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 identified Ebola virus species of the family Filoviridae. This paper develops the SEIR and the SEIHDR epidemic models that investigate the effects of the ante-mortem contact and post-mortem contact on the spread of the disease. The reproduction number of the models are determined. The equilibria and conditions for the existence of the equilibria are also determined. The models are solved numerically and the numerical simulations implemented to elucidate various scenarios. The results of the models are then compared to WHO data of confirmed cases for the 2014 Ebola outbreak in Liberia. It is observed that the SEIHDR model agrees better with the data than the SEIR model. Moreover, a new model, the SEIQDR model (a modification of the SEIHDR Model) is formulated which incorporates quarantine as an intervention. Again, this SEIQDR model is compared to the WHO data of confirmed cases for the 2014 Ebola outbreak in Liberia. The results of the SEIQDR model is found to agree better than those of the other models especially in respect of the latter stages of the disease outbreak. Finally, the effect of vaccination on both the SEIHDR and the SEIQDR models is investigated. Different rates of vaccination using numerical simulations in order to predict the effect of vaccination on the infected individuals over time is also discussed. The SEIQDR model with vaccination indicates a lower threshold which should not be less than 25\% as compared to the SEIHDR model for which vaccination should not be less than 65\%. It is observed that vaccination as an additional strategy helps to control the disease more effectively.
Highlights
There have been an overwhelming Ebola epidemic in West Africa (Yamin et al, 2015)
The SEIR model which does not consider the post-mortem contact effect and the SEIHDR model which takes into account the post mortem contact effect on the spread of the Ebola virus disease were analysed
We analysed the SEIHDR model which is a modification of the SEIR model and which takes into account hospitalized and dead individuals regarding them as infectious
Summary
There have been an overwhelming Ebola epidemic in West Africa (Yamin et al, 2015). Ebola virus disease (EVD), which was known as Ebola haemorrhagic fever, is a severe and often fatal disease in human beings and other non-humans such as monkeys and gorillas (WHO, 2015a; CDC, 2015a). Mathematical models have been used by several researchers to study the dynamics of the EVD outbreak but much emphases have not been placed on the post-mortem effect on the spread of the disease and modelling the interventions. It is important that we study and investigate the wide spread of EVD in humans as a result of post-mortem contact and analyse quarantine as an intervention strategy adapted by the health management authorities to control the spread. The main objective of this work is to study and investigate the effects of post-mortem contact on the spread of Ebola and quarantine as an intervention using mathematical models. We formulate the SEIQDR model which is a modification of the previous model to investigate and analyse quarantine as an intervention strategy adapted by the health management authorities to control the spread.
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