Modeling of Tumor-Immune Nonlinear Stochastic Dynamics with Hybrid Systems with Memory Approach

Abstract

In this paper, we address the well-known Tumor-Immune Model of Kuznetsov et al., converting it into a stochastic form, and for simulation purposes we employ Euler-Maruyama discretization process. Such a modeling, for being realistic in biology and medicine, requires the implication of memory components. We also explain how to calculate the state transition time and we elaborate on how to reduce the system dynamics after the state transition. In fact, we establish and evaluate Stochastic Kuznetsov et al. model, and we describe how to demonstrate the stability of the numerical method, addressing tumor growth in spleen of mice. This work ends with a conclusion and a prospective view at future research and application, with special focus on medicine and neuroscience of tumor analysis and treatment.