A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data
Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We c...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/12/2521 |
| _version_ | 1797431449126699008 |
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| author | Fehaid Salem Alshammari Fahir Talay Akyildiz Muhammad Altaf Khan Anwarud Din Pongsakorn Sunthrayuth |
| author_facet | Fehaid Salem Alshammari Fahir Talay Akyildiz Muhammad Altaf Khan Anwarud Din Pongsakorn Sunthrayuth |
| author_sort | Fehaid Salem Alshammari |
| collection | DOAJ |
| description | Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≈</mo><mn>1.1367</mn></mrow></semantics></math></inline-formula>. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically. |
| first_indexed | 2024-03-09T09:45:14Z |
| format | Article |
| id | doaj.art-cfebb66973084a53bd70b24ffe6c928c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T09:45:14Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-cfebb66973084a53bd70b24ffe6c928c2023-12-02T00:39:38ZengMDPI AGSymmetry2073-89942022-11-011412252110.3390/sym14122521A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real DataFehaid Salem Alshammari0Fahir Talay Akyildiz1Muhammad Altaf Khan2Anwarud Din3Pongsakorn Sunthrayuth4Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi ArabiaFaculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South AfricaDepartment of Mathematics, Sun Yat-Sen University, Guangzhou 510275, ChinaDepartment of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT) Thanyaburi, Pathumthani 12110, ThailandNatural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≈</mo><mn>1.1367</mn></mrow></semantics></math></inline-formula>. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically.https://www.mdpi.com/2073-8994/14/12/2521stochastic COVID-19 mathematical modelreal datastability resultsparameters estimationsnumerical results |
| spellingShingle | Fehaid Salem Alshammari Fahir Talay Akyildiz Muhammad Altaf Khan Anwarud Din Pongsakorn Sunthrayuth A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data Symmetry stochastic COVID-19 mathematical model real data stability results parameters estimations numerical results |
| title | A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data |
| title_full | A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data |
| title_fullStr | A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data |
| title_full_unstemmed | A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data |
| title_short | A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data |
| title_sort | stochastic mathematical model for understanding the covid 19 infection using real data |
| topic | stochastic COVID-19 mathematical model real data stability results parameters estimations numerical results |
| url | https://www.mdpi.com/2073-8994/14/12/2521 |
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