From 42f30ce2a564378e747d4c9704b407bab98fa50a Mon Sep 17 00:00:00 2001 From: jannisp 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 $f(x)$