Modelling the e ect of post-mortem contact on the spread of Ebola with quarantine as an intervention.
Abstract
Ebola virus disease (EVD) is a severe, often fatal disease in humans and other
non-human primates caused by infection with any of the four identifi ed Ebola
virus species of the family Filoviridae. This paper develops the SEIR and the
SEIHDR models that investigate the e ffects of the ante-mortem contact and postmortem
contact on the spread of the disease. We determine the reproduction
number of the models. The equilibria and conditions for the existence of the
equilibria are determined. We solve the models numerically and discuss the
numerical simulations to elucidate certain scenarios. We also compare the results
of the models to WHO data of con firmed cases for the 2014 Ebola outbreak in
Liberia. It is observed that the SEIHDR model agrees better with the data than
that of the SEIR model. Moreover, we formulate a new model, the SEIQDR
model (a modifi cation of the SEIHDR Model) which incorporates quarantine as
an intervention. We compare the SEIQDR model to the WHO data of con firmed
cases for the 2014 Ebola outbreak in Liberia. The results of the SEIQDR model
agrees better than that of the other models especially during the latter stages of
the disease outbreak. Finally, we investigate the eff ect of vaccination on both the
SEIHDR and the SEIQDR models. We discuss diff erent rates of vaccination using
numerical simulations in order to predict the e ffect of vaccination on the infected
individuals over time. The SEIQDR model with vaccination indicates a lower
threshold which should not be less than 25% as compared to that of the SEIHDR
model with vaccination which should not be less than 65%. It is observed that
vaccination as an additional strategy helps to control the disease more eff ectively.
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of M.Phil Applied Mathematics.