Long-Term Bifurcation and Stochastic Optimal Control of a Triple-Delayed Ebola Virus Model with Vaccination and Quarantine Strategies

Abstract

Despite its high mortality rate of approximately $90\%$, the Ebola virus disease (EVD) has not received enough attention in terms of in-depth research. This illness has been responsible for over 40 years of epidemics throughout Central Africa. However, during 2014–2015, the Ebola-driven epidemic in West Africa became, and remains, the deadliest to date. Thus, Ebola has been declared one of the major public health issues. This paper aims at exploring the effects of external fluctuations on the prevalence of the Ebola virus. We begin by proposing a sophisticated biological system that takes into account vaccination and quarantine strategies as well as the effect of time lags. Due to some external perturbations, we extend our model to the probabilistic formulation with white noises. The perturbed model takes the form of a system of stochastic differential equations. Based on some non-standard analytical techniques, we demonstrate two main approach properties: intensity and elimination of Ebola virus. To better understand the impact of applied strategies, we deal with the stochastic control optimization approach by using some advanced theories. All of this theoretical arsenal has been numerically confirmed by employing some real statistical data of Ebola virus. Finally, we mention that this work could be a rich basis for further investigations aimed at understanding the complexity of Ebola virus propagation at pathophysiological and mathematics levels.