ABSTRACT
Objective To study the effect of time delay on tumor-immune system in tumor growth through theoretical approaches. Methods A mathematical model of the tumor-immune system interactions was established, and a time delay in the logistic growth term was introduced to investigate the processes of the interaction between immune system and tumor cells through qualitative analysis and numerical simulations. The relationship between the states of tumor and time delay was analyzed and the results were compared with the stages of the cancer immunoediting. Results Qualitative analysis and numerical simulations indicated that the tumor-immune system was a stable equilibrium state if the time delay was small. With the time delay increasing, the tumor-immune system entered equilibrium and escape stages of the cancer immunoediting, which described the alteration from dormant state to malignant state. Conclusions The time delay plays a key role in the interaction between immune system and tumor cells. The different time delays can result in different behaviors of tumor. The results will help to deepen clinical understanding of the tumor-immune system and provide references for the analysis and treatment of tumor.