Let I be the number of infected people and S be the number of susceptible people in an

Chapter 9, Problem 1

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Let I be the number of infected people and S be the number of susceptible people in an outbreak of a disease. Explain why it is reasonable to model the interaction between these two groups by the differential equations dS dt = aSI dI dt = aSI bI where a, b are positive constants. Why have the signs been chosen this way? Why is the constant a the same in both equations?

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