Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy

Gliomas are the most frequent type of primary brain tumour. Low-grade gliomas (LGGs) in particular are infiltrative and incurable with a slow evolution that eventually causes death. In this paper, we propose a mathematical model for the growth of LGGs and its response to chemotherapy. We validate our model with medical data and show that the proposed model describes real patients’ data quite well. A mathematical analysis of the model shows the existence of a unique non-negative solution. We further investigate the stability of steady-state solutions. In particular, we demonstrate the global stability of a tumour-free equilibrium in the case of sufficiently strong constant and asymptotically periodic treatment. A sensitivity analysis of the model indicates that the proliferation rate has the biggest impact on solutions of the model. We also numerically investigate the stability of the fitting procedure.