Add SIR chapter

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jannisp 2021-07-22 16:54:20 +02:00
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@ -218,6 +218,21 @@ Eigenwerte $\det(\textbf{J} - \lambda \textbf{I}) = 0$ wobei $\lambda \in \mathb
\end{itemize} \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} \section{Taylor-Reihe}
An der stelle $a$ einer Funtkion $f(x)$ An der stelle $a$ einer Funtkion $f(x)$