Before revision:  The solution is created by constructing a single second-order nonlinear differential equation in ln(S ) and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model.
After revision:  The solution is created by constructing a single second-order nonlinear differential equation in \ln S and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model.