Joshi Hardik, Yavuz Mehmet, Taylan Osman, Alkabaa Abdulaziz
Department of Mathematics, LJ Institute of Engineering and Technology, LJ University, Ahmedabad, 382210, Gujarat, India.
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya 42090, Turkiye; Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek 720038, Kyrgyzstan.
Comput Methods Programs Biomed. 2025 Mar;260:108565. doi: 10.1016/j.cmpb.2024.108565. Epub 2024 Dec 24.
Cancer's complex and multifaceted nature makes it challenging to identify unique molecular and pathophysiological signatures, thereby hindering the development of effective therapies. This paper presents a novel fractal-fractional cancer model to study the complex interplay among stem cells, effectors cells, and tumor cells in the presence and absence of chemotherapy. The cancer model with effective treatment through chemotherapy drugs is considered and discussed in detail.
The numerical method for the fractal-fractional cancer model with a generalized Mittag-Leffler kernel is presented. The Routh-Hurwitz stability criteria are applied to confirm the local asymptotically stability of an endemic equilibrium point of the cancer model without treatment and with effective treatment under some conditions. The existence and uniqueness criteria of the fractal-fractional cancer model are derived. Furthermore, the stability analysis of the fractal-fractional cancer model is performed.
The temporal concentration pattern of stem cells, effectors cells, tumor cells, and chemotherapy drugs are procured. The usage of chemotherapy drugs kills the tumor cells or decreases their density over time and as a consequence takes a longer time to reach to equilibrium point. The decay rate of stem cells and tumor cells plays a crucial role in cancer dynamics. The notable role of fractal dimensions along with fractional order is observed in capturing the cancer cell concentration.
A dynamic analysis of the fractal-fractional cancer model is demonstrated to examine the impact of chemotherapy drugs with a generalized Mittag-Leffler kernel. The model possesses three equilibrium points among them two correspond to the cancer model without treatment namely the tumor-free equilibrium point and endemic equilibrium point. One additional endemic equilibrium point exists in the case of effective treatment through chemotherapy drugs. The Routh-Hurwitz stability criteria are applied to confirm the local asymptotically stability of an endemic equilibrium point of the cancer model with and without treatment under some conditions. The chemotherapy drug plays a crucial role in controlling the growth of tumor cells. The fractal-fractional operator provided robustness to study cancer dynamics by the inclusion of memory and heterogeneity.
癌症复杂多面的性质使其难以识别独特的分子和病理生理特征，从而阻碍了有效疗法的开发。本文提出了一种新颖的分形 - 分数阶癌症模型，用于研究在有化疗和无化疗情况下干细胞、效应细胞和肿瘤细胞之间的复杂相互作用。详细考虑并讨论了通过化疗药物进行有效治疗的癌症模型。
提出了具有广义米塔格 - 莱夫勒核的分形 - 分数阶癌症模型的数值方法。应用劳斯 - 赫尔维茨稳定性准则来确认在某些条件下未经治疗和经有效治疗的癌症模型地方病平衡点的局部渐近稳定性。推导了分形 - 分数阶癌症模型的存在唯一性准则。此外，还进行了分形 - 分数阶癌症模型的稳定性分析。
获得了干细胞、效应细胞、肿瘤细胞和化疗药物的时间浓度模式。化疗药物的使用会杀死肿瘤细胞或随着时间推移降低其密度，结果达到平衡点所需时间更长。干细胞和肿瘤细胞的衰减率在癌症动态中起关键作用。在捕获癌细胞浓度方面观察到分形维数与分数阶的显著作用。
展示了对分形 - 分数阶癌症模型的动态分析，以研究具有广义米塔格 - 莱夫勒核的化疗药物的影响。该模型有三个平衡点，其中两个对应于未经治疗的癌症模型，即无瘤平衡点和地方病平衡点。在通过化疗药物进行有效治疗的情况下存在一个额外的地方病平衡点。应用劳斯 - 赫尔维茨稳定性准则来确认在某些条件下有治疗和无治疗的癌症模型地方病平衡点的局部渐近稳定性。化疗药物在控制肿瘤细胞生长中起关键作用。分形 - 分数阶算子通过纳入记忆和异质性为研究癌症动态提供了稳健性。
