Great question! I hadn’t thought about it myself until you asked, so I’ll give it my best shot.

Looking at the equations, the difference is in the rate that the population transitions from exposed to infected (alpha) and then from infected to recovered (gamma). In this case, gamma > alpha, so people move more quickly from I->R then from E->I, meaning E peaks before I.

If I go back to the model and set these parameters to be equal, it looks as if the area is roughly the same — the peak of I is lower if gamma=alpha=0.2, but the curve is broader. Reversing these values (gamma=0.2, alpha=0.5) shows I peaking much higher then E. In this set-up, eventually everyone succumbs to the virus at some point (plotting S and R show this, which I did in a previous post), it just matters when it happens.

Does that clear up the peaking? I’ll admit, to your point, it still seems to me that the total area under both curves ought to equal 1 if we integrated over the entire time horizon. And I don’t have a good answer for why that isn’t the case here.