Mathematical Modeling with ordinary and partial differential equations, qualitative behavior of solutions, spatial inhomogeneous reaction diffusion equations.
Applications in life sciences, engineering and environmental sciences.
Building up a model family for inflammations Cordula Reisch, Sandra Nickel, Hans-Michael Tautenhahn Journal of Mathematical Biology, 2024 The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction–diffusion equations is built up on a mesoscopic scale and uses classes of feasible functions for reaction and taxis terms. The classes are found by translating biological knowledge into mathematical conditions and the analysis of the models further constrains the classes. Numerical simulations allow comparing single models out of the model family with available qualitative information on the solutions from observations. The method provides insight into a hierarchical order of the mechanisms. The method is applied to the clinics for liver inflammation such as metabolic dysfunction-associated steatohepatitis or viral hepatitis where reasons for the chronification of disease are still unclear and time- and space-dependent data is unavailable.
