Hyperbolic Systems and Transport Equations in Mathematical Biology

Abstract

The standard models for groups of interacting and moving individuals (from cell biology to vertebrate population dynamics) are reaction-diffusion models. They base on Brownian motion, which is characterized by one single parameter (diffusion coefficient). In particular for moving bacteria and (slime mold) amoebae, detailed information on individual movement behavior is available (speed, run times, turn angle distributions). If such information is entered into models for populations, then reaction-transport equations or hyperbolic equations (telegraph equations, damped wave equations) result.