Mathematical Modeling of the Spread of the Ebola Virus Disease

Résumé

Ebola, a viral and fatal disease with occasional outbreaks on the continent of Africa affects mostly humans and non-human primates, and poses a great health challenge to this part of the globe. The transmission of Ebola Virus can be through direct contact with blood, bodily fluids, or skin of Ebola Virus Disease patients or those who have passed away from the illness. In this paper, we formulate a mathematical model of the transmission of the Ebola virus disease in a population capturing its dynamics to study the impact of healthcare policies on its spread. The model is a four compartment model consisting of Susceptible, Latent, Infectious and Recovery compartments. To gain a good understanding of the model, the formulated model is transformed into difference equations. The basic
reproduction number R₀ is derived using the next generation matrix method. Further, the disease-free equilibrium of the model is obtained and its stability analysis is carried out. The result shows that the disease-free equilibrium point is locally stable if R₀ < 1 but may not be asymptotically stable, indicating that the disease will eventually die out. Conversely, if R₀ > 1, an endemic equilibrium exists, and the disease will persist at a stable level. Numerical simulations obtained illustrate the efforts of the parameters on the compartment of the model.