Research Article OntheDynamicsofaFractional-OrderEbolaEpidemicModelwith Nonlinear Incidence Rates Mirirai Chinyoka , 1 Tinashe B. Gashirai , 2 and Steady Mushayabasa 1 1 Department of Mathematics and Computational Sciences, University of Zimbabwe, P.O. Box MP 167, Harare, Zimbabwe 2 Department of Applied Mathematics, National University of Science and Technology, P. O. Box 939 Ascot, Bulawayo, Zimbabwe Correspondence should be addressed to Steady Mushayabasa; steadymushaya@gmail.com Received 7 August 2021; Revised 14 October 2021; Accepted 2 November 2021; Published 3 December 2021 Academic Editor: Yuriy Rogovchenko Copyright © 2021 Mirirai Chinyoka et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose a new fractional-order model to investigate the transmission and spread of Ebola virus disease. e proposed model incorporates relevant biological factors that characterize Ebola transmission during an outbreak. In particular, we have assumed that susceptible individuals are capable of contracting the infection from a deceased Ebola patient due to traditional beliefs and customs practiced in many African countries where frequent outbreaks of the disease are recorded. We conducted both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Model parameters were estimated based on the 2014-2015 Ebola outbreak in Sierra Leone. In addition, numerical simulation results are presented to demonstrate the analytical findings. 1.Introduction In recent decades, fractional calculus theory has been applied in many fields such as mechanical and mechanics, visco- elasticity, bioengineering, finance, optimal theory, optical and thermal system, and electromagnetic field theory [1–3]. Prior studies have shown that fractional calculus is capable of describing rules and development process of some phe- nomena in natural science [1]. In particular, it has been found that the fractional-order differential system has the advantages of simple modeling, clear parameter meaning, and accurate description for some materials and processes with memory and genetic characteristics [4]. Hence, there is growing interest among researchers to study the role of fractional calculus on modeling real-world problems. One field that has attracted a lot of interest in the application of fractional calculus is mathematical modeling of infectious diseases [2, 3]. In this paper, a fractional-order Ebola epidemic model that incorporates nonlinear incidence rates is proposed and analyzed. A plethora of mathematical models have been proposed to explain, predict as well as quantify the effec- tiveness of different Ebola virus disease (EVD) intervention strategies since the 2004 when the largest outbreak occurred in Africa (see, for example, [5–14], and references therein). ese studies and those cited therein have certainly pro- duced many useful results and improved the existing on Ebola dynamics. One of the limitations of these models, however, is that in most of the studies, the authors were utilizing integer-order mathematical modeling approach except in few recent studies such as [12–14]. In those studies that were based upon fractional calculus, most of the models used the bilinear incidence approach, to describe the spread of the disease. One limitation of the bilinear incidence function is that it assumes that the disease transmission increases whenever the susceptible population increases. is is highly unlikely in practice since an out- break of any disease is followed by pharmaceutical and nonpharmaceutical interventions. ese intervention strategies lead to a saturation in the available population. In mathematical modeling of infectious diseases, the incidence rate is defined as the number of infected individuals per unit time, and it regarded as an important tool for effectively mapping short- and long-term dynamics of the disease [15]. ere are several saturated incidence functions in literatures [15, 16]. Among them, the Crowley–Martin function Hindawi Discrete Dynamics in Nature and Society Volume 2021, Article ID 2125061, 12 pages https://doi.org/10.1155/2021/2125061