Guan, Likud, Yang, Jin, Tan, Yuanshun, Liu, Zijian and Cheke, Robert ORCID: 0000-0002-7437-1934 (2022) Bifurcation analysis of a tumour-immune model with nonlinear killing rate as state-dependent feedback control. International Journal of Bifurcation and Chaos, 32 (10):2250155. pp. 1-19. ISSN 0218-1274 (doi:https://doi.org/10.1142/S0218127422501553)

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Abstract

Impulsive control strategies have been widely used in cancer treatment and linear impulsive control has always been considered in previous studies. We propose a novel tumour-immune model with nonlinear killing rate as state-dependent feedback control, which can better reflect the saturation effects of the tumour and immune cell mortalities due to chemotherapy, and its dynamic behaviors are investigated. The paper aims to discuss the transcritical and subcritical bifurcations of the model. To begin with, the threshold conditions for tumour eradication and tumour persistence in the model without pulse interventions are provided. We define the Poincar´e map of the proposed model and then address the existence and orbital asymptotically stability of the model’s tumour-free periodic solution. Furthermore, by using the bifurcation theory of the discrete one-parameter family of maps, which is determined by the Poincar´e mapping, we investigate the model’s transcritical and subcritical pitchfork bifurcations with respect to the key parameter.

Item Type:	Article
Uncontrolled Keywords:	Tumour-immune model; nonlinear feedback control; Poincare map; bifurcations.
Subjects:	Q Science > Q Science (General)
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > Natural Resources Institute Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Last Modified:	04 Sep 2022 10:45
URI:	http://gala.gre.ac.uk/id/eprint/37213

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