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**mitch_nufc** In this model, let the number of those not yet ill, but susceptibles, be **S(t);** let the number currently infected be **I(t).** The rate at which the susceptibles are infected is given by:

**S'(t) = dS/dt = -alpha(SI)**

(Where alpha > 0 is a constant). The rate at which the number of those infected can change depends on both the susceptibles getting ill and others recovering; this process is described by:

**I'(t) = dI/dt = alpha(SI) - beta(I)**

(Where beta > 0 is a constant). Form the differential equation **I(S)** and, given that **I = 1** when **S = N**, find the solution for **I(S).**

**The part that really throws me is the stuff in blue :S how do I get the function I(S)? I tried dividing I'(t)/S'(t) to give dI/dS then integrating but this seemed totally wrong... Am I missing some sort of elementary trick here? Help very appreciated.**