Approximate solutions: leading front
To determine the value of the constant c0, we consider
x → ∞, far in front of the infection wave. In this
domain, S = 1 (and ln S = 0), R = 0 = d2R/dx
02
,
E = I = 0, d
2E/dx
02 = d2
I/dx
02 = 0 so that
c0 = 0. Consequently,