One way of solving this is to find out which terms appear in several places--
for instance, this one--the number of persons taken from the susceptible to the exposed compartment
and then the number of persons taken from the exposed to the infectious compartment,
and the number of persons taken from the infectious to the recovered compartment.
If you write it like that, it's easier to read and you can immediately see
that the total number is conserved.
The number of persons we lose here we gain here, the number of persons we lose here we gain here,
and the number of persons we lose here is gain here.
So up to very tiny round off errors of the total number and result you'll see that the infection
takes quite some time to evolve.
The maximum of the exposed compartment comes first and then comes
the maximum of the infectious compartment, and as we go, you'll see that the number of
susceptible persons shrinks drastically
and the number of recovered persons grows by the same amount.