Mathematical Modelling of Demographic and Migratory Dynamics

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


In the following we develop analytical and numerical methods to study the emergence of patterns in complex systems, with a particular focus on human mobility, migrations and population dynamics. The purpose is to provide a quantitative description of the urbanisation process by defining a general and flexible modelling framework able to reproduce the universal patterns of population distribution observed empirically in different countries, as well as to estimate the demographic evolution of cities.

Our aims are threefold: to determine which model of migration best describes the empirical relationship between the number of urban agglomerations and the population of a region, testing Heaps' Law for cities; to propose a theoretical framework to explain the emergence of the power law distribution of city sizes, Zipf's Law, from a microscopic birth-death process without fine tuning; to measure the relevance of social connections in determining migration decisions, analysing relocations of scientists.

Human migration and demographic growth are examples of complex phenomena showcasing the typical features of complex systems, namely the presence of heterogeneous distributions, long-range interactions, complicated individual (microscopic) dynamics and emergent collective (macroscopic) behaviour. The modelling techniques developed to describe the emergence of these general patterns in the context of urban dynamics and human migration can also find application in other complex systems, such as those in ecology and biology, where these patterns are also present.
Date of Award28 Nov 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorFilippo Simini (Supervisor) & R E Wilson (Supervisor)

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