The enormous progress made in recent years in the experimental life sciences provides a wealth of data on the functioning of living organisms. This is especially true for the immune system. There is general consensus that in order to turn these data into knowledge about the functioning of this system, mathematical modeling as well as theoretical and numerical analysis in conjunction with experimental data is essential for future progress. ImmunoSensation and HCM provide the ideal environment to make substantial advances in this direction. Based on encouraging achievements in the previous funding period, the clusters have decided to particularly strengthen this cooperation institutionally by the creation of three internationally visible junior research groups in the field of mathematical modeling in life and medical sciences. The new research groups are positioned at the interface of the two clusters. This provides a unique opportunity to develop new and challenging mathematical models with a significant impact on the understanding of the immune system and immune-mediated diseases. The range of research topics to be studied includes, but is not limited to, the analysis of information processing, the dynamics of the immune response, modeling and optimization of treatment protocols, sparse data problems in single cell approaches, predicting and modeling cell behavior from pertubation experiemnts, and the analysis of two to three-dimensional images including dynamic images in the context of immune responses.