", "Das SIR-Modell versucht, Funktionen zu berechnen, die\n", "
    \n", "
  • die Zahl der Infektiösen $I_{SIR}$
    • \n", "
  • die Zahl der Infizierbaren $S_{SIR}$ und
    • \n", "
  • die Zahl der Genesenen bzw. Verstorbenen $R_{SIR}$\n", "
\n", "beschreiben. Es gilt also für die im exponentiellen und logistischen Modell approximierte kumulative Zahl der Infizierten $I=I_{SIR}+R_{SIR}$ bzw. $I_{SIR}=I-R_{SIR}$. Die Zahl der Verstorbenen und Genesenen haben wir zu Beginn in die Variablen `deadsAll_de` bzw. `recoveredAll_de` abgespeichert und können damit nun auch $R_{SIR},I_{SIR}$ berechnen:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 46, "metadata": { }, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 46, "metadata": { }, "output_type": "execute_result" } ], "source": [ "R_SIR=[(n,deadsAll_de[n]+recoveredAll_de[n]) for n in range(0,dataNr_de)]\n", "I_SIR=[(n,infections_de[n]-R_SIR[n][1]) for n in range(0,dataNr_de)]\n", "md(u\"$R_{SIR}$ und $I_{SIR}$ berechnet\")\n", "show(list_plot(I_SIR,color='blue',legend_label='I_SIR: Infektioes'))\n", "show(list_plot(R_SIR,color='red',legend_label='R_SIR: Genesen oder Verstorben'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Die Berechnung der Zahl der Infizierbaren $S_{SIR}=N-I_{SIR}-R_{SIR}$ ist leider nicht unmittelbar möglich, da sie vom Parameter $N$ des Modells abhängt, der zunächst nicht bekannt ist." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "Funktion definiert" ], "text/plain": [ "Funktion definiert" ] }, "execution_count": 40, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def S_SIR(N):\n", " return [(n,N-I_SIR[n][1]-R_SIR[n][1]) for n in range(0,dataNr_de)]\n", "html(\"Funktion $S_{SIR}(N)$ definiert\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Das SIR-Modell nimmt an, dass die Zahl der in einem kurzen Zeitraum Genesenen oder Verstorbenen proportional zur vergangenen Zeit und zur Zahl der Infizierten ist: $$R_{SIR}(x+\\Delta x)-R_{SIR}(x) = w \\cdot \\Delta x\\cdot I_{SIR}(x)$$\n", "\n", "Daraus ergibt sich die Differentialgleichung $${R'}_{SIR}= w\\cdot I_{SIR}$$\n", "\n", "Wir bemerken, dass bei dieser Annahme nicht berücksichtigt wird, dass Genesung bzw. Versterben erst mehrere Tage (10-14 Tage) nach (Registrierung der) Infektion eintreten, so dass eher von einer Proportionalität mit $I_{SIR}(x-10)$ auszugehen wäre. Dies wird im SIR-Modell aber nicht berücksichtigt. \n", "\n", "Die Veränderung der Anzahl der Infizierten ergibt sich aus der Zahl der Neuinfektionen, die wie im SI-Modell berechnet wird, vermindert um die Zahl der in diesem Zeitraum Genesenen bzw. Verstorbenen: $$I_{SIR}(x+\\Delta x) -I_{SIR}(x) = \\Delta x\\cdot c \\cdot\\frac{S_{SIR}(x)}{N}\\cdot I_{SIR}(x)-(R_{SIR}(x+\\Delta x)-R_{SIR}(x))$$ woraus sich für $\\Delta x \\rightarrow 0$ die Differentialgleichung $${I'}_{SIR}=c\\cdot\\frac{S_{SIR}}{N}\\cdot I_{SIR}-{R'}_{SIR}=c\\cdot\\frac{S_{SIR}}{N}\\cdot I_{SIR}-w\\cdot I_{SIR}$$ ergibt.\n", "\n", "Aus diesen beiden Differentialgleichungen und dem Fakt, dass die Anzahl der Infizierten, Genesenen bzw. Verstorbenen und Infizierbaren als konstant gleich $N$ angenommen wird ergibt sich schließlich die dritte Differentialgleichung $${S'}_{SIR} = -c \\frac{S_{SIR}}{N} I_{SIR}$$\n", "\n", "Wir bemerken, dass das SI-Modell der Spezialfall des SIR-Modells mit der Genesungsrate $w=0$ ist.\n", "\n", "Wir speichern die rechten Seiten des SIR-Differentialgleichungssystems\n", "\n", "${S'}_{SIR} = -c \\frac{S_{SIR}}{N} I_{SIR}$\n", "\n", "${I'}_{SIR}=c\\cdot\\frac{S_{SIR}}{N}\\cdot I_{SIR}-w\\cdot I_{SIR}$\n", "\n", "${R'}_{SIR}= w\\cdot I_{SIR}$\n", "\n", "in der Funktion `DGL_right` ab, die von den Parametern $N,c,w$ abhängt:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "Differentialgleichungssystem definiert" ], "text/plain": [ "Differentialgleichungssystem definiert" ] }, "execution_count": 35, "metadata": { }, "output_type": "execute_result" } ], "source": [ "I,R,S,x = var('I R S x')\n", "def DGL_right(N,c,w):\n", " return [-c*(S/N)*I,c*(S/N)*I -w*I,w*I]\n", "html(\"Differentialgleichungssystem definiert\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Leider lässt sich diese Differentialgleichungssystem nicht in geschlossener Form lösen, so dass wir mit numerischen Näherungslösungen vorlieb nehmen müssen. SageMath stellt uns dafür die Funktion `desolve_system_rk4` zur Verfügung, die Differentialgleichungssysteme numerisch mit dem [Runge-Kutta-Verfahren](https://de.wikipedia.org/wiki/Klassisches_Runge-Kutta-Verfahren) löst. \n", "\n", "Dabei werden die Anfangswerte zum Beginn einer zu untersuchenden Periode vorgegeben und das Runge-Kutta-Verfahren berechnet schrittweise den Verlauf der Lösungen des Differentialgleichungssystems während dieser Periode. Um Datenreihen für die Lösung des SRI-Differentialgleichungssystems ab einem Tag $x_0$ zu berechnen benötigen wir also\n", "
    \n", "
  • Werte für die Parameter $N,c,w$ des Differentialgleichungssystems und
    • \n", "
  • Anfangswerte $i_0=I_{SRI}(x_0),r_0=R_{SRI}(x_0),s_0=S_{SRI}(x_0)$.
    • \n", "
\n", "Außerdem benötigen wir $x_0$ als Start der Periode, das Ende der Periode und die Schrittweite für die $x$-Werte, für die die Lösung berechnet werden soll." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "outputs": [ { "data": { "text/html": [ "Lösung des DGL-Systems definiert" ], "text/plain": [ "Lösung des DGL-Systems definiert" ] }, "execution_count": 48, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def SIR_solve(N,c,w,Ics,Start,End,Step):\n", " sol=desolve_system_rk4(DGL_right(N,c,w), [S,I,R], ics=Ics, ivar=x, end_points=[Start,End], step=Step)\n", " S_sol=[(s[0],s[1]) for s in sol]\n", " I_sol=[(s[0],s[2]) for s in sol]\n", " R_sol=[(s[0],s[3]) for s in sol]\n", " return [S_sol,I_sol,R_sol]\n", "html('Lösung des DGL-Systems definiert')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Berechnen wir als Erstes einmal eine Lösung für den Tag $x_0=64$ (28.4.2020), den Tag der besten Passung des logistischen Modells. Die logistische Regression lieferte für diesen Tag $N_0=157086.77914178697, c_0=0.14679874435677764$. Für $w_0$ wählen wir - angeregt durch die dritte Differentialgleichung unseres System $w_0=\\frac{R_{SIR}(x_0+1)-R_{SIR}(x_0)}{I_{SIR}(x_0)}$.\n", "Als Anfangswerte wählen wir $I_0=I_{SIR}(x_0),R_0=R_{SIR}(x0),S_0=N_0-R_0-I_0$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w0= 0.0969597868217054\n", "I0= 33024.0000000000 R0= 123313.000000000 S0= 749.779141786974\n" ] } ], "source": [ "x0=64; N0=157086.77914178697; c0=0.14679874435677764\n", "w0=(R_SIR[x0+1][1]-R_SIR[x0][1])/I_SIR[x0][1]\n", "print(\"w0=\",w0)\n", "I0=I_SIR[x0][1];R0=R_SIR[x0][1];S0=N0-I0-R0\n", "print(\"I0=\",I0,\" R0=\",R0,\" S0=\",S0)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "**Was dabei auffällt:** Der berechnete Wert $S_0$ von etwa 750 noch zu infizierenden ist - verglichen mit den Werten für $I_0,R_0$ - sehr klein. Dies könnte darauf hindeuten, dass $N_0$ zu klein gewählt ist.\n", "\n", "**Aufgabe:** Versuchen Sie, mit dem Schieberegler einen Wert für $N_0$ zu finden, der zu einer möglichst guten Approximation der realen Zahl der Infizierten führt." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "199ae48a068842798566f56b0e89b60b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " N1: TransformIntSlider(value=150000, descr…" ] }, "execution_count": 41, "metadata": { }, "output_type": "execute_result" } ], "source": [ "@interact\n", "def _(N1=slider(150000,300000,step_size=10000,default=150000,label=\"N0\")):\n", " global N0\n", " N0=N1\n", " sol0=SIR_solve(N1,c0,w0,[x0,N1-I0-R0,I0,R0],x0,dataNr_de,1)\n", " show(list_plot(sol0[1],color='red',plotjoined=True,legend_label=\"Infiziert - berechnet\")+list_plot(I_SIR[x0+1:dataNr_de],color='blue',legend_label=\"Infiziert - real\"))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "source": [ "Da das Runge-Kutta-Verfahreneine Datenreihe, keine Funktion, liefert (auch wenn wir dies hier durch eine Kurve darstellen), müssen wir unser Toleranzmaß neu definieren, wobei Funktionswerte durch die Daten ersetzt werden:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "Residuen sind für Datenreihen definiert" ], "text/plain": [ "Residuen sind für Datenreihen definiert" ] }, "execution_count": 49, "metadata": { }, "output_type": "execute_result" } ], "source": [ "# Definition Residuum\n", "# Es wird vorausgesetzt, dass dataP und dataQ Reihen von Punkten (i,_) der selben Länge für die selben Werte i sind\n", "def R2D(dataP,dataQ):\n", " return (vector([(dataP[i][1]-dataQ[i][1]) for i in range(0,len(dataP))]).norm().n())^2\n", "#Definition Residuum mit relativem Fehler\n", "def rR2D(dataP,dataQ):\n", " return vector(RR,[(dataP[i][1]-dataQ[i][1]) for i in range(0,len(dataP))]).norm()/vector(RR,[dataP[i][1] for i in range(0,len(dataP))]).norm()\n", "def rR3D(dataP,dataQ,x0,x1):\n", " return rR2D(dataP[x0:x1+1],dataQ[x0:x1+1])\n", "#Definition Modell-Toleranz\n", "def MTD(dataP,dataQ,x):\n", " return rR3D(dataP,dataQ,0,x)\n", "#Definition Vorhersage-Toleranz\n", "def VTD(dataP,dataQ,x,z):\n", " return rR3D(dataP,dataQ,x,x+z)\n", "html(\"Residuen sind für Datenreihen definiert\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Da das Runge-Kutta-Verfahren historische Werte vor den Anfangswerten nicht approximiert, macht die Berechnung der Modell-Toleranz keinen Sinn. Wir berechnen stattdessen die Vorhersage-Toleranz für die Zeit von Tag 64 bis Tag 104 für die drei Datenreihen, die mit Hilfe des Runge-Kutta-Verfahrens gefunden werden." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "text/html": [ "Wir verwenden dafür den von Ihnen gefundenen Wert 200000. Passen Sie diesen Wert ggf. mit dem obigen Schieberegler an und berechnen Sie die folgende Zelle neu." ], "text/plain": [ "Wir verwenden dafür den von Ihnen gefundenen Wert 200000. Passen Sie diesen Wert ggf. mit dem obigen Schieberegler an und berechnen Sie die folgende Zelle neu." ] }, "execution_count": 50, "metadata": { }, "output_type": "execute_result" } ], "source": [ "html(\"Wir verwenden dafür den von Ihnen gefundenen Wert $N_0=$%i. Passen Sie diesen Wert ggf. mit dem obigen Schieberegler an und berechnen Sie die folgende Zelle neu.\"%(N0))" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false, "jupyter": { "source_hidden": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vorhersage-Toleranz für Infizierte (Tag 64-104):0.207462\n" ] }, { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 51, "metadata": { }, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Vorhersage-Toleranz für Genesene/Verstorbene (Tag 64-104):0.037835\n" ] }, { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 51, "metadata": { }, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Vorhersage-Toleranz für Infizierbare (Tag 64-104):0.331696\n" ] }, { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 51, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "Maximale Voehersage-Toleranz: 0.331696" ], "text/plain": [ "Maximale Voehersage-Toleranz: 0.331696" ] }, "execution_count": 51, "metadata": { }, "output_type": "execute_result" } ], "source": [ "sol1=SIR_solve(N0,c0,w0,[x0,N0-I0-R0,I0,R0],x0,dataNr_de,1)\n", "solI=sol1[1]\n", "tolI=VTD(I_SIR[x0:],solI,0,104-x0)\n", "print(u\"Vorhersage-Toleranz für Infizierte (Tag %i-%i):%f\"%(x0,104,tolI))\n", "show(list_plot(sol1[1],color='red',plotjoined=True,legend_label=\"Infiziert - berechnet\")+list_plot(I_SIR[x0+1:dataNr_de],color='blue',legend_label=\"Infiziert - real\"))\n", "solR=sol1[2]\n", "tolR=VTD(R_SIR[x0:],solR,0,104-x0)\n", "print(u\"Vorhersage-Toleranz für Genesene/Verstorbene (Tag %i-%i):%f\"%(x0,104,tolR))\n", "show(list_plot(solR,color='red',plotjoined=True,legend_label=\"Genesen/Verstorben - berechnet\")+list_plot(R_SIR[x0+1:dataNr_de],color='blue',legend_label=\"Genesen/Verstorben - real\"))\n", "solS=sol1[0]\n", "tolS=VTD(S_SIR(N0)[x0:],solS,0,104-x0)\n", "print(u\"Vorhersage-Toleranz für Infizierbare (Tag %i-%i):%f\"%(x0,104,tolS))\n", "show(list_plot(solS,color='red',plotjoined=True,legend_label=\"Infizierbar - berechnet\")+list_plot(S_SIR(N0)[x0+1:dataNr_de],color='blue',legend_label=\"Infizierbar - real\"))\n", "maxTol=max(tolI,tolR,tolS)\n", "html(\"Maximale Vorhersage-Toleranz: %f\"%(maxTol))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Wenn Sie mit unterschiedlichen Werten für $N_0$, bzw. allgemein mit unterschiedlichen Parametern $N,c,w$ für das SRI-Differentialgleichungssystem experimentieren so werden Sie bemerken, dass sich bei manchen Änderungen der Parameter die Vorhersage-Toleranz für eine der Datenreihen verbessert, während sie sich für eine andere verschlechtert. Somit ist es vom Ziel der Analyse abhängig, wie man ein Maß für die Qualität eines konkreten SIR-Modells definieren wird." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Fazit\n", "\n", "Wir haben gesehen, dass die COVID-19-Pandemie sich in Deutschland 2020 in mehreren Phasen entwickelt hat, in denen Sie sich durch unterschiedliche mathematische Modelle mehr oder weniger gut beschreiben lässt.\n", "\n", "* In der ersten Phase, etwa bis Ende März erfolgt die Ausbreitung des Virus im Wesentlichen ungehemmt, so dass sie sich am Besten mit einem exponentiellen Modell beschreiben lässt.\n", "* In der zweiten Phase, die etwa bis Anfang Mai 2020 geht, wird die Ausbreitung des Virus gehemmt - das SI-Modell erweist sich als optimal zur Beschreibung der Situation.\n", "* Die dritte Phase umfasst den Zeitraum von Anfang Mai bis Mitte Juni 2020. Die Lockdown-Maßnahmen wirken, Infektionsketten werden unterbrochen, immer mehr Personen scheiden nach überstandener Krankheit aus dem Infektionsgeschehen aus. Jetzt kann das SIR-Modell die Entwicklung am Besten beschreiben.\n", "* Schließlich werden in Phase 4 Lockdown-Maßnahmen gelockert, das Infektionsgeschehen ist örtlich sehr unterschiedlich. Damit verlieren Deutschland-weite Modelle an Bedeutung; andere Modelle, insbesondere zur Modellierung der räumlichen Ausbreitung des Virus, gewinnen an Bedeutung.\n", "\n", "Wir haben auch gesehen, wie Modelle altern. Um die Vorhersagequalität eines Modells zu erhalten ist es erforderlich, seine Parameter kontinuierlich anzupassen - solange wie dies möglich ist und kein kein besseres Modell zur Verfügung steht." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Ausblick\n", "\n", "Dieses Notebook stellt notwendigerweise eine subjektive Auswahl der Möglichkeiten und Ansätze zur Modellierung einer Pandemie dar. So gibt es auch viele ebenso berechtigte Möglichkeiten zur Analyse der Pandemie-Daten, die sich durch Erweiterung und/oder Modifikation dieses Notebooks implementieren lassen. Hier einige Anregungen.\n", "* Analyse der Todesfallzahlen, deren Daten in der Variablen `deadsAll_de` zur Verfügung stehen\n", "* Regression der Parameter des SIR-Modells zur Modell-Optimierung\n", "* Analyse der Entwicklung der für den jeweiligen Tag optimierten Modell-Parameter\n", "\n", "So möge dieses Notebook vor allem Anregung zu eigener aktiver Beschäftigung mit mathematischen Modellen sein." ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "metadata": { "cocalc": { "description": "Open-source mathematical software system", "priority": 1, "url": "https://www.sagemath.org/" } }, "name": "sage" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }