A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior

Noureddine Djenina, Adel Ouannas, Iqbal M. Batiha, Giuseppe Grassi, Taki-Eddine Oussaeif and Shaher Momani
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Noureddine Djenina: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Adel Ouannas: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Iqbal M. Batiha: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
Taki-Eddine Oussaeif: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates

Mathematics, 2022, vol. 10, issue 13, 1-16

Abstract: During the broadcast of Coronavirus across the globe, many mathematicians made several mathematical models. This was, of course, in order to understand the forecast and behavior of this epidemic’s spread precisely. Nevertheless, due to the lack of much information about it, the application of many models has become difficult in reality and sometimes impossible, unlike the simple SIR model. In this work, a simple, novel fractional-order discrete model is proposed in order to study the behavior of the COVID-19 epidemic. Such a model has shown its ability to adapt to the periodic change in the number of infections. The existence and uniqueness of the solution for the proposed model are examined with the help of the Picard Lindelöf method. Some theoretical results are established in view of the connection between the stability of the fixed points of this model and the basic reproduction number. Several numerical simulations are performed to verify the gained results.

Keywords: SIR model; fractional-order discrete operators; stability; existence and uniqueness; Picard Lindelöf method; basic reproduction number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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