Dynamical Properties of a Stochastic Tumor-Immune Model with Pulsed Chemotherapeutic Dose Response

Abstract

Comprehensive pulsed chemotherapy and immunotherapy are widely employed in clinical tumor treatment. Given the periodically pulsed nature of this approach, we propose a stochastic tumor-immune dynamical model with a pulsed chemotherapeutic dose response. The model accounts for the combined effects of pulsed chemotherapy and pulsed immunotherapy, as well as the influence of environmental random disturbances. We prove the existence and uniqueness of a global positive solution to the proposed model. By using comparison theorems for impulsive differential equations, we show the boundedness of the solution’s expectation. Furthermore, we derive sufficient conditions for the extinction and non-persistence in the mean of tumor cells, hunting T-cells, and helper T-cells, as well as for the weak persistence in the mean of tumor cells and helper T-cells, and the stochastic persistence of tumor cells. The results of our study, supported by numerical simulations, demonstrate that random disturbances can effectively inhibit tumor cell growth.