title: Dual role of delay effects in a tumour-immune system.
abstract: In this paper, a previous tumour-immune interaction model is simplified by neglecting a relatively weak direct immune activation by the tumour cells, which can still keep the essential dynamics properties of the original model. As the immune activation process is not instantaneous, we now incorporate one delay for the activation of the effector cells (ECs) by helper T cells (HTCs) into the model. Furthermore, we investigate the stability and instability regions of the tumour-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of ECs by HTCs and the HTCs stimulation rate by the presence of identified tumour antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumour-presence equilibrium. Besides, our results reveal that an appropriate immune activation time delay plays a significant role in control of tumour growth.
authors.affiliation: a College of Science and Engineering , Aoyama Gakuin University , Sagamihara , Japan.
authors.forename: Min
authors.initials: M
authors.lastname: Yu
authors.affiliation: b Graduate school of Medicine , The University of Tokyo , Tokyo , Japan.
authors.forename: Yueping
authors.initials: Y
authors.lastname: Dong
authors.affiliation: a College of Science and Engineering , Aoyama Gakuin University , Sagamihara , Japan.
authors.forename: Yasuhiro
authors.initials: Y
authors.lastname: Takeuchi
mesh_terms: D006801:Humans; D007107:Immune System; D008954:Models, Biological; D009369:Neoplasms / Q000276:immunology*; D006377:T-Lymphocytes, Helper-Inducer / Q000276:immunology
keywords: 34C23; 92D25; Hopf bifurcation; Tumour–immune system; destabilization and stabilization; time delay