Multiscale modeling and simulation of traveling waves in biology: A review
Martinson WD., Byrne HM., Maini PK.
© 2019 Universita degli Studi di Roma La Sapienza. All rights reserved. Traveling waves are a near-ubiquitous phenomenon in mathematical biology, and have been studied in the context of embryonic development, cancer growth, wound healing, and epidemiology. Fisher's equation is the prototypical example of a problem that admits a traveling wave solution; it is a partial difierential equation that was proposed to describe the spread of an advantageous gene. Although past investigators formulated and analyzed models for such translationally invariant systems at a macroscopic scale of interest, recent work has focused on analyzing and simulating traveling wave behavior in greater detail. This paper reviews the difierent scales and approaches by which researchers can model and simulate wave-like behavior, using the Fisher equation as a pedagogic example. We discuss difierent algorithms for simulating traveling waves, from traditional_nite di_erence approaches to more recent hybrid multiscale algorithms.