The Volterra-Lyapunov matrix theory and nonstandard finite difference scheme to study a dynamical system

Muhammad Riaz, Kamal Shah, Aman Ullah, Manar A. Alqudah, Thabet Abdeljawad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A compartmental model is considered to study the transmission dynamics of COVID-19. The proposed model is investigated for different results by using Volterra-Lyapunov (V-L) matrix theory. In this regard, first we presented a modified form of SEIR model by incorporating three new compartments C (protected), D (death due to corona) and Q (quarantined). Both equilibrium points are computed together with basic reproductive number. In addition, local stability of both equilibrium points for our proposed model is examined by assuming that wearing of mask, testing of the unaware infected individuals and medical care of the individuals that got infected should constantly be maintained. Hence, subsequently by combining the V-L stable matrix theory with the traditional methodology of constructing the Lyapunov functions, a procedure for the global stability analysis of COVID-19 is presented. Furthermore, based on LaSalle and Lipschitz invariance principle, the global stability of disease free equilibrium point is also examined. The technique we introduced in this paper will provide the more profound comprehension to understand the basic structure of COVID-19. Moreover, for numerical interpretation of our proposed model non-standard finite difference (NSFD) scheme is utilized for simulations. Different graphical illustrations are provided to understand the transmission dynamics.

Original languageEnglish
Article number106890
JournalResults in Physics
Publication statusPublished - Sept 2023
Externally publishedYes


  • Basic reproductive number
  • Epidemic model
  • Local and global stability
  • Lyapunov and V-L function
  • Matrix theory
  • NSFD scheme


Dive into the research topics of 'The Volterra-Lyapunov matrix theory and nonstandard finite difference scheme to study a dynamical system'. Together they form a unique fingerprint.

Cite this