A review of mathematical modeling of tumour growth and treatment

This review paper explores the pivotal role of mathematical modelling within cancer research, with a specific focus on the prominent mathematical models employed for this purpose, including ordinary differential equations (ODEs), partial differential equations (PDEs), cellular automata (CA), agent-based models (ABMs), and hybrid models. These models are crafted to simulate and predict how tumours respond to various treatment strategies, thereby facilitating the evaluation of hypotheses and therapeutic options before clinical application. The emergence of in silico trials, which can predict patient-specific responses to treatment variations, holds promise for optimising personalised patient care. Nevertheless, it is essential to acknowledge that mathematical models come with inherent limitations, often oversimplifying intricate biological systems and potentially overlooking subtleties in tumour dynamics. The accuracy of these models is heavily reliant on the quality and quantity of data used for calibration. Therefore, to achieve a more comprehensive understanding of tumour biology and treatment outcomes, these models together use both experimental and clinical data.