  The Susceptible-Exposed-Infectious-Recovered (SEIR) model is applied in
several countries to ascertain the spread of the coronavirus disease 2019
(COVID-19). We consider discrete-time SEIR epidemic model in a closed system
which does not account for births or deaths, total population size under
consideration is constant. This dynamical system generated by a non-linear
evolution operator depending on four parameters. Under some conditions on
parameters we reduce the evolution operator to a quadratic stochastic operator
(QSO) which maps 3-dimensional simplex to itself. We show that the QSO has
uncountable set of fixed points (all laying on the boundary of the simplex). It
is shown that all trajectories of the dynamical system (generated by the QSO)
of the SEIR model are convergent (i.e. the QSO is regular). Moreover, we
discuss the efficiency of the model for Uzbekistan.
