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Title: Ebola Model and Optimal Control with Vaccination Constraints
Author: Area, Iván
Ndairou, Faiçal
Nieto, Juan J.
Silva, Cristiana J.
Torres, Delfim F. M.
Keywords: Ebola virus
Mathematical modelling
Transmission of Ebola
Control of the spread of the Ebola disease
Optimal control with vaccination constraints
Vaccination scenarios
Issue Date: 2018
Publisher: American Institute of Mathematical Sciences
Abstract: 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 uids 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.
Peer review: yes
DOI: 10.3934/jimo.2017054
ISSN: 1547-5816
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Appears in Collections:CIDMA - Artigos
SCG - Artigos

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