# Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease
## 1 Introduction  
Coronavirus disease 2019 (COVID-19) is an acute infectious disease of the respiratory system that is caused by the SARS-CoV-2 virus infection. The World Health Organization (WHO) issued the official name and explained it as CO for corona, VI for virus, D for disease, and 19 for the year of first identification. The infection symptoms are usually a fever, dry cough, fatigue, loss of appetite, and shortness of breath. COVID-19 was first recognized and described on December 8, 2019, in the Wuhan, Republic of China. As a result of rapidly spreading the virus into other countries and continents, on March 11, 2020, WHO classified COVID-19 as a pandemic. With both mortality and infectiousness rates, COVID-19 is recognized as the worst pandemic in modern times since the flu pandemic of the early 20 th century. Mathematical modeling theories of infectious disease transmission dynamics have prompted considerable research interest, as the worldwide issue of the COVID-19 outbreak has attracted scientists from different areas [1; 2; 3]. The Susceptible-Infected-Removed (SIR) epidemic model is a classical compartmental model that is widely used to predict the progress of infectious disease [4; 5; 6]. Its origins date to the fundamental work by [PERSON] and [PERSON] in the early 20 th century [7]. Although the SIR model may be useful in modeling several epidemic processes, it may not be sufficient to describe the COVID-19 spread dynamics. Therefore, there are some modifications to the SIR model used in the approximation of COVID-19 disease [8]. [PERSON] et al. [9] used the SEIR (susceptible-exposed-infectious-removed) compartment model in order to study the transmission and control of COVID-19. [PERSON] et al. [10] proposed an SEIR model extended by adding contact tracing and other interventions, such as quarantine, lockdown, and social distancing. The SIDARTHE (susceptible-infected-diagnosed-ailing-recognized-threatened-healed-extinct) model with differentiating between diagnosed and non-diagnosed individuals has been presented by [PERSON] et al. [11] in order to analyze the COVID-19 epidemic in Italy. In [12], [PERSON] et al. introduced the SEIPAHRF (susceptible-exposed-symptomatic infectious-super spreaders-asymptomatic infectious-hospital-recoveredfatality) model that considers the class of super-spreaders in order to study the transmission dynamics for the outbreak that occurred in Wuhan, China. On the other hand, it is well known that the implementation of fractional calculus in differential equations of various processes, which lead to fractional-order generalizations of the modeling approaches, can significantly improve the modeling performance in several processes. Hence, many scientists have paid attention to this mathematical analysis branch, as it may give a better understanding of some complex physical phenomena, where ordinary calculus fails to provide a precise explanation. [PERSON] and [PERSON] [13] applied fractional derivative to model chaos and statistics. [PERSON] and [PERSON] [14] used the Atangana--Baleanu definition for the fractional derivative to introduce the new fractional mask for image denoising. [PERSON] et al. [15] obtained solutions of a cancer chemotherapy effect model involving the Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. There are some papers considering the fractional-order derivate implemented in the compartment models. A fractional-order extended SEIR (susceptible-exposed-infectious-removed) model considering interaction among people and the reservoir of the infection (seafood market) has been presented and studied by [PERSON] and [PERSON] [16]. [PERSON] and [PERSON] [17] used the conformable fractional differential transform method to compute an approximate solution of the fractional-order SIR epidemic model of childhood disease. [PERSON] et al. [18] presented a nonlinear fractional-order model under the fractional Adam-BashForth method.