Mathematical modeling of the immune-chemotherapeutic treatment of breast cancer under some control parameters

Advances in Difference Equations

article

Yousef, Ali¹  Bozkurt, Fatma¹  Abdeljawad, Thabet³ 

[1] Department of Mathematics, Kuwait College of Science and Technology;Department of Mathematics, Faculty of Education, Erciyes University;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University

关键词: Fractional-order differential equations;    Stability analysis;    Allee effect;    Breast cancer;    Immune-chemotherapeutic treatment;   

DOI  :  10.1186/s13662-020-03151-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We consider a system of fractional-order differential equations to analyze breast cancer growth in the immune-chemotherapeutic treatment process under some control parameters: ketogenic diet, immune booster, and anti-cancer drugs. The established model assumes the growth of the tumor density under chemotherapy treatment and the immune response during the interaction between the normal cells and tumor cells. For the local stability of the critical points (tumor-free critical point, dead critical point, and co-existing critical point), we used the Routh-Hurwitz criteria to show the necessary effect of the immune booster; moreover, we addressed the ketogenic rate in the treatment process. Our theoretical and numerical studies pointed out that on early detection of the tumor density (with weak Allee effect) the treatment should be supported by ketogenic nutrition. Several examples are shown to present our theoretical findings.

【 授权许可】

CC BY