A MATHEMATICAL ANALYSIS OF THE TRANSMISSION DYNAMICS OF EBOLA VIRUS DISEASES

Abstract

A mathematical model to investigate the transmission dynamics of Ebola virus disease (EVD), which causes acute viral haemorrhagic fever, is established in this paper. Based on the mechanism and characteristics of EVD transmission, we propose a susceptible-exposed-infectious-recovered-susceptible (SEIRS) epidemic model with the understanding that the recovered individuals can become infected again. The equilibria of the model and their stability are discussed in details. Basic reproduction number ($R_0$) is obtained by using the next generation approach and proved that the disease free equilibrium (DFE) of our system is locally asymptotically stable if $R_0<1$, which means that the disease can be eradicated under such condition in finite time and unstable if $R_0>1$. When the associated reproduction number, $R_0>1$ then the endemic equilibrium is stable, otherwise unstable. We contemplate our proposed model numerically and compare the results with existing literature.