  The Ebola virus disease is a severe viral haemorrhagic fever syndrome caused
by Ebola virus. This disease is transmitted by direct contact with the body
fluids of an infected person and objects contaminated with virus or infected
animals, with a death rate close to 90% in humans. Recently, some mathematical
models have been presented to analyse the spread of the 2014 Ebola outbreak in
West Africa. In this paper, we introduce vaccination of the susceptible
population with the aim of controlling the spread of the disease and analyse
two optimal control problems related with the transmission of Ebola disease
with vaccination. Firstly, we consider the case where the total number of
available vaccines in a fixed period of time is limited. Secondly, we analyse
the situation where there is a limited supply of vaccines at each instant of
time for a fixed interval of time. The optimal control problems have been
solved analytically. Finally, we have performed a number of numerical
simulations in order to compare the models with vaccination and the model
without vaccination, which has recently been shown to fit the real data. Three
vaccination scenarios have been considered for our numerical simulations,
namely: unlimited supply of vaccines; limited total number of vaccines; and
limited supply of vaccines at each instant of time.
