During World War I, a particularly lethal form of flu killed about 40 million people around the world. The epidemic started in an army camp of 45,000 soldiers outside of Boston, where the first soldier fell sick on September 7, 1918. With time, t, in days since September 7, values of the constants in the SIR model,

are estimated to be a = 0.000267, b = 9.865.
(a) What are the initial values, S₀ and I₀?
(b) Explain how you know that this model predicts an epidemic in this case.
(c) Find the differential equation for dI∕dS. Sketch its slope field and estimate the total number of soldiers infected over the course of the disease.
(d) Solve the differential equation for dI∕dS analytically. Use the solution to solve approximately for the number of soldiers affected over the course of the disease.

Transcribed Image Text:

SP at IP dt = = -ASI aSI - bl,