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Assuming that in the problem above, a medication is applied that cures people at a rate...

Assuming that in the problem above, a medication is applied that cures people at a rate q > 0, proportional to the number I(t) of infected people at time t, find a explicit formula for I(t) in terms of t, r, S, I0, q and estimate the number of infected habitants after a big (extended) period of time, i.e., t → ∞, when: (a) q ≥ rS; (b) q < rS.

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