Thanks again Christian for your response and also for the separate email from Robert Mařík whose comments helped me develop the following ‘understanding’ of the dynamics of the model, which I hope is correct and helpful.
The analogy that I found to be useful is to think of the SEIR model as a set of buckets connected by pipes of different diameters and to imagine the flow of liquid through these pipes to represent the flow of people from one compartment to the next.
So, there is a flow of liquid/people into container E (from S) at a certain rate and there is a flow from E to I at a certain rate and a flow from I to R at rate. In your model container I is generally emptying faster than it is filling from E; the out-flow from I is greater than the out-flow from E (which is the in-flow to I). So the level in I declines faster than that in E
If instead we made alpha = gamma then the flows into and out of I will be more closely matched, and we find then that the levels in E and I are more similar. And if alpha > gamma, so that I fills more quickly than it empties, then we find the number of individuals in I to increase beyond those in E.
I think that this explanation is heading in the right direction …