Dynamical analysis of tumor model with obesity and immunosuppression
In this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is pr...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-12-01
|
| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016822002769 |
| _version_ | 1797978760898674688 |
|---|---|
| author | Mahmoud A. Abd-Rabo Mohammed Zakarya A.A. Alderremy Shaban Aly |
| author_facet | Mahmoud A. Abd-Rabo Mohammed Zakarya A.A. Alderremy Shaban Aly |
| author_sort | Mahmoud A. Abd-Rabo |
| collection | DOAJ |
| description | In this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is proven that TNF model undergoes codimension-1 bifurcation, while Hopf bifurcation does not occur in the non-delay model. For delayed TNF, we take into the late response of fat cells to tumor cells. Consequently, the delay factor is a considerable parameter in TNF model. Hence, we presented a formula of the time delay value for the occurrence of periodic solutions. Additionally, the stability of Hopf bifurcation was analysed. Numerical simulations are provided to illustrate and extend the theoretical results, we provide our study with numerical simulations inclusive families of periodic solutions. |
| first_indexed | 2024-04-11T05:29:14Z |
| format | Article |
| id | doaj.art-607415016a0c43a8a0bd89d012651010 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-11T05:29:14Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-607415016a0c43a8a0bd89d0126510102022-12-23T04:38:37ZengElsevierAlexandria Engineering Journal1110-01682022-12-0161121089710911Dynamical analysis of tumor model with obesity and immunosuppressionMahmoud A. Abd-Rabo0Mohammed Zakarya1A.A. Alderremy2Shaban Aly3Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt; Corresponding author at: Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt; Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, EgyptIn this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is proven that TNF model undergoes codimension-1 bifurcation, while Hopf bifurcation does not occur in the non-delay model. For delayed TNF, we take into the late response of fat cells to tumor cells. Consequently, the delay factor is a considerable parameter in TNF model. Hence, we presented a formula of the time delay value for the occurrence of periodic solutions. Additionally, the stability of Hopf bifurcation was analysed. Numerical simulations are provided to illustrate and extend the theoretical results, we provide our study with numerical simulations inclusive families of periodic solutions.http://www.sciencedirect.com/science/article/pii/S1110016822002769Cancer modelImmunosuppressionObesityCompetition modelTime delay model |
| spellingShingle | Mahmoud A. Abd-Rabo Mohammed Zakarya A.A. Alderremy Shaban Aly Dynamical analysis of tumor model with obesity and immunosuppression Alexandria Engineering Journal Cancer model Immunosuppression Obesity Competition model Time delay model |
| title | Dynamical analysis of tumor model with obesity and immunosuppression |
| title_full | Dynamical analysis of tumor model with obesity and immunosuppression |
| title_fullStr | Dynamical analysis of tumor model with obesity and immunosuppression |
| title_full_unstemmed | Dynamical analysis of tumor model with obesity and immunosuppression |
| title_short | Dynamical analysis of tumor model with obesity and immunosuppression |
| title_sort | dynamical analysis of tumor model with obesity and immunosuppression |
| topic | Cancer model Immunosuppression Obesity Competition model Time delay model |
| url | http://www.sciencedirect.com/science/article/pii/S1110016822002769 |
| work_keys_str_mv | AT mahmoudaabdrabo dynamicalanalysisoftumormodelwithobesityandimmunosuppression AT mohammedzakarya dynamicalanalysisoftumormodelwithobesityandimmunosuppression AT aaalderremy dynamicalanalysisoftumormodelwithobesityandimmunosuppression AT shabanaly dynamicalanalysisoftumormodelwithobesityandimmunosuppression |