Approaches to Geo-mathematical Modelling

Chapter 11Richardson Models with Space

Peter Baudains

The author would like to acknowledge the contributions of Steven Bishop, Alex Braithwaite, Toby Davies, Hannah Fry, Shane Johnson and Alan Wilson, each of whom contributed with a number of insightful discussions and points.

11.1 Introduction

Defining a set of differential equations (DEs) to model the evolution of some variable of interest is one way of representing social systems' dynamics. In contrast to agent-based simulations (another popular method, examples of which are presented in Part 7 of this volume), in which the interest is often focussed on individuals, the dependent variable in a DE-based model of a social system is often taken to be some attribute associated with a group of individuals. DEs are therefore typically used for more aggregate scenarios than agent-based models (although there are exceptions: DEs are employed with individual perspectives in Liebovitch et al. (2008) and Curtis and Smith (2008), and agent-based models are employed with aggregated perspectives in Cederman (2003)).

There are many examples of DEs being applied to conflict and warfare. The dependent variable of such models is often taken to be the number of individuals on each side of a conflict. For example, Lanchester (1916) uses DEs to model different types of attrition warfare between two adversaries. A number of studies have built upon Lanchester's work by modelling the change in the population size of adversaries with DEs (e.g. ...