Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy
In the present study, we formulate a mathematical model to understand breast cancer in the population of Saudi Arabia. We consider a mathematical model and study its mathematical results. We show that the breast cancer model possesses a unique system of solutions. The stability results are shown for...
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/1975 |
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| author | Ebraheem Alzahrani M. M. El-Dessoky Muhammad Altaf Khan |
| author_facet | Ebraheem Alzahrani M. M. El-Dessoky Muhammad Altaf Khan |
| author_sort | Ebraheem Alzahrani |
| collection | DOAJ |
| description | In the present study, we formulate a mathematical model to understand breast cancer in the population of Saudi Arabia. We consider a mathematical model and study its mathematical results. We show that the breast cancer model possesses a unique system of solutions. The stability results are shown for the model. We consider the reported cases in Saudi Arabia for the period 2004–2016. The data are given for the female population in Saudi Arabia that is suffering from breast cancer. The data are used to obtain the values of the parameters, and then we predict the long-term behavior with the obtained numerical results. The numerical results are obtained using the proposed parameterized approach. We present graphical results for the breast cancer model under effective parameters such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>2</mn></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>3</mn></msub></semantics></math></inline-formula> that cause decreasing future cases in the population of stages 3 and 4, and the disease-free condition. Chemotherapy generally increases the risk of cardiotoxicity, and, hence, our model result shows this fact. The combination of chemotherapy stages 3 and 4 and the parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>2</mn></msub></semantics></math></inline-formula> together at a low-level rate and also treating the patients before the chemotherapy will decrease the population of cardiotoxicity. The findings of this study are intended to reduce the number of cardiotoxic patients and raise the number of patients who recover following chemotherapy, which will aid in public health decision making. |
| first_indexed | 2024-03-11T04:13:15Z |
| format | Article |
| id | doaj.art-7464f9a050464bd096f5b34b164bf2a1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:13:15Z |
| publishDate | 2023-04-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7464f9a050464bd096f5b34b164bf2a12023-11-17T23:18:22ZengMDPI AGMathematics2227-73902023-04-01119197510.3390/math11091975Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and TherapyEbraheem Alzahrani0M. M. El-Dessoky1Muhammad Altaf Khan2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaInstitute for Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaIn the present study, we formulate a mathematical model to understand breast cancer in the population of Saudi Arabia. We consider a mathematical model and study its mathematical results. We show that the breast cancer model possesses a unique system of solutions. The stability results are shown for the model. We consider the reported cases in Saudi Arabia for the period 2004–2016. The data are given for the female population in Saudi Arabia that is suffering from breast cancer. The data are used to obtain the values of the parameters, and then we predict the long-term behavior with the obtained numerical results. The numerical results are obtained using the proposed parameterized approach. We present graphical results for the breast cancer model under effective parameters such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>2</mn></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>3</mn></msub></semantics></math></inline-formula> that cause decreasing future cases in the population of stages 3 and 4, and the disease-free condition. Chemotherapy generally increases the risk of cardiotoxicity, and, hence, our model result shows this fact. The combination of chemotherapy stages 3 and 4 and the parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mn>2</mn></msub></semantics></math></inline-formula> together at a low-level rate and also treating the patients before the chemotherapy will decrease the population of cardiotoxicity. The findings of this study are intended to reduce the number of cardiotoxic patients and raise the number of patients who recover following chemotherapy, which will aid in public health decision making.https://www.mdpi.com/2227-7390/11/9/1975breast cancer datastability resultsmathematical modelnumerical results |
| spellingShingle | Ebraheem Alzahrani M. M. El-Dessoky Muhammad Altaf Khan Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy Mathematics breast cancer data stability results mathematical model numerical results |
| title | Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy |
| title_full | Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy |
| title_fullStr | Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy |
| title_full_unstemmed | Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy |
| title_short | Mathematical Model to Understand the Dynamics of Cancer, Prevention Diagnosis and Therapy |
| title_sort | mathematical model to understand the dynamics of cancer prevention diagnosis and therapy |
| topic | breast cancer data stability results mathematical model numerical results |
| url | https://www.mdpi.com/2227-7390/11/9/1975 |
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