Dynamic equation approach to forecast long-range demographic scenarios

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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.