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\begin{itemize}  \item how to estimate $R_0$  \end{itemize}  The recovery time for yellow fever is between 4-6 days. The graphs below have time intervals of one day on the x-axis, hence the parameter $\gamma$ should be calculated as the rate of recovery per day. Using the 4-6 day recovery time data, taking 5 as an average, it can be estimated the the parameter $\gamma$ is $\frac{1}{5}. $\frac{1}{5}$.  \subsection{Graphical Representation}  Public ASU (find correct name for source) has developed multiple programs in which parameters can be entered to produce a graph that shows the transition of individuals in a population between the three classification of susceptible, infected and removed. Having calculated $R_0$ to be roughly 18, and taking gamma to be $\frac{1}{5}$, we are able to calculate the value for $\beta$. This can be done such:  \begin{equation}