From 42f30ce2a564378e747d4c9704b407bab98fa50a Mon Sep 17 00:00:00 2001
From: jannisp <jannisp@student.ethz.ch>
Date: Thu, 22 Jul 2021 16:54:20 +0200
Subject: [PATCH] Add SIR chapter

---
 Mathematik-V-ZF.tex | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/Mathematik-V-ZF.tex b/Mathematik-V-ZF.tex
index 38b5eee..c54dd78 100644
--- a/Mathematik-V-ZF.tex
+++ b/Mathematik-V-ZF.tex
@@ -218,6 +218,21 @@ Eigenwerte $\det(\textbf{J} - \lambda \textbf{I}) = 0$ wobei $\lambda \in \mathb
 \end{itemize}
 
 
+\subsection{SIR-Modell}
+SIR: Susceptible-Infected-Recovered \\
+\vspace{10px}
+$\Lambda$: Geburten- oder Immigrationsrate \\
+$\delta_S, \delta_I, \delta_R$: Sterberaten der jeweiligen (Teil-)populationen
+$r$: Erholungsrate von $I$
+$\beta S I$: Mass-action Infektionsrate
+
+\begin{itemize}
+    \item Disease-free equilibrium: 
+        $$S_f = \Lambda / \delta_S, I_f=0, R_f=0$$
+    \item Endemic equilibrium:
+        $$S = \frac{\delta_1 + r}{\beta} , I_e=\frac{\Lambda}{\delta_1} - \frac{\delta_S}{\beta}, R_e = \frac{r}{\delta_R}(\frac{\Lambda}{\delta_1 + r} - \frac{\delta_S}{\beta})$$
+    \item 
+\end{itemize}
 
 \section{Taylor-Reihe}
 An der stelle $a$ einer Funtkion $f(x)$