1. There are 100,000 students, staff, and faculty with an account at ASU, and when the virus was discovered, there were already 1000 accounts infected and 2000 account recovered from the virus.From the data of the first hours of the virus spreading through the system, we know that = 0.001% and it takes 10 hours for an account to recover.See textbook for formulas.

A. What is the value of R0?

B. How many accounts need to be vaccinated to avoid an epidemic (users need to install a patch on their computer)? Round to the nearest percentage and do not include the % symbol (Example: if the answer is 82%, type 82 into the box below).

nothing%

2.Suppose a rumor is spreading that the government plans to give each college student $2000. Asssume that 40 people have heard the rumor as of today and that each day the number of people (past and present) who have heard it triples.

Let f(t) be the number of people (past and present) who have heard the rumor at t days since today.

a.	Find an equation of f.
b.	How many people (past and present) will have heard the rumor 10 days from now?
c.	How many people (past and present) will have heard the rumor 15 days from now? Has model breakdown occurred? [Hint: Assume that the population is 401 million.]

3.

Given is a predator-prey model with the following parameters: Carrying capacity is 1000, the regrowth rate of the prey is 10% per time step (0.10), the relative harvesting rate of predators of prey is 0.005, the relative growth burst of the predator population due to the availability of prey meat is 0.002, and the per capita death rate of the predators per time step is 0.7.

What are the equilibria? Equilibrium 1: No prey and No predators.

Equilibrium 2: 1000 prey and no predators.

A. Find the co-existence equilibrium

Prey:

Predator: