Eur. Phys. J. Plus (2019) 134: 171
https://doi.org/10.1140/epjp/i2019-12661-7

Regular Article

Fractional derivatives applied to MSEIR problems: Comparative study with real world data

¹ Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, 76062, Jamshoro, Pakistan
² Firat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey
³ Federal University Dutse, Science Faculty, Department of Mathematics, 7156, Jigawa, Nigeria

^* e-mail: sania.qureshi@faculty.muet.edu.pk

Received: 7 March 2019
Accepted: 25 March 2019
Published online: 26 April 2019

Abstract

In the present study, an epidemiological model (MSEIR) of varicella disease outbreak, also called the chickenpox, among school children in the Shenzhen city of China in 2015 is proposed under three most commonly used approaches, such as the Caputo, Caputo-Fabrizio and the Atangana-Baleanu-Caputo operators, while taking care of the dimensional consistency of the proposed model. With the help of the fixed point theory, it is proved that the dynamical model under consideration possesses a unique solution. Numerical simulations are carried out for the analysis of the model. Availability of the real data helps to provide evidence for the claims made in the present analysis for the three operators under consideration. Using the root sum squared approach, the efficiency rate of the fractional-order versions is found to be about 20%, 22.5% and 24.7% for the Caputo, the Caputo-Fabrizio and the Atangana-Baleanu-Caputo operators, respectively, for this particular MSEIR model.