Far in the tail of the wave, the de

Far in the tail of the wave, the densities of the
recovered and of the susceptibles reach their limiting
values: I = 0, E = 0, R = R∗ = constant, and
R∗ + S∗ = 1. Hence the invariant (14) takes the
form ln S∗ = sc(S∗ − 1) or S∗ = esc(S∗−1). This
transcendental equation has the solution