Fractional Modeling of Cancer with Mixed Therapies

• Published in: Frontiers in bioscience (Landmark. Print) Vol. 28; no. 8; p. 174
• Main Authors: Javeed, Shumaila, Abdeen, Zain Ul, Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: IMR Press 01.08.2023
• Subjects: adams bashforth-moulton method; fractional modeling; mixed therapies; stability analysis
• ISSN: 2768-6701; 2768-6698
• DOI: 10.31083/j.fbl2808174

BACKGROUNDCancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer. METHODSIn this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method. RESULTSFor all fractional models the reasonable range of fractional order is between β = 0.6 and β = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment. CONCLUSIONSAt the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.