ANON-LINEARDYNAMICALMODELOFTUMOUR-HEALTHY-IMMUNE CELLINTERACTIONSUNDERTHERAPEUTICINTERVENTION

Abstract

Cancer therapy remains a major biomedical challenge due to the coexistence of healthy,tumour, quiescent, and immune cells that interact in complex and often unpredictableways. This thesis presents a mathematical model of tumour-host interactions underradiotherapy and chemotherapy. The limited understanding of how radiotherapy andchemotherapy when applied singly or in combination, influences tumour-immune dynamics and long-term treatment efficacy is the problem to be addressed. The model incorporates four compartments: healthy cells, tumour cells, quiescent tumour cells,and immune cells. The system of non-linear ordinary differential equations is analysedfor positivity, boundedness, invariant regions, and equilibria. The basic reproductionnumber R0 is derived, and stability analysis establishes conditions for tumour persis tence or eradication. Sensitivity analysis identifies the parameters most influential totreatment outcomes. Numerical simulations, conducted using biologically consistent parameter values, reveal key dynamics. In the absence of therapy, tumour and quiescent populations expand while healthy cells decline, corresponding to R0 > 1. Radiotherapy efficacy ε exerts a threshold effect: low values slow tumour growth without elimination, while sufficiently high values reduce R0 below one, driving eradication.Chemotherapy schedules show similar behavior. In both modalities, continuous administration consistently outperforms pulsed or fractionated delivery. Combination therapy achieves the most rapid and sustained suppression, highlighting non-linear synergy between the two interventions. Timing is also decisive: early treatment stabilizes the system and prevents resurgence, whereas late initiation produces larger oscillations and slower recovery. These findings demonstrate the value of mathematical modelling in oncology by showing how efficacy, scheduling, and timing jointly determine long-term therapeutic success. The results provide quantitative insights that may guide clinical decision-making and the design of optimized cancer treatment strategies.