The Impact of Vaccination on a Nonlinear Ebola Virus Disease Mathematical Model

Resumen

 This study examines the spread of Ebola Virus Disease (EVD) among human populations by creating a nonlinear mathematical model that assesses the effects of vaccination. The analysis shows that the equilibrium without disease (DFE) maintains local stability when the associated reproduction number ($\mathcal{R}_0$) is below one. Conversely, the DFE loses global stability, whereas the endemic equilibrium (EE) achieves global stability. The presence of the endemic equilibrium is established for all values where $\mathcal{R}_0 > 1$. Sensitivity analysis reveals that the infection rate ($\beta_2$) among susceptible individuals has a dominant effect on $\mathcal{R}_0$, emphasizing the critical need for interventions targeting susceptible populations. Furthermore, vaccination ($\tau$) significantly influences the epidemic management, as lower vaccination rate lead to persistently elevated $\mathcal{R}_0$ values. The findings underscore the importance of high vaccination coverage to mitigate disease transmission. Numerical simulations, performed using MATLAB, compare the model’s predictions with analytical results and highlight the global impact of vaccination and public response on disease control.