A mathematical model for control of Ebola virus disease with vaccination as a control measure and bifurcation analysis

Abstract

This study presents a mathematical model for the control of Ebola virus disease (EVD) incorporating vaccination as a control measure, alongside a bifurcation analysis to investigate the dynamics of the disease spread and control. The model's disease-free equilibrium is locally asymptotically stable (LAS) if the effective reproduction number (E_CR < 1),  implying that Ebola can be eliminated from the population over time. Sensitivity analysis reveals that parameters such as the contact rate between susceptible humans and Ebola-infected animals and the rate of immunity loss from vaccination, which have positive sensitivity indices, significantly enhance disease spread. Reducing these parameters is crucial for controlling Ebola. Conversely, parameters like vaccination rate and disease-induced death rate in animals, with negative sensitivity indices, contribute to disease reduction. Numerical simulations showed that effective vaccination leads to a substantial decrease in the number of infected and isolated individuals, demonstrating strong disease control. Furthermore, bifurcation analysis indicates that the model exhibits backward bifurcation when parameters  a > 0 and b > b, meaning a stable disease-free equilibrium can coexist with a stable endemic equilibrium, complicating disease eradication efforts. In contrast, forward bifurcation occurs when a < 0 and b < 0, suggesting that controlling Ebola might not depend on initial infection levels, with the disease potentially going extinct quickly if E_CR < 1.