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

Abdallah Al-Husban, Noureddine Djenina (), Rania Saadeh, Adel Ouannas and Giuseppe Grassi
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Abdallah Al-Husban: Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan
Noureddine Djenina: Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Rania Saadeh: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
Adel Ouannas: Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy

Mathematics, 2023, vol. 11, issue 3, 1-16

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 S E I R 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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