Mathematical Modelling of Tumour Treatment With Chemotherapy

In this study, a cancer disease model incorporating dynamics between immune cells and tumour cells, as well as competition between tumour cells and normal cells, was formulated in an attempt to understand the interaction dynamics that govern the complex interplay within the tumour microenvironment. Mathematical analysis has been employed to derive conditions for the boundedness of solutions and to discuss disease thresholds such as the basic reproduction number. Numerical simulations have been conducted, utilising the Runge–Kutta scheme to solve the model. Furthermore, the model was extended to include chemotherapy treatment and reformulated as an optimal control problem. Optimal control techniques have been applied to examine the role of chemotherapy in enhancing tumour cell elimination and minimising adverse effects on immune cells and normal cells. The results indicate that a low concentration of the drug leads to a prolonged period for tumour clearance. Conversely, a higher drug concentration resulted in a quicker tumour clearance, albeit with adverse effects on normal and effector cells. The optimal control identifies when to stop the treatment once the tumour clears. Furthermore, optimal control facilitates the regeneration of normal and immune cells beyond treatment, in contrast to a control scenario. The findings highlight the importance of early detection and careful chemotherapy dosage selection for effective and personalised cancer treatment strategies.