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

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 (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 (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

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