IMR Press / FBL / Volume 28 / Issue 8 / DOI: 10.31083/j.fbl2808174
Open Access Original Research
Fractional Modeling of Cancer with Mixed Therapies
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1 Department of Mathematics, COMSATS University Islamabad, 45550 Islamabad, Pakistan
2 Department of Computer Sciences and Mathematics, Lebanese American University, 1102-2801 Beirut, Lebanon
3 Department of Mathematics, Research Centre, Near East University 99138 Nicosia / TRNC Mersin 10, Turkey
4 Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
5 Institute of Space Sciences, R-76900 Magurele-Bucharest, Romania
6 Medical University Hospital, China Medical University, 404327 Taichung, Taiwan
*Correspondence: shumaila_javeed@comsats.edu.pk (Shumaila Javeed)
Front. Biosci. (Landmark Ed) 2023, 28(8), 174; https://doi.org/10.31083/j.fbl2808174
Submitted: 25 March 2023 | Revised: 20 June 2023 | Accepted: 19 July 2023 | Published: 18 August 2023
Copyright: © 2023 The Author(s). Published by IMR Press.
This is an open access article under the CC BY 4.0 license.
Abstract

Background: Cancer 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. Methods: In 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. Results: For 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. Conclusions: At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.

Keywords
mixed therapies
fractional modeling
stability analysis
Adams Bashforth-Moulton method
Figures
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