Partial Differential Equations in the Life Sciences

Abstract

In Section 1.4 we introduced simple advection and diffusion models to describe the motion of organisms, cells, and chemicals in a biological science context. In this chapter we extend these ideas to more complicated phenomena involving age structure of a population, the propagation of epidemic waves, and the relationship between spatial pattern formation and chemical instability. These advanced models will show why PDEs have vast application in the life sciences. The mathematical methods we introduce to analyze these problems will extend the ideas and techniques presented in the earlier chapters. The reader can find extensive applications of PDEs to life science problems in Edelstein-Keshet (1988), Kot (2001), Britton (2003), and Murray (2003).