Modelling the e ect of post-mortem contact on the spread of Ebola with quarantine as an intervention.

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November, 2016
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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.
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.