Qualitative analysis and numerical simulations of new model describing cancer

Abstract

Cancer is a major illness which still results in the loss of human lives regardless of the inroads we make in the scientific and medical world. For this reason, recently, the medical world has started to use protocol containing interleukine-10 (IL-10) and anti-PD-L1 inhibitor in order to further activate the fight of immune system cells against cancer cells. This is why it is vital to scrutinize this illness in mathematical terms by means of enhancing the immune system’s reaction against cancer cells through anti-PD-L1 and IL-10. This study introduces the quadrivariant system where cancer cells, CD8+T cells, IL-10 and anti-PD-L1 variables are generated for the first time. After it is obtained that the solutions of this new system are positive, stability analysis of the equilibrium points of the system is made. The existence and uniqueness of the solutions of the system is given by fixed point theory, and the outcomes are put into practice through a number of explanatory diagrams. One of our aims in creating this model is to try to see the behavior of cancer cells by administering a dose of medicine and to analyze the process. As a result, it has been observed that immune system cells fight cancer cells effectively under the effect of single-dose IL-10 and anti-PD-L1.