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Modeling transmission dynamics of Ebola virus disease

International Center for Applied Mathematics and Computational Bioengineering, Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Hawally, Kuwait

E-mail Address: mimran@asu.edu

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Adnan Khan

Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan

E-mail Address: adnan.khan@lums.edu.pk

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Ali R. Ansari

International Center for Applied Mathematics and Computational Bioengineering, Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Hawally, Kuwait

E-mail Address: ansari.a@gust.edu.kw

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, and

Syed Touqeer Hussain Shah

Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan

E-mail Address: touqirshah@gmail.com

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https://doi.org/10.1142/S1793524517500577Cited by:11 (Source: Crossref)

Abstract

Ebola virus disease (EVD) has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, $ℛ_{0}$ is less than unity. It is also shown that there exists a unique endemic equilibrium when $ℛ_{0} > 1$ . Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.

Keywords:

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