A Mathematical Model for the Control of Ebola Virus Disease with Vaccination Effect

Abstract

Ebola Virus Disease (EVD) remains a major global health threat, marked by periodic outbreaks with severe mortality and socioeconomic consequences. In this study, a comprehensive mathematical model to analyze the transmission dynamics of EVD, explicitly incorporating key epidemiological factors such as vaccination, treatment efficacy, and human contact rates. The model stratifies the total human population into seven compartments: Susceptible (S), Vaccinated (V), Exposed (E), Infected (I), Hospitalized (H), Deceased (D), and Recovered (R) is formulated. Using the next-generation matrix method, the basic reproduction number ( $R_{0}$ ) is derived to assess the potential for disease spread. Stability analysis demonstrates that the disease-free equilibrium is locally asymptotically stable when $R_{0}<1$ and unstable otherwise. Numerical simulations and sensitivity analyses are conducted to explore the model's dynamics under various intervention scenarios. The findings highlight the crucial role of high vaccination coverage and effective treatment in significantly reducing EVD incidence and prevalence. Sensitivity analysis identifies the contact rate as a critical driver of transmission, indicating that minimizing contact with infectious individuals substantially lowers outbreak magnitude. Furthermore, the study determines threshold values for vaccination and treatment effectiveness that must be achieved to ensure outbreak containment. The model emphasizes the necessity of integrated control strategies that combine vaccination, timely treatment, and public health behaviour modifications. These results offer actionable insights for policymakers and health authorities aiming to design effective response plans. The study recommends prioritizing sustained vaccination campaigns, strengthening healthcare infrastructure, and implementing public awareness programs to enhance community compliance and preparedness against future EVD outbreaks.