Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods
In the search for causes and cures of cancer diseases, many mathematical models developed have resulted in systems of nonlinear stiff ordinary differential equations. With these models, many numerical estimates of biological knowledge of the parameters have been obtained, a number of phenomena inter...
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MDPI AG
2023-03-01
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| author | Dauda Gulibur Yakubu Abdulhameed Mohammed Adamu Garba Tahiru Kadas Saidu Abubakar Magaji Yunbunga Adamu |
| author_facet | Dauda Gulibur Yakubu Abdulhameed Mohammed Adamu Garba Tahiru Kadas Saidu Abubakar Magaji Yunbunga Adamu |
| author_sort | Dauda Gulibur Yakubu |
| collection | DOAJ |
| description | In the search for causes and cures of cancer diseases, many mathematical models developed have resulted in systems of nonlinear stiff ordinary differential equations. With these models, many numerical estimates of biological knowledge of the parameters have been obtained, a number of phenomena interpreted, and predictions were made in order to gain further knowledge of cancer development and possible treatment. In this study, numerical simulations of the models were performed using continuous block implicit hybrid methods and the results obtained support the theoretical and clinical findings. We analyzed the interactions among the various tumor cell populations and present the results graphically. From the graphical representation of results, one can clearly see the effects of all the tumor cell populations involved in the competition, as well as the effects of some treatments by the applications of some therapeutic agents which have been heavily used in the clinical treatments of breast cancer. The treatments in the past were mostly conventional chemotherapies, which were used either singly (alone) or in combination with each other or other therapies, and all played vital roles, except for the side effects that these therapies incur in normal tissues and organs. Thus, from recent research works, it is now clear that in many cases they do not represent a complete cure. Therefore, the need to address not only the preventative measures of breast cancer, but also more successful treatment, is clear, and can be successfully achieved to increase the survival rate of breast cancer patients. |
| first_indexed | 2024-03-11T06:31:19Z |
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| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T06:31:19Z |
| publishDate | 2023-03-01 |
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| spelling | doaj.art-b52f03c1d17240e491843c268b5751fa2023-11-17T11:12:14ZengMDPI AGFractal and Fractional2504-31102023-03-017323710.3390/fractalfract7030237Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid MethodsDauda Gulibur Yakubu0Abdulhameed Mohammed1Adamu Garba Tahiru2Kadas Saidu Abubakar3Magaji Yunbunga Adamu4Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi PMB0248, NigeriaSchool of Science and Technology, The Federal Polytechnic Bauchi, Bauchi 741102, NigeriaDepartment of Mathematical Sciences, Bauchi State University Gadau, Bauchi P.O. Box 65, NigeriaDepartment of Obstetrics Gynaecology, Abubakar Tafawa Balewa University Teaching Hospital, Bauchi 74027, NigeriaDepartment of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi PMB0248, NigeriaIn the search for causes and cures of cancer diseases, many mathematical models developed have resulted in systems of nonlinear stiff ordinary differential equations. With these models, many numerical estimates of biological knowledge of the parameters have been obtained, a number of phenomena interpreted, and predictions were made in order to gain further knowledge of cancer development and possible treatment. In this study, numerical simulations of the models were performed using continuous block implicit hybrid methods and the results obtained support the theoretical and clinical findings. We analyzed the interactions among the various tumor cell populations and present the results graphically. From the graphical representation of results, one can clearly see the effects of all the tumor cell populations involved in the competition, as well as the effects of some treatments by the applications of some therapeutic agents which have been heavily used in the clinical treatments of breast cancer. The treatments in the past were mostly conventional chemotherapies, which were used either singly (alone) or in combination with each other or other therapies, and all played vital roles, except for the side effects that these therapies incur in normal tissues and organs. Thus, from recent research works, it is now clear that in many cases they do not represent a complete cure. Therefore, the need to address not only the preventative measures of breast cancer, but also more successful treatment, is clear, and can be successfully achieved to increase the survival rate of breast cancer patients.https://www.mdpi.com/2504-3110/7/3/237competition modelimmune systemmathematical modelpopulation modeldifferential equation |
| spellingShingle | Dauda Gulibur Yakubu Abdulhameed Mohammed Adamu Garba Tahiru Kadas Saidu Abubakar Magaji Yunbunga Adamu Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods Fractal and Fractional competition model immune system mathematical model population model differential equation |
| title | Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods |
| title_full | Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods |
| title_fullStr | Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods |
| title_full_unstemmed | Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods |
| title_short | Numerical Simulation of Nonlinear Dynamics of Breast Cancer Models Using Continuous Block Implicit Hybrid Methods |
| title_sort | numerical simulation of nonlinear dynamics of breast cancer models using continuous block implicit hybrid methods |
| topic | competition model immune system mathematical model population model differential equation |
| url | https://www.mdpi.com/2504-3110/7/3/237 |
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