From 29c8f0722989773f342e891f4e0f3ebc565b92db Mon Sep 17 00:00:00 2001 From: Jannis Portmann Date: Fri, 23 Jul 2021 12:18:47 +0200 Subject: [PATCH] Expand SIR --- Mathematik-V-ZF.tex | 23 +++++++++++++++++++---- img/SIR.png | Bin 0 -> 60406 bytes 2 files changed, 19 insertions(+), 4 deletions(-) create mode 100644 img/SIR.png diff --git a/Mathematik-V-ZF.tex b/Mathematik-V-ZF.tex index bc00fa1..893330d 100644 --- a/Mathematik-V-ZF.tex +++ b/Mathematik-V-ZF.tex @@ -219,12 +219,26 @@ Eigenwerte $\det(\textbf{J} - \lambda \textbf{I}) = 0$ wobei $\lambda \in \mathb \subsection{SIR-Modell} + SIR: Susceptible-Infected-Recovered \\ -\vspace{10px} + +\begin{figure}[H] + \centering + \includegraphics[width=.3\textwidth]{SIR.png} + \caption{SIR-Modell} + \label{fig:sir} +\end{figure} + +\begin{align*} + \frac{dS}{dt} &= \Lambda - \delta_SS - \beta S I \\ + \frac{dI}{dt} &= \beta S I - \delta_I - rI \\ + \frac{dR}{dt} &= rI - \delta_R \\ +\end{align*} + $\Lambda$: Geburten- oder Immigrationsrate \\ -$\delta_S, \delta_I, \delta_R$: Sterberaten der jeweiligen (Teil-)populationen -$r$: Erholungsrate von $I$ -$\beta S I$: Mass-action Infektionsrate +$\delta_S, \delta_I, \delta_R$: Sterberaten der jeweiligen (Teil-)populationen \\ +$r$: Erholungsrate von $I$ \\ +$\beta S I$: Mass-action Infektionsrate \\ \begin{itemize} \item Disease-free equilibrium: @@ -268,6 +282,7 @@ Jannis Portmann, FS21 \section*{Bildquellen} \begin{itemize} \item Abb. \ref{fig:geo-coordinates}: E\^(nix) \& ttog, \url{https://de.wikipedia.org/wiki/Geographische_Koordinaten#/media/Datei:Geographic_coordinates_sphere.svg} + \item Abb. \ref{fig:sir}: Vorlesungsunterlagen \end{itemize} \end{multicols*} diff --git a/img/SIR.png b/img/SIR.png new file mode 100644 index 0000000000000000000000000000000000000000..a54f0d95a768e54e208359b4df14e9916b6a65e0 GIT binary patch literal 60406 zcmag_1ytVZ)&&X!1&X!s;_hA?in}`$cXxMpcemmc_u^jMp|}-yC~n2!PxtQL=NtdM z=iGOUkdWj_9$jnBxmLpEWyRjXVZ(uefxVLu7ghiRgW?4P122Pt2F?(pYwm-AA()v9 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