Numerical Solution of Coupled Delay Differential Equations in the Field of Oncology

Abstract

In the dissertation, the models of delay differential equations from the math- ematical biology are considered, focusing on the oncology. For the study of these kinds of models, one should be capable to establish linear stability of the steady states. In Chapter 2, I have apply the method on models. Adoptive im- munotherapy against cancer has received remarkable consideration. The cyto- toxic CD8+ T cells have been studied for a long time and experimented with re- ceptor engineering techniques through the creation of chimeric receptors called CAR (Chimeric Antigen Receptor). This fact puts a cell line in the background which, on the other hand, is fundamental for the organization of the antitumor response: “CD4+” T cells. In this article, a model is constructed in which the ability of “CD4+” T cells to induce control of the tumor cell population is ana- lyzed, using a mediator such as the cytokine IFN- , and to quantify the action of the same which, although indirect, also carry out a control of the persistence of the antitumor action itself. The model focuses on the modalities of cellular interaction where it is possible to imagine a future development on the basis of recent data and idealize a therapeutic scheme where “CD4+” T cells play a leading role. The linear stability analysis is analyzed and analysis of Hopf bifur- cation is established. Finally, the numerical simulations are executed to validate analytical results.