MATHEMATICAL MODEL OF EBOLA VIRUS DISEASE WITH VACCINATION

Abstract

he continued reoccurrences of Ebola virus disease (EVD) among human population has given a great cause for concern. This paper studied the impact of vaccination on the transmission dynamics of EVD by constructing a deterministic model. A threshold quantity called basic reproduction number, 𝑅0, is computed and used to discuss the persistent and eradication of disease in the population. The local and global stability of the disease-free equilibrium are established to show the asymptotic behavior of the infection. The stability analysis shown that the disease–free equilibrium is locally and globally asymptotically stable whenever𝑅0 < 1 and unstable whenever 𝑅0 > 1. Furthermore, sensitivity analysis is carried out to ascertain the model parameters that have high impact on𝑅0 for intervention planning. The sensitivity result shown that vaccination rate has high impact compare on 𝑅0, as the rate of vaccination increases, the disease reduces in the population. The numerical simulations of the model are carried out using fourth order Runge–Kutta scheme in order to investigate the dynamics of EVD in the presence of vaccination. The result shown the important of vaccination in eliminating EVD in the population. It indicates that if a good proportion of the population are vaccinated with a vaccine that does not wane off on time, it will reduce the number of infected individuals in the population and this will help to eradication of EVD in the population.