Numerical Simulations of the Fractional-Order SIQ Mathematical Model of Corona Virus Disease Using the Nonstandard Finite Difference Scheme

Abstract

This paper proposes a novel nonlinear fractional-order pandemic model with Caputo derivative for corona virus disease. A nonstandard finite difference (NSFD) approach is presented to solve this model numerically. This strategy preserves some of the most significant physical properties of the solution such as non-negativity, boundedness and stability or convergence to a stable steady state. The equilibrium points of the model are analyzed and it is determined that the proposed fractional model is locally asymptotically stable at these points. Non-negativity and boundedness of the solution are proved for the considered model. Fixed point theory is employed for the existence and uniqueness of the solution. The basic reproduction number is computed to investigate the dynamics of corona virus disease. It is worth mentioning that the non-integer derivative gives significantly more insight into the dynamic complexity of the corona model. The suggested technique produces dynamically consistent outcomes and excellently matches the analytical works. To illustrate our results, we conduct a comprehensive quantitative study of the proposed model at various quarantine levels. Numerical simulations show that can eradicate a pandemic quickly if a human population implements obligatory quarantine measures at varying coverage levels while maintaining sufficient knowledge.

Fractional Block Method for the Solution of Fractional Order Differential Equations

“…This is because FDEs allow for the description of memory effects, as stated in [15]. Mathematical models that employ FDEs include the Prey-Predator Model [14], the SIR Model [15], the Corona Virus Disease Model [28], the HIV Model [26], and the Pharmacokinetics Model [27].…”

Exact Finite-Difference Calculus: Beyond Set of Entire Functions

“…The Grunwald-Letnikov fractional derivatives have been used in numerical analysis to discretize the fractional differential equations. From this year, the non-standard discretization scheme began to be actively studied and applied to fractional differential equations of the non-integer orders in various works [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84]. However, the disadvantages of this scheme after generalization for operators of the non-integer order remained almost the same.…”

A New Compact Numerical Scheme for Solving Time Fractional Mobile-Immobile Advection-Dispersion Model

“…Fractional calculus has recently proven to be useful in mimicking aberrant behaviours that can occur in a range of scientific and engineering fields. Many mathematical models are developed using the fractional derivatives like the nonlinear behaviour of earthquake [6], continuum fluid-dynamics [7], porous media [8], hydrology [18], fractured media at regional scales [40], complex dynamics in biological tissues [17], non-Fickian transport [37,38], optimization of radiotherapy cancer treatments [5], SIQ mathematical model of Corona virus disease [23].…”