Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approac...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/2/95 |
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| author | Fawaz K. Alalhareth Mohammed H. Alharbi Noura Laksaci Ahmed Boudaoui Meroua Medjoudja |
| author_facet | Fawaz K. Alalhareth Mohammed H. Alharbi Noura Laksaci Ahmed Boudaoui Meroua Medjoudja |
| author_sort | Fawaz K. Alalhareth |
| collection | DOAJ |
| description | The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution’s uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>) and fractal dimensions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models. |
| first_indexed | 2024-03-07T22:31:21Z |
| format | Article |
| id | doaj.art-1f41a024291f45f5aae02d709810281f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-07T22:31:21Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-1f41a024291f45f5aae02d709810281f2024-02-23T15:17:12ZengMDPI AGFractal and Fractional2504-31102024-02-01829510.3390/fractalfract8020095Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi ArabiaFawaz K. Alalhareth0Mohammed H. Alharbi1Noura Laksaci2Ahmed Boudaoui3Meroua Medjoudja4Department of Mathematics, College of Arts & Sciences, Najran University, Najran 66462, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi ArabiaLaboratory of Mathematics Modeling and Applications, University of Adrar, Adrar 01000, AlgeriaLaboratory of Mathematics Modeling and Applications, University of Adrar, Adrar 01000, AlgeriaLaboratory of Applied Mathematics, Kasdi Merbah University, Ouargla 30000, AlgeriaThe severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution’s uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>) and fractal dimensions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models.https://www.mdpi.com/2504-3110/8/2/95COVID-19real datafractal–fractional derivativestability analysissimulations |
| spellingShingle | Fawaz K. Alalhareth Mohammed H. Alharbi Noura Laksaci Ahmed Boudaoui Meroua Medjoudja Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia Fractal and Fractional COVID-19 real data fractal–fractional derivative stability analysis simulations |
| title | Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia |
| title_full | Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia |
| title_fullStr | Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia |
| title_full_unstemmed | Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia |
| title_short | Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia |
| title_sort | investigating a fractal fractional mathematical model of the third wave of covid 19 with vaccination in saudi arabia |
| topic | COVID-19 real data fractal–fractional derivative stability analysis simulations |
| url | https://www.mdpi.com/2504-3110/8/2/95 |
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