Analysis, simulation and optimal control of a SEIR model for Ebola virus with demographic effects

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. This is a preprint of a paper whose final and definite form is with 'Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.', ISSN: 1303-5991. Submitted 27 Sept 2016; Article revised 05 Apr 2017; Article accepted for publication 01 May 2017. arXiv admin note: text overlap with arXiv:1603.05794