Dynamics of COVID-19 via singular and non-singular fractional operators under real statistical observations

Abstract

Coronavirus has paralyzed various socio-economic sectors worldwide. Such unprecedented outbreak was proved to be lethal for about 1,069,513 individuals based upon information released by Worldometers on October 09, 2020. In order to fathom transmission dynamics of the virus, different kinds of mathematical models have recently been proposed in literature. In the continuation, we have formulated a deterministic COVID-19 model under fractional operators using six nonlinear ordinary differential equations. Using fixed-point theory and Arzela Ascoli principle, the proposed model is shown to have existence of unique solution while stability analysis for differential equations involved in the model is carried out via Ulam-Hyers and generalized Ulam-Hyers conditions in a Banach space. Real COVID-19 cases considered from July 01 to August 14, 2020, in Pakistan were used to validate the model, thereby producing best fitted values for the parameters via nonlinear least-squares approach while minimizing sum of squared residuals. Elasticity indices for each parameter are computed. Two numerical schemes under singular and non-singular operators are formulated for the proposed model to obtain various simulations of particularly asymptomatically infectious individuals and of control reproduction number Rc. It has been shown that the fractional operators with order alpha=9.8254e-01 generated Rc=2.5087 which is smaller than the one obtained under the classical case ( alpha=1). Interesting behavior of the virus is explained under fractional case for the epidemiologically relevant parameters. All results are illustrated from biological viewpoint.