141 lines
3.5 KiB
TeX
141 lines
3.5 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Modélisation suite - Cours}
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\date{septembre 2020}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\section{Modélisation avec des suites}
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En se basant sur les premières données de malade du covid19, nous avons cherché à prédire le nombre de contaminés les jours suivants.
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\begin{center}
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\begin{tabular}{|l|c|}\hline%
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\bfseries Jour & \bfseries Nombre de cas
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\csvreader[head to column names]{./covid_0226_0301.csv}{}%
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{\\\jours & \cas}%
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\\\hline
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\end{tabular}
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\smallskip
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\textbf{Document:} Nombre de cas cumulé de covid
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\end{center}
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Pour cela, nous avons étudié deux modèles
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\bigskip
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\begin{minipage}{0.5\textwidth}
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\begin{center}
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Modèle 1: Linéaire
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\end{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[0.5cm]{}};
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\node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{}};
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%Lines
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\path[->] (leftterme.east) edge [bend left] node [above] {$+$....} (centerterm.west);
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\end{tikzpicture}
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\hspace{1cm}
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$ u_{n+1} = u_n + .... $
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\medskip
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C'est une suite \textbf{arithmétique}.
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\medskip
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\begin{center}
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\begin{tabular}[b]{|c|p{4cm}|}
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\hline
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Jour & Prévisions \\
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\hline
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01/03 & $u_0 = 130$ \\
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\hline
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02/03 & $u_1 = ...$ \\
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\hline
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03/03 & $u_2 = ...$ \\
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\hline
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04/03 & $u_3 = ...$ \\
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\hline
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05/03 & $u_4 = ...$ \\
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\hline
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16/03 & $u_{...} = ...$ \\
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\hline
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\end{tabular}
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\medskip
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\begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=1]
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\tkzInit[xmin=0,xmax=5,xstep=1,
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ymin=0,ymax=5,ystep=1]
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\tkzDrawX[noticks]
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\tkzDrawY[noticks]
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{center}
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Modèle 2: Exponentiel
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\end{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[0.5cm]{}};
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\node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{}};
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%Lines
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\path[->] (leftterme.east) edge [bend left] node [above] {$\times$....} (centerterm.west);
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\end{tikzpicture}
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\hspace{1cm}
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$ u_{n+1} = u_n \times .... $
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\medskip
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C'est une suite \textbf{géométrique}.
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\medskip
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\begin{center}
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\begin{tabular}{|c|p{4cm}|}
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\hline
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Jour & Prévisions \\
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\hline
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01/03 & $u_0 = 130$ \\
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\hline
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02/03 & $u_1 = ...$ \\
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\hline
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03/03 & $u_2 = ...$ \\
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\hline
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04/03 & $u_3 = ...$ \\
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\hline
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05/03 & $u_4 = ...$ \\
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\hline
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16/03 & $u_{...} = ...$ \\
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\hline
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\end{tabular}
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\medskip
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\begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=1]
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\tkzInit[xmin=0,xmax=5,xstep=1,
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ymin=0,ymax=5,ystep=1]
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\tkzDrawX[noticks]
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\tkzDrawY[noticks]
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\end{document}
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