The Emory Class of 2018 is roughly 1800 students. Five seniors, while traveling

Question

The Emory Class of 2018 is roughly 1800 students. Five seniors, while traveling abroad during Spring Break, arrive back on campus infected with a highly contagious disease known as Folivorous Senioritis. Unfortunately, it begins to spread quickly. Initial estimates from Emory Student Health Services (SHS) indicate that the spread of the disease may be modeled by the S-I-R model discussed in class, taking = 0.001 and µ = 0.59.

a. Supposing we measure the rate in days, what is the rate of infection?

b. What is the rate of recovery?

c. What is the average duration of the infected period?

d. What value of S maximizes I?

e. Find I(S), that is, the number of infected seniors as a function of the susceptible population. (Hint: You will need the differential equations, the Chain Rule, the initial conditions, and a calculator )

f. Find the maximum value, Imax, of I(S).

g. If 900 of the seniors are vaccinated right at the start of the outbreak, how does the new value of Imax compare to the one in part f? What if 1300 seniors are vaccinated?

h. What is the maximum number of beds that SHS would need in the infirmary? (Hint: Assume a bed is immediately clean and ready whenever a senior recovers.)

i. Using an online calculator, estimate S = lim t S(t). What do you think this number signifies?

Explanation / Answer

Ans a. Considering the rate of infection as I'= µSI, {where µ= infection coefficient , S= No. of susceptible students and I= infected students}

S= 1795 (1800-5) and I = 5 (as given in the question) and µ= 0.59

I'= µSI, So, I'= 0.59 * 1795 * 5 = 2.95 days

b. Rate of recovery R'= * I = 0.001 * 5 = 0.005

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