Bifurcation Analysis of a Tumour-Immune Model with Nonlinear Killing Rate as State-Dependent Feedback Control

Impulsive control strategies have been widely used in cancer treatment and linear impulsive has always considered 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 tumour immune cell mortalities due to chemotherapy, its dynamic behaviors are investigated. The paper aims discuss transcritical subcritical bifurcations model. To begin with, threshold conditions for eradication persistence without pulse interventions provided. define Poincaré map proposed then address existence orbital asymptotically stability model’s tumour-free periodic solution. Furthermore, by using bifurcation theory discrete one-parameter family maps, is determined mapping, we investigate pitchfork respect key parameter.