A Mathematical Model for the Control of the Spread of Ebola Virus Disease in West Africa – A Disease-free Equilibrium Approach
A. U. Kalu *
Department of Mathematics, Abia State Polytechnic, Aba, Abia State, Nigeria.
N. Agbanyim Akuagwu
Department of Chemistry, Abia State Polytechnic, Aba, Abia State, Nigeria.
I. A. Agwu
Department of Mathematics, Abia State Polytechnic, Aba, Abia State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The current Ebola Virus disease outbreak in West Africa is so far, the worst outbreak of the disease in any part of the world. It began in Guinea in December 2013 and then spread to Liberia, Sierra-Leone, Nigeria, Mali and Senegal. It has already claimed so many thousand lives and threatening those of so many others. In order to help control the spread or even completely eradicate the disease in West Africa in particular, we present a mathematical model based on the standard SEIR model. The disease-free equilibrium point of the model was established and its stability analysis carried out using the Routh-Hurwitz criteria. From the stability analysis it was found out that the necessary and sufficient condition for the control or possibly total eradication of the disease in West Africa is that the product of total break-down of the susceptible and latent classes must be less than the product of the total removal rates from both the latent and the infectious classes. We made recommendations on what should be done in order to meet the established condition.
Keywords: Disease free equilibrium, stability analysis, Jacobian matrix, Routh-Hurwitz criteria.