Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu

Abstract

This research study is conducted with the aim of getting analysis based upon four different types of frequently used models of ordinary differential equations related to the chickenpox outbreak among school children of Schenzen city of China in 2013. In this regard, three new models under kernels of power law type (Caputo), exponentially decaying type kernel (Caputo-Fabrizio), and the Mittag-Leffler type kernel (Atangana-Baleanu in the Caputo sense) have been proposed and deeply investigated to determine the model with highest efficiency rate. Within the proposed models, the dimensions of each differential equation for all state variables and parameters have been balanced by carrying the respective fractional-order parameter on every dimensional quantity involved in the model. The fixed point theory employed in the present study yielded the proof for existence and uniqueness of the solutions of the fractional-order models under investigation. Using true data for 25 weeks, it is found that the model consisting of Mittag-Leffler type non-singular and non-local kernel has highest capability to capture various features of the disease. (C) 2019 Elsevier Ltd. All rights reserved.