Dynamic equation approach to forecast long-range demographic scenarios
Lead Research Organisation:
University of Bristol
Department Name: Engineering Mathematics and Technology
Abstract
We live in a time of big social change: economic development and medical innovations have contributed to produce an unprecedented demographic boom that is affecting the lives of billions of people and impacting the environment at an unprecedented rate. In less than three centuries the world population increased ten times, causing a major shift in the distribution of population in most countries, where a continuing growth of urbanisation is observed globally.
Although urbanisation is reshaping many aspects of human societies and the natural environment, presenting both opportunities and challenges, a general, quantitative theory on the growth and formation of cities that would enable us to forecast future demographic scenarios still remains elusive.
The observed trends of population growth can be quantitatively characterised by precise statistical laws, such as the distribution of city sizes, the spatial distribution of cities, and the spatiotemporal correlations of population growth rates. The analysis of empirical data reveals that these statistical laws are common to many countries, suggesting that the formation of the observed patterns might be explained by a general mechanism. In particular, the spatial distribution of population within a country changes over time due to natural increase (births-deaths) and migrations (people relocating). An accurate mathematical model of these two processes should be able to reproduce the observed statistical patterns, and allow us to investigate the stability of these patterns to specific events, such as the global or local change of the rate of natural increase or the range of migrations.
In this research, I aim to develop a dynamical model of population dynamics based on simple yet realistic descriptions of demographic processes and to characterise the emerging patterns of population distribution.
An accurate mathematical description of migration flows is of primary importance to determine how population redistributes in space. To model migrations, I propose a generalised version of singly-constrained gravity and intervening opportunities models of spatial flows, which will be investigated to estimate net migration in the UK and the United States.
I will develop different forms of dynamic equations to describe the temporal evolution of the density of population, combining models of spatial flows with stochastic processes to model population growth.
I will assess the models' ability to reproduce the characteristic statistical patterns about the size, number, position, and spatiotemporal correlations of growth of cities.
The proposed research will offer a mathematical framework to relate the emerging statistical patterns of population distribution with the characteristic properties of the underlying microscopic processes: births, deaths, migrations.
It will contribute to shed light on the long term effect on our society of various phenomena, from the development of new forms of transportation to the consequences of conflicts and extreme natural events, with the potential to inform strategic decisions toward a sustainable and balanced growth.
Although urbanisation is reshaping many aspects of human societies and the natural environment, presenting both opportunities and challenges, a general, quantitative theory on the growth and formation of cities that would enable us to forecast future demographic scenarios still remains elusive.
The observed trends of population growth can be quantitatively characterised by precise statistical laws, such as the distribution of city sizes, the spatial distribution of cities, and the spatiotemporal correlations of population growth rates. The analysis of empirical data reveals that these statistical laws are common to many countries, suggesting that the formation of the observed patterns might be explained by a general mechanism. In particular, the spatial distribution of population within a country changes over time due to natural increase (births-deaths) and migrations (people relocating). An accurate mathematical model of these two processes should be able to reproduce the observed statistical patterns, and allow us to investigate the stability of these patterns to specific events, such as the global or local change of the rate of natural increase or the range of migrations.
In this research, I aim to develop a dynamical model of population dynamics based on simple yet realistic descriptions of demographic processes and to characterise the emerging patterns of population distribution.
An accurate mathematical description of migration flows is of primary importance to determine how population redistributes in space. To model migrations, I propose a generalised version of singly-constrained gravity and intervening opportunities models of spatial flows, which will be investigated to estimate net migration in the UK and the United States.
I will develop different forms of dynamic equations to describe the temporal evolution of the density of population, combining models of spatial flows with stochastic processes to model population growth.
I will assess the models' ability to reproduce the characteristic statistical patterns about the size, number, position, and spatiotemporal correlations of growth of cities.
The proposed research will offer a mathematical framework to relate the emerging statistical patterns of population distribution with the characteristic properties of the underlying microscopic processes: births, deaths, migrations.
It will contribute to shed light on the long term effect on our society of various phenomena, from the development of new forms of transportation to the consequences of conflicts and extreme natural events, with the potential to inform strategic decisions toward a sustainable and balanced growth.
Planned Impact
- Infrastructure and urban planning
One of the main outcomes of this proposal is the development of non-parametric (NP) statistical models to estimate spatial flows.
Although, the main application of NP models in this proposal will be to estimate migration flows and, in particular, to accurately compute the net migration in each location, NP models are a general framework to model various types of spatial flows, such as logistic services (e.g. courier shipment) and human mobility (e.g. commute trips).
In particular, the proposed research includes a specific activity in collaboration with the KDD Lab (Pisa, Italy) aiming at evaluating the possibility to use NP models to estimate regional origin-destination matrices.
The expected outcome of this joint work is the development of a methodology to estimate the changes of mobility flows resulting from the construction of a new transportation infrastructure.
This methodology will have a potential impact on urban planning and could be used to inform cost-benefit analysis of transportation investments.
- Social impact.
An intriguing application of the proposed research is forecasting medium and long-term socio-demographic scenarios.
With Ann Singleton of the School for Policy Studies at the University of Bristol we foresee to apply the dynamical models of population dynamics to study the socio-demographic consequences that could result from legislation (e.g. immigration policy) and to investigate the links between internal and international migration within a framework of global economic and social restructuring.
- Emergency management.
The proposed simulation methodology is expected to have an impact in informing emergency management plans.
In particular, NP models of mobility and migration flows can be used to assess the response of human communities to disruptive natural events, like floods or earthquakes, and to the consequences of climate change, like the rise of sea level.
I will liaise with the Earthquake and Geotechnical Engineering research group at the University of Bristol to apply NP models of spatial flows to estimate the potential destinations of individuals evacuating from an area affected by a natural disaster, in order to plan effective response and recovery strategies.
One of the main outcomes of this proposal is the development of non-parametric (NP) statistical models to estimate spatial flows.
Although, the main application of NP models in this proposal will be to estimate migration flows and, in particular, to accurately compute the net migration in each location, NP models are a general framework to model various types of spatial flows, such as logistic services (e.g. courier shipment) and human mobility (e.g. commute trips).
In particular, the proposed research includes a specific activity in collaboration with the KDD Lab (Pisa, Italy) aiming at evaluating the possibility to use NP models to estimate regional origin-destination matrices.
The expected outcome of this joint work is the development of a methodology to estimate the changes of mobility flows resulting from the construction of a new transportation infrastructure.
This methodology will have a potential impact on urban planning and could be used to inform cost-benefit analysis of transportation investments.
- Social impact.
An intriguing application of the proposed research is forecasting medium and long-term socio-demographic scenarios.
With Ann Singleton of the School for Policy Studies at the University of Bristol we foresee to apply the dynamical models of population dynamics to study the socio-demographic consequences that could result from legislation (e.g. immigration policy) and to investigate the links between internal and international migration within a framework of global economic and social restructuring.
- Emergency management.
The proposed simulation methodology is expected to have an impact in informing emergency management plans.
In particular, NP models of mobility and migration flows can be used to assess the response of human communities to disruptive natural events, like floods or earthquakes, and to the consequences of climate change, like the rise of sea level.
I will liaise with the Earthquake and Geotechnical Engineering research group at the University of Bristol to apply NP models of spatial flows to estimate the potential destinations of individuals evacuating from an area affected by a natural disaster, in order to plan effective response and recovery strategies.
People |
ORCID iD |
Filippo Simini (Principal Investigator) |
Publications
Barbosa H
(2018)
Human mobility: Models and applications
in Physics Reports
Barbosa-Filho H
(2017)
Human Mobility: Models and Applications
Eyre R
(2020)
Social media usage reveals recovery of small businesses after natural hazard events.
in Nature communications
James C
(2018)
Zipf's and Taylor's Laws
James C
(2018)
Zipf's and Taylor's laws
in Physical Review E
Pappalardo L
(2022)
scikit-mobility : A Python Library for the Analysis, Generation, and Risk Assessment of Mobility Data
in Journal of Statistical Software
Pappalardo L
(2019)
Human Mobility from theory to practice:Data, Models and Applications
Pappalardo L
(2018)
Data-driven generation of spatio-temporal routines in human mobility.
in Data mining and knowledge discovery
Pappalardo Luca
(2022)
scikit-mobility: A Python Library for the Analysis, Generation, and Risk Assessment of Mobility Data
in JOURNAL OF STATISTICAL SOFTWARE
Description | A new class of stochastic processes that are able to reproduce Zipf's law for the distribution of city sizes has been studied in this grant. This work revealed a general connection between Zipf's law and Taylor's law, which appear quite ubiquitous in many and diverse domains and appear to be seemingly unrelated. Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. I showed that Zipf's law and Taylor's law can emerge from a general class of stochastic processes at the individual level, which incorporate one of two features: environmental variability, i.e. fluctuations of parameters, or correlations, i.e. dependence between individuals. This reveals a general connection between Zipf's law and Taylor's law in microscopic stochastic processes of population dynamics under realistic assumptions. |
Exploitation Route | This work will likely stimulate further progress in understanding and modelling the emergence of both Zipf's and Taylor's laws from microscopic dynamical processes. In addition to describe the evolution of urban systems, these results can find application in modelling ecological, biological and economic systems, where Zipf's and Taylor's laws have also been observed. |
Sectors | Education,Environment,Transport,Other |
Description | Collaboration with S Azaele |
Organisation | University of Leeds |
Department | School of Mathematics Leeds |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | intellectual input |
Collaborator Contribution | intellectual input, technical expertise |
Impact | https://doi.org/10.1103/physreve.98.032408 |
Start Year | 2018 |
Description | CCS 2017 |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | I presented a general framework to test the assumptions behind singly-constrained models of spatial flows at the Conference on Complex Systems 2017. |
Year(s) Of Engagement Activity | 2017 |
Description | Quantifying success |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | I presented my work on the migration of researchers at the satellite "Quantifying success" held at NetSci 2018. |
Year(s) Of Engagement Activity | 2018 |
Description | Tutorial at ECML/PKDD |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | Half-day tutorial on "Human Mobility Analysis: Data, Measures, Generative Models and Predictive Algorithms" organised at ECML/PKDD 2019, where I presented an overview on the fundamental modelling principles of human mobility to researchers and practitioners. |
Year(s) Of Engagement Activity | 2018 |
URL | https://humanmobility-tutorial.github.io/ |
Description | UrbanSys2018 at CCS18, Thessaloniki, Greece. |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Workshop to present and discuss the latest advancements and open problems in the areas of urban systems, human mobility and sustainability. |
Year(s) Of Engagement Activity | 2018 |
URL | https://urbansys2018.ifisc.uib-csic.es/ |