Applications in the Life Sciences
In Chapter 1 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 show why PDEs have vast applications in the life sciences. The mathematical methods we introduce to analyze these problems extend the ideas and techniques presented in the earlier chapters. The topics include age structure of a population, traveling wave fronts, and reaction-diffusion equations with diffusive driven instabilities.