Malaysian Journal of Mathematical Sciences, September 2022, Vol. 16, No. 3
Numerical Simulations of the Fractional-Order SIQ Mathematical Model of Corona Virus Disease Using the Nonstandard Finite Difference Scheme
Raza, N., Bakar, A., Khan, A., and Tunç, C.
Corresponding Email: cemtunc@yahoo.com
Received date: 30 June 2022
Accepted date: 10 August 2022
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 analyticalworks. 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.
Keywords: corona virus disease; Caputo fractional derivative; basic reproduction number; local stability; nonstandard finite difference method
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