In this talk I will discuss several spatio-temporal mathematical models arising in the modeling of life science problems. The main feature of these realistic life science models is based on the fact that their governing equations are characterized by highly-nonlinear density-dependent reaction-diffusion-transport systems comprising both porous media and singular diffusion type degeneracy as well as ODE-PDE type coupling. These kind of equations arise in particular, in the modelling of antibiotic disinfection of biofilms, biofilm growth in porous media as well as mitochondria swelling scenarios in vitro, in vivo. Well-posedness, long-time dynamics of solutions in terms of global attractors, and asymptotics of their Kolmogorov entropy will be treated.