RESUMEN
Background: Ebola Virus causes disease both in human and non-human primates especially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date. Materials and Methods: We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus in a population where control measures 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 Matrix approach and the disease- endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle's Invariant principle. Results: The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation. Conclusions: Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.
RESUMEN
BACKGROUND: Ebola Virus Disease (EVD) has brought the human population, especially the West African race, great losses in so many areas such as economic productivity and human life. During the 2014 Ebola Virus outbreak, the disease devastated and threatened the whole world. EVD symptoms (fever, diarrhea, vomiting, etc) may appear anywhere between two to twenty-one days after infection. Those that recovered from the disease return to being susceptible again and can transmit the virus through semen as research has shown the virus presence in semen even after recovery. MATERIAL AND METHODS: Mathematical modeling method with the combination of vaccine, condom use, quarantine, isolation and treatment drug together as control measures in a population consisting of human and animals. A model system of non-linear differential equations for the control of EVD was formulated and the model effective reproduction number (RE ) was obtained using the next generation matrix method and used in the stability analysis of the model. Center manifold theorem was used in the bifurcation analysis of the model. RESULTS: The result shows that the stability analysis of the model shows that the EVD - Free Equilibrium is locally asymptotically stable when RE > 1 and EVD - Endemic Equilibrium is locally asymptotically stable when RE > 1. The model was shown to exhibit a forward bifurcation. CONCLUSIONS: Numerical simulations and analysis of the model show that EVD could be effectively controlled and eradicated within a short period of time when vaccine, condom use, quarantine, isolation and treatment drug control measures are implemented together.