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

Year 2020, Volume: 3 Issue: 1, 24 - 34, 31.03.2020

Nurgül Gökgöz Hakan Öktem Gerhard-wilhelm Weber

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.

Keywords

Hybrid systems, Regime switching, Pattern memorization, , Multistationarity, Regulatory dynamical systems, Medicine

Project Number

104T133

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