Mathematical Modeling of Cancer Cell Dynamics Under Chemotherapy: An Analytical Approach

Abstract

This paper introduces a mathematical model that focuses on both periodic and continuous dose regimes in order to investigate the dynamics of cancer cells while they are undergoing chemotherapy to treat the disease. In order to characterize the interactions between cancer cells, healthy cells, and the chemotherapy medication, the model makes use of a set of ordinary differential equations. It has been demonstrated through simulations that both periodic and continuous chemotherapy has the ability to reduce the size of tumors. However, continuous delivery has been shown to be more effective in reducing tumor size, despite the fact that it causes greater damage to healthy cells. On the other hand, periodic chemotherapy makes it easier for good cells to recover to some degree while simultaneously allowing tumors to proliferate between sessions. A sensitivity study is a type of research that investigates the effects of chemotherapy on both its efficacy and its toxicity. This type of study highlights the importance of developing personalized treatment regimens that can effectively control tumors while also protecting healthy tissue. The model is modified to include the concept of medicine resistance, which illustrates the likelihood of treatment failure becoming more prevalent over time. The results of this study shed light on the optimization of chemotherapy schedules and suggest potential avenues for further research. These avenues include combination drugs and adaptive treatment strategies.