MATHEMATICAL MODELLING APPROACH OF THE STUDY OF EBOLA VIRUS DISEASE TRANSMISSION DYNAMICS IN A DEVELOPING COUNTRY.

Abstract

Background: Ebola Virus causes disease both in human and non-human primates especially in developing countries.  Materials and Methods: Here we studied the spread of Ebola virus in and hence obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus in a population where control measures like vaccination, treatment, quarantine, isolation of infectious patients while on treatment and use of condom were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian approach and the global stability using the center manifold theorem. We also investigated the local and global stability of the endemic theorem by constructing a Lyapunov function using the LaSalle’s Invariant principle. Results: This modeled system of equations was analyzed, and result showed that the disease-free equilibrium where both local and globally stable and that the system exhibits a forward bifurcation. The endemic equilibrium also was showed to be stable when the reproduction number is greater than one. Conclusions: Furthermore, numerical simulations were carried out to further see the impacts of the various control measures on the various compartments of the population. Our graphs show that isolation is the best option for an infectious person to be treated to avoid the disease been spread further and leads to quicker and better recovery.