Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy. (March 2021) - Zhao, Zhong; Pang, Liuyong; Li, Qiuying
Highlights: A tumour-immune model with pulsed treatment with different frequency is given. The effect of period, dosage and times of drug delivery on the critical threshold is addressed. In addition, an hybrid impulsive model with chemotherapeutic threshold is investigated by means of numerical simulations. Abstract: In this paper, a tumour-immune model with pulsed treatment of different frequency is proposed. The globally attractive conditions of the tumour-free periodic solution are presented in views of the comparison theorem for impulsive differential equations. Furthermore, the effect of period, dosage and times of drug delivery on the critical threshold is addressed by means of computer simulation, which indicates that there exists an optimal frequency of chemotherapeutic application. In addition, a tumour-immune model with fixed-time pulsed of immunotherapy and state feedback impulsive chemotherapy is given to keep the normal cells above and toxicity below the acceptable levels. Some numerical results are also provided to investigate the effect of the initial densities, predetermined threshold, drug dose and impulsive period on the dynamical behavior of hybrid impulsive system.