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Commit 4060a45b authored by Martin Lehoux's avatar Martin Lehoux
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add article tex files

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\relax
\catcode `:\active
\catcode `;\active
\catcode `!\active
\catcode `?\active
\select@language{french}
\@writefile{toc}{\select@language{french}}
\@writefile{lof}{\select@language{french}}
\@writefile{lot}{\select@language{french}}
\@writefile{toc}{\contentsline {section}{\numberline {1}Mod\IeC {\`e}le math\IeC {\'e}matique de la dynamique d'un r\IeC {\'e}servoir}{1}}
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\documentclass[twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\title{Rapport sur la dynamique de l'évolution des populations, appliquée à l'épidémiologie}
\author{Martin \textsc{Lehoux} \and Paul \textsc{Cacheux}}
\date{\today}
\begin{document}
\maketitle
\newpage
\tableofcontents
\newpage
\section{Modèle mathématique de la dynamique d'un réservoir}
On s'intérèsse à l'évolution d'une population sans échanges avec l'extérieur. Cette population est composée de catégories, que nous expliciterons dans la suite.
On peut représenter les échanges entre différentes catégories dans cette population, par un graphe stochastique, dont les différents coefficients peuvent dépendre
des catégories elles mêmes. On tombe ici sur une première problématique : notre système n'est alors pas linéaire,
et on ne peut le représenter par une chaîne de Markov. Deux options se présentent alors à nous :
\begin{itemize}
\item Pour Matlab, il est nécessaire de linéariser le système autour d'un point d'équilibre afin d'effectuer des analyses de stabilité.
\item Pour Python, on peut tout simplement recalculer la matrice de transition à chaque pas de calcul.
\end{itemize}
\end{document}
\ No newline at end of file
\select@language {french}
\contentsline {section}{\numberline {1}Mod\IeC {\`e}le math\IeC {\'e}matique de la dynamique d'un r\IeC {\'e}servoir}{1}
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