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(searched for: doi:10.53391/mmnsa.2022.008)
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Published: 10 October 2022
by MDPI
Fractal and Fractional, Volume 6; https://doi.org/10.3390/fractalfract6100578

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.
Published: 26 September 2022
by MDPI
Mathematical and Computational Applications, Volume 27; https://doi.org/10.3390/mca27050082

Abstract:
This article develops a within-host viral kinetics model of SARS-CoV-2 under the Caputo fractional-order operator. We prove the results of the solution’s existence and uniqueness by using the Banach mapping contraction principle. Using the next-generation matrix method, we obtain the basic reproduction number. We analyze the model’s endemic and disease-free equilibrium points for local and global stability. Furthermore, we find approximate solutions for the non-linear fractional model using the Modified Euler Method (MEM). To support analytical findings, numerical simulations are carried out.
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