Consider a community of 2,000 people in which five members get sick with the flu. The following week, ten new cases of t

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Consider a community of 2,000 people in which five members get
sick with the flu. The following week, ten new cases of the flu are
reported. We are interested in modeling the spread of the disease
through the community using SIR model.
Consider the following assumptions:
a. Nobody enters or leaves the community and no one in the
community has contact with anyone outside the community.
b. Each person is either Susceptible (able to get the flu),
Infected (currently has the flu and able to spread it), or Removed
(already had the flu and is not able to get it again). Initially
each person is either susceptible or infected.
c. A susceptible person can get the flu only by contact with an
infected person.
d. Once a person gets the flu, he/she cannot get it again.
e. The average duration of the flu is 2 weeks, during which time an
infected person can spread the disease to a susceptible person.
Answer the following questions
i. Formulate and write the system of Discrete Dynamical System that
models this situation.
ii. Plot S(n), I(n) and R(n) overlaid together using Ms Excel and
interpret the result.
iii. Approximately when was the epidemic at its worst?
iv. How many people were sick at the peak of the epidemic?
v. Approximately how long did the epidemic last?
vi. Approximately how many people contracted the disease during the
course of the epidemic?