  Compartmental transmission models have become an invaluable tool to study the
dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR)
model is known to have an exact semi-analytical solution. In the current study,
the approach of Harko et al. (2014) is generalised to obtain an approximate
semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR)
model. The SEIR model curves have nearly the same shapes as the SIR ones, but
with a stretch factor applied to them across time that is related to the ratio
of the incubation to infectious periods. This finding implies an approximate
characteristic timescale, scaled by this stretch factor, that is universal to
all SEIR models, which only depends on the basic reproduction number and
initial fraction of the population that is infectious.
