A mathematical tumor growth model for exploring saturated response of M2 macrophages
This study addresses a tumor–macrophage interaction model to examine the role of the saturated response of M2 macrophages. We find the equilibrium point of the model and analyze local stability at each equilibrium. We show that tumor-free equilibrium is always stable, whereas, under certain conditio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Healthcare Analytics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S277244252400008X |
| _version_ | 1827223298372534272 |
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| author | Kaushik Dehingia Yamen Alharbi Vikas Pandey |
| author_facet | Kaushik Dehingia Yamen Alharbi Vikas Pandey |
| author_sort | Kaushik Dehingia |
| collection | DOAJ |
| description | This study addresses a tumor–macrophage interaction model to examine the role of the saturated response of M2 macrophages. We find the equilibrium point of the model and analyze local stability at each equilibrium. We show that tumor-free equilibrium is always stable, whereas, under certain conditions, the tumor-dominant and interior equilibrium are asymptotically stable. Moreover, stable and unstable limit cycles and period-doubling bifurcation have been observed at the interior equilibrium point. A remarkable result has been observed: in the presence of a saturated response of M2 macrophages, with a relatively higher activation rate of M2 macrophages due to tumor cells, the disease spreads more quickly in the body. Hence, M1 macrophages cannot stabilize the system, and aperiodic oscillations are observed. Furthermore, we show that a better immune response can reverse that system’s unstable nature. Numerical simulations verify the analytical results. |
| first_indexed | 2024-03-08T09:00:31Z |
| format | Article |
| id | doaj.art-6e86a7a22c844ea1a70b5b6cad131578 |
| institution | Directory Open Access Journal |
| issn | 2772-4425 |
| language | English |
| last_indexed | 2025-03-21T16:52:09Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Healthcare Analytics |
| spelling | doaj.art-6e86a7a22c844ea1a70b5b6cad1315782024-06-15T06:14:53ZengElsevierHealthcare Analytics2772-44252024-06-015100306A mathematical tumor growth model for exploring saturated response of M2 macrophagesKaushik Dehingia0Yamen Alharbi1Vikas Pandey2Department of Mathematics, Sonari College, Sonari 785690, Assam, India; Corresponding author.Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi ArabiaNIPS, National Institute of Natural Science, Okazaki, 4448585, JapanThis study addresses a tumor–macrophage interaction model to examine the role of the saturated response of M2 macrophages. We find the equilibrium point of the model and analyze local stability at each equilibrium. We show that tumor-free equilibrium is always stable, whereas, under certain conditions, the tumor-dominant and interior equilibrium are asymptotically stable. Moreover, stable and unstable limit cycles and period-doubling bifurcation have been observed at the interior equilibrium point. A remarkable result has been observed: in the presence of a saturated response of M2 macrophages, with a relatively higher activation rate of M2 macrophages due to tumor cells, the disease spreads more quickly in the body. Hence, M1 macrophages cannot stabilize the system, and aperiodic oscillations are observed. Furthermore, we show that a better immune response can reverse that system’s unstable nature. Numerical simulations verify the analytical results.http://www.sciencedirect.com/science/article/pii/S277244252400008XTumorMacrophagesLimit cyclesHopf bifurcationEquilibriumTime series |
| spellingShingle | Kaushik Dehingia Yamen Alharbi Vikas Pandey A mathematical tumor growth model for exploring saturated response of M2 macrophages Healthcare Analytics Tumor Macrophages Limit cycles Hopf bifurcation Equilibrium Time series |
| title | A mathematical tumor growth model for exploring saturated response of M2 macrophages |
| title_full | A mathematical tumor growth model for exploring saturated response of M2 macrophages |
| title_fullStr | A mathematical tumor growth model for exploring saturated response of M2 macrophages |
| title_full_unstemmed | A mathematical tumor growth model for exploring saturated response of M2 macrophages |
| title_short | A mathematical tumor growth model for exploring saturated response of M2 macrophages |
| title_sort | mathematical tumor growth model for exploring saturated response of m2 macrophages |
| topic | Tumor Macrophages Limit cycles Hopf bifurcation Equilibrium Time series |
| url | http://www.sciencedirect.com/science/article/pii/S277244252400008X |
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