Mathematical Analysis of Effect of Isolation on the Transmission of Ebola Virus Disease in a Population

Outbreak of Ebola virus disease in early 2014 in West Africa is a major highlight for many researchers throughout the world because of the high mortality rate. Ebola disease is caused by a virus called the Ebola virus which can be transmitted from infected humans to uninfected humans through direct contact with the body fluids. Research has placed evidence that Ebola virus can be transmitted through the bodies of humans who recently died of the disease. Because of that, an epidemic model of (S, E, Iu, Id, Is, R, D) is presented to study the dynamical spread of Ebola in the population. The existences of the disease free and unique endemic equilibrium were determined under certain conditions. Furthermore, the Local Stability analysis of the disease – free equilibrium (DFE) was investigated via the threshold parameter (Reproduction number R0 ) obtained using the next generation matrix technique. The result shows that the DFE is asymptotically stable at Reproduction number less than unity (R0 <1) and Unstable whenever Reproduction number is greater than unity (R0 >1). Numerical simulations are carried out to confirm the analytical results and explore the possible behaviour of the formulated model. Numerical simulation shows that if the detection rate of infected undetected is sufficiently large, then the isolation techniques can lead to the eradication of the disease in the population.