  The aim of this study is to propose a modified
Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the
behaviour of symptomatic, asymptomatic and hospitalized patients of COVID-19
epidemic, including the effect of demographic variation of population. It is
shown that considering a population growth proportional to the total population
leads to solutions with a qualitative behaviour different from the behaviour
obtained in many studies, where constant growth ratio is assumed. An exhaustive
theoretical study is carried out and the basic reproduction number $R_0$ is
computed from the model equations. It is proved that if $R_0<1$ then the
disease-free manifold is globally asymptotically stable, that is, the epidemics
remits. Global and local stability of the equilibrium points is also studied.
Numerical simulations are used to show the agreement between numerical results
and theoretical properties. The model is fitted to experimental data
corresponding to the pandemic evolution in the Rep\'ublica de Cuba, showing a
proper behaviour of infected cases which let us think that can provide a
correct estimation of asymptomatic cases. In conclusion, the model seems to be
an adequate tool for the study and control of infectious diseases in particular
the COVID-19 disease transmission.
