MODELLING TRANSMISSION DYNAMICS OF EBOLA VIRUS DISEASE WITH QUARANTINE AND ISOLATION: OPTIMAL CONTROL APPROACH

Abstract

Ebola virus is a virus that causes a deadly disease called Ebola virus disease (EVD). It has an average case fatality rate of 70%. EVD is a public health disease of global concern. It is endemic in Sub-Saharan Africa where it has caused several epidemics, especially the 2018 epidemic in the Democratic Republic of Congo (DRC). In this paper, a nonlinear deterministic model of EVD with quarantine and isolation as control measures is discussed. The effective reproduction number that governs the spread of the disease is calculated using next generation method. The conditions for the existence and stabilities of equilibrium states of the model are established. The sensitivity analysis of the parameters of effective reproduction number is performed using forward index method. Next, the optimal control model is presented by incorporating control efforts for quarantine and isolation. The Pontryagin’s maximum principle is used to obtain the optimality system that is solved using fourth order Runge – Kutta scheme. The result indicates that quarantine and isolation measures can help eliminate the spread of EVD in the population. However, in a resource constrained setting where there is limited resources to implement both quarantine and isolation controls, it is advisable to quarantine only the exposed persons. This will be more significant in eliminating EVD in a reduced time and in return minimize the cost of control efforts, morbidity and mortality of EVD in the population.