A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment

• 作者: Abdon Atangana Sachin Kumar
• 来源期刊: 生物数学学报:英文版
• 学科: 数学
• 关键词: Fractional PDE diffusion equation operational matrix Genocchi polynomial collocation method
• 年，卷（期）: 2020,（3）
• 页码范围: 165-181
• 页数: 17页
• 分类号: O17

摘要

Cancer belongs to the class of discascs which is symbolized by out of control cells growth.These cells affect DNAs and damage them.There exist many treatments avail-able in medical science as radiation therapy,targeted therapy,surgery,palliative care and chemotherapy.Cherotherapy is one of the most popular treatments which depends on the type,location and grade of cancer.In this paper,we are working on modeling and prediction of the effect of chemotherapy on cancer cells using a fractional differen-tial equation by using the differential operator in Caputos sense.The presented model depicts the interaction between tumor,norrnal and immune cells in a tumor by using a system of four coupled fractional partial differential equations(PDEs).For this system,initial conditions of tumor cells and dimensions are taken in such a way that tumor is spread out enough in size and can be detected easily with the clinical machines.An operational matrix method with Genocchi polynomials is applied to study this system of fractional PDFs(FPDEs).An operational matrix for fract.ional differentiation is derived.Applying the collocation method and using this matrix,the nonlinear system is reduced to a system of algebraic equations,which can be solved using Newton iteration method.The salient features of this paper are the pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of fractional exponent on diffusive nature of immune cells,tumor cells,normal cells and chemother-apeutic drug and depict the interaction among immune cells,normal cells and tumor cells in a tumor site.