Mathematical analysis and simulation of Ebola virus disease spread incorporating mitigation measures

Abstract

In order to understand the dynamics of the Ebola virus disease (EVD), this research developed a mathematical model that includes quarantine and public education campaigns as control measures. The model’s equilibrium points are displayed and the effective basic reproduction number is estimated. Bifurcation theory is used for the stability analysis of endemic equilibrium state and general bifurcation theory is used to prove the existence of endemic equilibrium state. We evaluated the nature of the endemic equilibrium state of the model’s equation near the disease-free equilibrium, and introduce a bifurcation parameter. The results of the centre manifold theory are used to demonstrate that there is nontrivial endemic equilibrium near the disease-free equilibrium. We demonstrated the characteristics of the endemic equilibrium state that is close to the disease-free equilibrium as well as the fact that there is a potentially unstable endemic equilibrium condition. In other words, the sickness is slowly declining and will eventually disappear, as in the case of West Africa. Finally, we simulated the model developed to study the dynamics of the diseases with varying parameters using Homotopy Perturbation Method (HPM) to validate the qualitative analysis of the model. The result confirmed the hypothesis of our research that if quarantine and public enlightenment is properly used for the mitigation of the disease, the disease outcomes will drastically reduced. The results presented in this research will be useful for public health experts to contain the Ebola disease spread most especially in Africa.