A disease transmission model of SEIR type with
exponential demographic structure is
formulated, with a natural death rate constant
and an excess death rate constant for infective
individuals. The latent period is assumed to be
constant, and the force of the infection is
assumed to be of the standard form, namely,
proportional to
 where
 is the total (variable) population size and
 is the size of the infective population. The
infected individuals are assumed not to be able
to give birth and when an individual is removed
from the  -class, it recovers, acquiring permanent immunity
with probability  
and dies from the disease with probability
 . The global attractiveness of the disease-free
equilibrium, existence of the endemic equilibrium
as well as the permanence criteria are
investigated. Further, it is shown that for the
special case of the model with zero latent
period,  leads to the global stability of the endemic
equilibrium, which completely answers the
conjecture proposed by Diekmann and Heesterbeek.
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