A New Incommensurate Fractional-Order COVID 19: Modelling and Dynamical Analysis

Abstract

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the SEIR model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings.

Keywords

• SEIR model
• existence and uniqueness
• stability analysis
• Picard–Lindelöf method
• Lyapunov function
• basic reproduction number