Modeling the dynamics of the novel coronavirus using Caputo-Fabrizio derivative

Abstract

The virus that begins from Wuhan China, known as COVID-19 or coronavirus is still a huge panic for humans around the globe. The elimination of this virus from our society needs proper attentions to follows the rule suggested by World Health Organization (WHO). A vast literature on the modeling of this infection in various perspective is available. In the present work, we design a new mathematical model for COVID-19 pandemic by utilizing the real infected cases reported from Kingdom of Saudi Arabia. Initially, we formulate the model with the help of classical integer order nonlinear differential equations. The treatment class is considered the model to analyze the impact of treatment on the disease dynamics. The Caputo-Fabrizio derivative with the non-singular exponential kernel is applied in order to reformulate the proposed COVID-19 transmission model with a fractional order. The biologically important parameter called the basic reproductive number is investigated both theoretically and numerically. The estimated values of R0 for the selected period are approximated to be 1.63. Further, by making use of the Picard Lindelöf theorem we provide the existence and uniqueness of the COVID-19 fractional epidemic model. Moreover, the fractional model is solved numerically and a number of simulation results are depicted using the real estimated parameters. The impact of various model parameters and memory index are shown graphically. We conclude that the fractional order epidemic models are more appropriate and provide deep insights into the disease dynamics.

Keywords

• Coronavirus infection
• Real data
• Existence and uniqueness
• Caputo-Fabrizio derivative
• Numerical results