In this model  the host population is partitioned into four classes: the susceptible, exposed, infectious, and recovered, with
denoting the fraction of each class; the disease spreads through direct contact, and a host stays in a latent period after contact with an infected host before becoming infective; an infectious host may die from the disease or recover with acquired immunity.
is the time delay that a susceptible host must be in contact with an infectious host to be considered exposed,
represents both the birth and death rate,
is the rate at which the exposed become infective,
is the rate at which the infective recover, and
is the contact rate at which susceptibles come into contact with the infective. The system is solved with
. If we take the total population
, the value of
can be obtained from the other three values. The system has a stable equilibrium when
is increased, this equilibrium is approached asymptotically; further increases of
cause the trajectories to reach first periodic and then chaotic oscillations.