Komplexe Systeme

Persistent subspaces of reaction-diffusion systems

Reaction-diffusion systems use partial differential equations to model dynamics basing on reactions in time and space. For several reasons, analytical as well as numerical solutions of such systems are hard to acquire. The theory of organizations provides developped in our recent publication provides measures to identifiy all persistent subspaces of these systems even when they are comparatively big and precise knowledge about the kinetics is missing. An example application of the theory of organizations is virus infection dynamics. 

Modeling of virus infection dynamics

Models of virus infection dynamics are used to understand the dynamics of virus infection, to find optimal treatment strategies for patients or to help in identifying vaccinations. In our last publication we applied the theory of organizations mentioned above to Influenza-A and Sars-COV-II models of infection dynamics. In this way, we identifed and described many different types of models using a precise mathematical method. This might help in building and analyzing more complex models in future.