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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
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+\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}