MATHEMATICAL MODEL OF EBOLA VIRUS DISEASE WITH VACCINATION

Abstract

The 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 whenever

R0 < 1 and unstable whenever R0 > 1. Furthermore, sensitivity analysis

is carried out to ascertain the model parameters that have high impact on

R0 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.