On the dynamics and optimal control of a mathematical model of neuroblastoma and its treatment: Insights from a mathematical model

Abstract

Celyvir is an advanced therapy medicine, consisting of mesenchymal stem cells (MSCs) containing the oncolytic virus ICOVIR 5. This paper sets out a dynamic system which attempts to capture the fundamental relationships between cancer, the immune system and adenoviruses. Two forms of treatment were studied: continuous and periodic, the second being closer to the real situation. In the analysis of the first model, in addition to identifying the critical points, their properties and bifurcation points, a number of numerical simulations were carried out. It has thus been shown that there are bistability regimes in which Celyvir can produce an equilibrium of tumor progression, or even freedom from tumor. A sensitivity analysis was also performed to determine which parameters are most important in the system. Subsequently, an optimal control problem with nonlinear objective functional has been formulated, where the therapeutic goal is not only to minimize the size of the tumor cell population and the total cost of treatment, but also to prevent the tumor from reaching a critical size. It has been shown that the optimal control is bang–bang. With the second model, a threshold value of viral load has been identified at which the success of the treatment could be ensured. It is clear in both models that a low viral load would lead to relapse of the disease. Finally, it is shown that a periodic bang–bang regime should be used to optimize treatment with Celyvir.