What Partial Differential Equations Can Teach Us Social Behavior and Movement of Populations
Models based on partial differential equations have been used extensively to describe fundamental and ubiquitous phenomena in several areas of ecology and more recently in the social sciences. While these models are simplified versions of reality, their mathematical analysis has contributed to the understanding of many important phenomena, such as the effect of climate change on the persistence of species and the propagation of crime. I will spend the first part of this talk discussing the benefits of using partial differential equations to gain insight into a variety of complex systems in ecology and sociology. For the second part of the talk I will introduce a model for rioting activity and discuss some of the mathematical and sociological insights that can be gained from combining PDEs with an epidemiological approach. I specifically will discuss how this epidemic-like model, with just a few parameters and a single sociological variable characterizing neighborhood deprivation, accounts quantitatively for the full spatio-temporal dynamics of the 45-day riot that spread throughout France in 2005.