The Application Outbreaks, from Ebola to Zika and currently the flu, have long caught the attention of the world. In this homework, we will use a timestepping algorithm to model a hypo- thetical Ebola outbreak. The basis of your analysis will be the Kermack-McKendrick model for an epidemiological outbreak. Let V(t) e R' be your outbreak vector, where Vi(t)-susceptible population Vs(t) = recovered population then the governing set of differential equations are (t)-infected population V,(t) = number of deaths dV(t) P 100 100 F(t, V) V(0) = 1.0 = dt where the rate equation is given by The model parameters are (with initial values given) c(t) g(t) 7(t) 6(t) 3(t) P average number of contacts per individual per day ( 100) likelihood infection contact results in transmission (q = 0.001) per capita recovery rate ( = 1 /30) per capita fatality rate (8-1/30) c(t)g(t-transmission rate total population at onset of outbreak (P = 3 x 108). = = = = = The unit of time is measured in days. Given the suddenness of this outbreak, there are two options being considered on how to use resources: Option 1 The first option is to spend resources on treatment so that ninety percent of the infected fully recover. This will take three months to implement. This means that 1/30 1,150 t