A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel

Abstract

In this paper, we investigate an epidemic model of the novel coronavirus disease or COVID-19 using the Caputo-Fabrizio derivative. We discuss the existence and uniqueness of solution for the model under consideration, by using the the Picard-Lindelöf theorem. Further, using an efficient numerical approach we present an iterative scheme for the solutions of proposed fractional model. Finally, many numerical simulations are presented for various values of the fractional order to demonstrate the impact of some effective and commonly used interventions to mitigate this novel infection. From the simulation results we conclude that the fractional order epidemic model provides more insights about the disease dynamics.

Keywords: 26A33; 65D05; 65R20; 93E24; COVID-19 pandemic; Caputo–Fabrizio fractional derivative; Epidemic model; Existence and uniqueness; Isolation; Numerical simulation; Quarantine.

Fig. 1

Diagram of different stages of transmission of a novel coronavirus in different compartment.

Fig. 2

Simulations of the COVID-19 model (8) for different values of fractional order $\nu$.

Fig. 3

The impact of parameter $c$ (contact rate) on total infective population where (a) $\nu =1,$ (b) $\nu =0.9,$ (c) $\nu =0.8,$ (d) $\nu =0.7$.

Fig. 4

The impact of parameter ${\delta }_I$ (isolation rate) on total infective population where (a) $\nu =1,$ (b) $\nu =0.9,$ (c) $\nu =0.8,$ (d) $\nu =0.7$.

Fig. 5

The impact of parameter $q$ (quarantine rate) on total infective population where (a) $\nu =1,$ (b) $\nu =0.9,$ (c) $\nu =0.8,$ (d) $\nu =0.7$.