Stability analysis and simulation of the novel Coronavirus mathematical model via the caputo fractional-order derivative: A case study in Algeria


Moussa Y. E. H. , Boudaoui A., Ullah S., Bozkurt Yousef F. , Abdeljawad T., Alqudah M. A.

Results in Physics, cilt.26, sa.2021, ss.1-14, 2021 (SCI İndekslerine Giren Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Konu: 2021
  • Basım Tarihi: 2021
  • Dergi Adı: Results in Physics
  • Sayfa Sayıları: ss.1-14

Özet

The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a

huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical

epidemic models have been adopted and simulated using the statistical data of COVID-19 in various

regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and

simulate the dynamics of this viral disease with a case study of Algeria. Initially, after the model formulation, we

utilize the well-known least square approach to estimate the model parameters from the reported COVID-19

cases in Algeria for a selected period of time. We perform the existence and uniqueness of the model solution

which are proved via the Picard-Lindel¨of method. We further compute the basic reproduction numbers and

equilibrium points, then we explore the local and global stability of both the disease-free equilibrium point and

the endemic equilibrium point. Finally, numerical results and graphical simulation are given to demonstrate the

impact of various model parameters and fractional order on the disease dynamics and control.