Eur. Phys. J. Plus (2020) 135: 952
https://doi.org/10.1140/epjp/s13360-020-00991-8

Regular Article

Mathematical modeling of breast cancer in a mixed immune-chemotherapy treatment considering the effect of ketogenic diet

¹ Department of Mathematics, Kuwait College of Science and Technology, 27235, Kuwait City, Kuwait
² Department of Mathematics Education, Erciyes University, 38039, Kayseri, Turkey
³ Department of Mathematics and General Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia
⁴ Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
⁵ Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
⁶ Department of Computer Engineering, Erciyes University, 38039, Kayseri, Turkey
⁷ Presidency Office, Rectorate, Middle East Technical University, 06800, Cankaya, Turkey

^a fbozkurt@erciyes.edu.tr
^c tabdeljawad@psu.edu.sa

Received: 21 July 2020
Accepted: 7 December 2020
Published online: 21 December 2020

Abstract

We present a mathematical model of breast cancer as a system of differential equations with piecewise constant arguments to analyze the tumor growth and chemotherapeutic treatment. We initiate a model by assuming the malignant-tumor growth under the chemotherapeutic treatment in considering the immune response by investigating the competition among both normal and tumor cells. The local stability of the system was considered by using the stability theorems for difference equations. For global stability, we assume a suitable Lyapunov function. Some sensitive parameters are considered in the stability and oscillation behaviors. To analyze the breast cancer population for the extinction case, we incorporate the Allee effect at time t. We support the theoretical results through numerical simulations.