2. Upon returning from leave, an individual returns to a remote research base with a staff of 9000 individuals. This individual is infected with the weird Austin flu! Suppose those who contact the Austin flu must be hospitalized and given fluids intravenously; the research base hospital has a total of 500 beds. The transmission coefficient depends on many factors, but for the Austin flu in a confined facility, it is thought that a reasonable value is a = 0.00004/day and the illness typically lasts for 5 days. You are the director for the infectious disease unit at the research station and you decide to predict what will happen with this virus using the SIR model! (a) Is the condition for an epidemic satisfied? (b) Use SIREuler to make a plot for S, I, and R over the course of this illness. (Provide these plots in your write up) (c) Will the research base have enough hospital beds? (d) How many at the base will eventually get the virus? 3. Suppose there is a vaccine for the Austin-influenza and a proportion p of the of the 9000 people are the base have been vaccinated. (a) Adjust the SIR model to account for the proportion that has been vaccinated (hint: the proportion 1p of the susceptible have not been vaccinated).