The stability analysis and control transmission of mathematical model for Ebola Virus

Author(s): Muhammad Tahir1, Gul Zaman2, Syed Inayat Ali Shah3, Sher Muhammad 1, Syed Asif Hussain1, Mohammad Ishaq1
1Department of Mathematics, Islamia College Peshawar, 25000, K.P.K Pakistan.
2Department of Mathematics, University of Malakand, Chakdara District Lower Dir, K.P.K Pakistan.
3Department of Mathematics, Islamia College Peshawar, 25000, K.P.K Pakistan
Copyright © Muhammad Tahir, Gul Zaman, Syed Inayat Ali Shah, Sher Muhammad, Syed Asif Hussain, Mohammad Ishaq. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Mathematical modeling of infectious diseases has progressed dramatically over the past four decades and continues to flourish at the nexus of mathematics, epidemiology, and infectious diseases research. Now recognized as a valuable tool, mathematical models are being integrated into the public health decision-making process more than ever before. In this article, a mathematical model of Ebola virus which is named as SEIVR (susceptible, exposed, infected, vaccinated, recovered) model is considered. First, we formulate the model and present the basic properties of the proposed model. Then, basic reproductive number is obtained by using the next-generation matrix approach. Furthermore, the sensitivity analysis of \(R_0\) is also discussed, all the endemic equilibrium points related to the disease are derived, a condition to investigate all possible equilibria of the model in terms of the basic reproduction number is obtained. In last, numerical simulation is presented with and without vaccination or control for the proposed model.

Keywords: Ebola virus, sensitivity analysis, reproduction number, formulation of model, endemic equilibrium points, local stability, global stability, numerical simulation through Matlab programming.