Dynamics analysis and optimal control of a fractional-order lung cancer model
This study presented a novel Caputo fractional-order lung cancer model aimed at analyzing the population dynamics of cancer cells under untreated conditions and different treatment strategies. First, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241697 |
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| _version_ | 1832590738290900992 |
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| author | Xingxiao Wu Lidong Huang Shan Zhang Wenjie Qin |
| author_facet | Xingxiao Wu Lidong Huang Shan Zhang Wenjie Qin |
| author_sort | Xingxiao Wu |
| collection | DOAJ |
| description | This study presented a novel Caputo fractional-order lung cancer model aimed at analyzing the population dynamics of cancer cells under untreated conditions and different treatment strategies. First, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the stability of the tumor-free equilibrium state and the internal equilibrium state. Second, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the stability of the tumor-free equilibrium state and the internal equilibrium state. We calculated the basic reproduction number and conducted a sensitivity analysis to evaluate the impact of various parameters on cancer cell growth. Next, by considering surgery and immunotherapy as control measures, we discussed the existence of an optimal solution and derived its expression using the Pontryagin maximum principle. We then performed numerical simulations of limit cycles, chaos, and bifurcation phenomena under uncontrolled conditions, as well as the dynamic behavior of cells under different control strategies. Finally, using real data from lung cancer patients, we conducted parameter estimation and curve fitting through the least squares method. The results indicated that combined therapy showed better effectiveness in inhibiting tumor cell growth, significantly outperforming single treatment strategies and more effectively controlling the progression of cancer. |
| format | Article |
| id | doaj-art-3ef484d0782941268ce13a914e43d5eb |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-3ef484d0782941268ce13a914e43d5eb2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912357593579910.3934/math.20241697Dynamics analysis and optimal control of a fractional-order lung cancer modelXingxiao Wu0Lidong Huang1Shan Zhang2Wenjie Qin3Department of Mathematics, Yunnan Minzu University, Kunming 650500, ChinaDepartment of Mathematics, Yunnan Minzu University, Kunming 650500, ChinaDepartment of Mathematics, Yunnan Minzu University, Kunming 650500, ChinaDepartment of Mathematics, Yunnan Minzu University, Kunming 650500, ChinaThis study presented a novel Caputo fractional-order lung cancer model aimed at analyzing the population dynamics of cancer cells under untreated conditions and different treatment strategies. First, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the stability of the tumor-free equilibrium state and the internal equilibrium state. Second, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the stability of the tumor-free equilibrium state and the internal equilibrium state. We calculated the basic reproduction number and conducted a sensitivity analysis to evaluate the impact of various parameters on cancer cell growth. Next, by considering surgery and immunotherapy as control measures, we discussed the existence of an optimal solution and derived its expression using the Pontryagin maximum principle. We then performed numerical simulations of limit cycles, chaos, and bifurcation phenomena under uncontrolled conditions, as well as the dynamic behavior of cells under different control strategies. Finally, using real data from lung cancer patients, we conducted parameter estimation and curve fitting through the least squares method. The results indicated that combined therapy showed better effectiveness in inhibiting tumor cell growth, significantly outperforming single treatment strategies and more effectively controlling the progression of cancer.https://www.aimspress.com/article/doi/10.3934/math.20241697caputo fractional-ordertumor modelbifurcation analysiscombined therapyoptimal control |
| spellingShingle | Xingxiao Wu Lidong Huang Shan Zhang Wenjie Qin Dynamics analysis and optimal control of a fractional-order lung cancer model AIMS Mathematics caputo fractional-order tumor model bifurcation analysis combined therapy optimal control |
| title | Dynamics analysis and optimal control of a fractional-order lung cancer model |
| title_full | Dynamics analysis and optimal control of a fractional-order lung cancer model |
| title_fullStr | Dynamics analysis and optimal control of a fractional-order lung cancer model |
| title_full_unstemmed | Dynamics analysis and optimal control of a fractional-order lung cancer model |
| title_short | Dynamics analysis and optimal control of a fractional-order lung cancer model |
| title_sort | dynamics analysis and optimal control of a fractional order lung cancer model |
| topic | caputo fractional-order tumor model bifurcation analysis combined therapy optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241697 |
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