Entropy functionals for finding requirements in hierarchical reaction-diffusion models for inflammations

Based on an established model for liver infections, we open the discussion on the used reaction terms in the reaction-diffusion system. The mechanisms behind the chronification of liver infections are widely unknown, therefore we discuss a variety of reaction functions. By using theorems about existence, uniqueness, and nonnegativity, we identify properties of reaction functions which are indispensable to modelling liver infections. We introduce an entropy functional for reaction-diffusion models of this type, which allows predictions of the longtime behavior of the solutions. As a result, we find more conditions on the reaction functions to derive a model covering different inflammation courses. Finally, we discuss the models in the frame of a hierarchical model family.