Stability of Sets for Ebola Virus Disease Models Through Impulsive Conformable Approach

In this paper, we extend some existing models of the Ebola virus disease through a hybrid impulsive conformable approach. The base of the introduced model is a class of partial differential equations that incorporate diffusion terms to describe the development of the Ebola virus disease in time and space. In the extended model, we have considered impulsive effects at fixed moments of time, which is of high significance in investigating opportunities for impulsive vaccination strategies and impulsive control drug treatment on disease evolution. In addition, conformable setting is proposed, which provides modeling flexibility without the complications inherent in classical fractional derivatives. Instead of studying the global stability of an equilibrium, the more general notion of stability of sets is introduced and analyzed. The main stability of sets results are obtained by using the impulsive conformable Lyapunov technique and comparison principle. The proposed framework, concepts and techniques may serve as effective tools for analyzing numerous phenomena in medicine and biology.