Abstract
The purpose of this article is to discuss the dynamics of the spread of Ebola virus disease (EVD), a kind of fever commonly known as Ebola hemorrhagic fever. It is rare but severe and is considered to be extremely dangerous. Ebola virus transmits to people through domestic and wild animals, called transmitting agents, and then spreads into the human population through close and direct contact among individuals. To study the dynamics and to illustrate the stability pattern of Ebola virus in human population, we have developed an SEIR type model consisting of coupled nonlinear differential equations. These equations provide a good tool to discuss the mode of impact of Ebola virus on the human population through domestic and wild animals. We first formulate the proposed model and obtain the value of threshold parameter mathcal{R}_{0} for the model. We then determine both the disease-free equilibrium (DFE) and endemic equilibrium (EE) and discuss the stability of the model. We show that both the equilibrium states are locally asymptotically stable. Employing Lyapunov functions theory, global stabilities at both the levels are carried out. We use the Runge–Kutta method of order 4 (RK4) and a non-standard finite difference (NSFD) scheme for the susceptible–exposed–infected–recovered (SEIR) model. In contrast to RK4, which fails for large time step size, it is found that the NSFD scheme preserves the dynamics of the proposed model for any step size used. Numerical results along with the comparison, using different values of step size h, are provided.
Highlights
Six species of Ebola virus have been discovered till out of which four cause Ebola virus disease in humans
8 Conclusions In this paper, we have considered an SEIR epidemic model of Ebola virus affected by wild and domestic animals, which spread the infection within the human population at any time t
We have studied the dynamical behavior of the proposed model and the dynamics is determined by the basic reproduction number R0 that acts virtually in controlling the infection of Ebola virus
Summary
Six species of Ebola virus have been discovered till out of which four cause Ebola virus disease in humans. In West Africa, after the first case was discovered in 2014, the EVD outbreak ended by 2016 with 113,10 confirmed deaths and nearly 286,16 suspected deaths with fatality rate of 39% (2014–2016 Ebola Outbreak in West Africa reported by CDC) officially recorded in June 2016 as discussed in [7,8,9,10,11,12] and [2,3,4] Another outbreak of Ebola virus disease in North Kivu Province began on 1 August 2018 reported by the Ministry of Health of the DRC. The set B ⊂ R4+ is compact and positively invariant with respect to model (1)–(5) with nonnegative initial conditions in R4+
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