Reaction transport equations in biological modeling

Reaction transport equations are models for interactions within or between species and for spatial spread such that individuals assume positions in space and also their individual velocities. These equations have much in common with reaction diffusion equations but, being hyperbolic rather then parabolic, do not show the undesired feature of infinitely fast propagation. They are particularly useful for biological situations where detailed description of moving individuals is important, e.g., in the reaction of microorganisms to gradients of substances. Several modeling approaches by reaction transport equations are outlined and insights into the qualitative behavior of such systems are given.