Long-term bifurcation and stochastic optimal control of a triple-delayed Ebola illness model with vaccination and quarantine strategies

Abstract

Discovered in 1976, Ebola illness (EI) has long been neglected despite its high mortality rate, which can be as high as 90%. For more than 40 years, this illness has been responsible for epidemics throughout Central Africa. But only recently, during the 2014-2015 epidemic in West Africa, which is the deadliest to date, has the entire world considered this disease as one of the major public health issues. This paper aims to explore the effect of external fluctuations on the prevalence of EI. 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 EI. In order to better understand the impact of applied strategies, we deal with the stochastic control optimization approach by using some advanced theories. All this theoretical arsenal has been numerically confirmed by employing some real statistical data of EI. Finally, we mention that this work could be a rich basis for further investigations aimed at understanding the complexity of EI propagation at a pathophysiological and mathematics levels.