In 1914 McKendrick came up with a method inspired by L. Boltzmann to describe the evolution of statistical distributions in an - in principle continuous - parameter space, also for the life sciences and the social sciences.This method leads to partial differential equations. Nevertheless, the Kermack-McKendrick models are often misinterpreted solely as the well-known SIR ODE-system for the...
At the individual scale, bacteria as E. coli move by performing so-called run-and-tumble movements. This means that they alternate a jump (run phase) followed by fast re-organization phase (tumble) in which they decide of a new direction for run. For this reason, the population is described by a kinetic-Botlzmann equation of scattering type. Nonlinearity occurs when one takes into account...
Epithelial tissues at a pre-tumoral stage exhibit morphological changes: in particular epithelial ducts depart from the cylindrical shape, showing invaginations and evagination in the regions of the surface with malignant cells. Experiments report that at the inner and outer boundary of the epithelial sheets are concentrated molecular motors able to generate a surface active tension, that can...
Biochemical networks are notoriously large and complex and involve many unknown parameters. As a consequence, various reduction methods for their analysis have been proposed. A common critique of this approach is that biochemical complexity is intrinsic and that any “reduced” model is therefore doomed to miss essential features. However, minimal models can be particularly valuable to...
Mathematical analysis plays a crucial role in advancing the field of mathematical biology. By providing rigorous frameworks and tools, it enables the development of consistent mathematical models for complex biological systems, the analysis of underlying mechanisms, and predictions of long-term dynamics. This minisymposium will present several modelling and analysis results addressing...
