[Math4u] Differential equation question (Kermack-McKendrick model)

Hello all,

I'm currently working with the Kermack-McKendrick deterministic
epidemic model and am trying to figure out how to solve the
differential equation that tell you the number of recovered
individuals after time t. The book I'm working from doesn't solve it
explicitly, stating that the methods are "rather complicated" and
instead uses a Taylor approximation to estimate the e term. I'm
curious as to how this is solved without using an approximation and
was wondering if anyone could help. Here's the equation:

dR/dt = g[N-R(t)-S0e^(-R(t)/a)]

Where:

R(0) = 0
S(0) = S0, a constant
N,g,a are also constants.

Thanks,

Paul

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