  Ebola virus is one of the most virulent pathogens for humans. We present a
mathematical description of different Susceptible-Exposed-Infectious-Recovered
(SEIR) models. By using mathematical modeling and analysis, the latest major
outbreak of Ebola virus in West Africa is described. Our aim is to study and
discuss the properties of SEIR models with respect to Ebola virus, the
information they provide, and when the models make sense. We added to the basic
SEIR model demographic effects in order to analyze the equilibria with vital
dynamics. Numerical simulations confirm the theoretical analysis. The control
of the propagation of the virus through vaccination is investigated and the
case study of Liberia is discussed in detail.
