Question $4$: Sensitivity Analysis on Parameters

The value of $\backslash$mu is related to the flu$$s infectious period and the value of $\backslash$beta is an approximation of the flu$$s $$infectiousness$.$ Unfortunately, there is no way to directly observe $\backslash$beta $.$ Taken together, these values determine the disease$$s spread. In reality, $\backslash$mu and $\backslash$beta are a function of a city$$s population, density, and $$mixing rate$.$

Let$$s experiment with changes in $\backslash$beta $.$ Keep $\backslash$mu fixed at $1/3,$ and plot the graph of i$($t$)$ with several different values of $\backslash$beta between $0\mathrm{.}5$ and $2\mathrm{.}0.$

$4$a$.$

Use the slider in the script below to adjust $\backslash$beta $.$ You may also want to increase the interval of interest for time $($tspan$)$ to see the results for the lower levels of contact rate.

The code below also stores the peak levels of the infected population in an array and when they occur. Add a code to plot those results versus $\backslash$beta $.$