Modeling of Tumor-Immune System Interaction with Stochastic Hybrid Systems with Memory: A Piecewise Linear Approach

Authors : Nurgul GOKGOZ, Hakan ÖKTEM

Pages : 25-38

Doi:10.31197/atnaa.773390

View : 11 | Download : 8

Publication Date : 2021-03-31

Article Type : Research Paper

Abstract :In this work, we benefit from hybrid systems that are advantageous because of their analytical and computational usefulness in the case of inferential modeling. In fact, many biological and physiological systems exhibit historical responses such that the system and its responses depend on the whole history rather than a combination of historical events. In this work, we use and improve hybrid systems with memory insert ignore into journalissuearticles values(HSM); in the subclass of piecewise linear differential equations. We also include stochastic calculus to our model to exhibit uncertainties and random perturbations clearly, and we call this model stochastic hybrid systems with memory insert ignore into journalissuearticles values(SHSM);. Finally, we choose tumor-immune system data from the literature and show that the model is capable to model history dependent behavior.
Keywords : hybrid systems, functional differential equations, pattern memorization, multistationarity, regulatory dynamical systems