Deterministic vs stochastic formulations and qualitative analysis of a recent tumour growth model

Mathematical modeling and control have recently played a pivotal role in the understanding of tumour growth and in treatment planning, with a special emphasis in the search for personalized therapies. In this note a recent tumour growth model is investigated. The model entails the proliferating and necrotic tumour cells dynamics, as well as the administered drug level. Inspired by a recent reaction-rate characterization of the model, the approach is further deepened with respect to cells and drug molecules copy numbers, hence resulting relevant under the double facet of the deterministic and stochastic frameworks. With regards to the deterministic model, the qualitative behavior analysis is carried out under the basic assumption of a baseline drug delivery: results are encouraging, since they show which parameter space regions allow effective control law results. Stochastic simulations are carried out by properly exploiting parameter values taken from the available experimental literature, and are consistent with the average value evolution inferred from the deterministic approach, paving the way to further stochastic investigation oriented to frameworks involving a reduced copy number.