As an epidemic spreads through a population the number of

Question

Question: As an epidemic spreads through a population, the number of infected people, I, is expressed as a function of the number of susceptible people, S, by

I = k ln (S/S₀) - S + S₀ + I₀, for k, S₀, I₀ > 0

(a) Find the maximum number of infected people.

(b) The constant k is a characteristic of the particular disease; the constants S0 and I0 are the values of S and I when the disease starts. Which of the following affects the maximum possible value of I? Explain.

• The particular disease, but not how it starts.

• How the disease starts, but not the particular disease.

• Both the particular disease and how it starts.