Modelling The Coupled Economic-Demographic Dynamics In Time And Space

The aim of this work is to present and analyse various dynamical models of the human population, including external migration flows, as well as models that consider the interplay of demography and economy. In chapter 1, we present theoretical, methodological, and computational advances in the study of population growth, as well as combined economic and demographic dynamics. In chapter 2, we introduce a two-component PPM model with external migration. Using this model, we have analysed both temporary and long-term population dynamics, using data from Destatis for specific calculations, and introduced a significant concept of the threshold degree of migrant flow growth. In chapter 3, we introduce a continuous analogy of the model from previous chapter - McKendrickvon Foerster model, which is a system of first order PDE’s with non-lassical boundary conditions, and reduce its solution to Volterra integral equation of the second type. In chapter 4, we introduce a spatial-temporal economic-demographic model, which is a system of partial differential equations of the diffusion-reaction type. Using computer calculations, we investigated the underlying dynamical system, i.e. the corresponding nonspatial model. We have found unexpected regimes that show that in the long run, with a large initial wealth, the population may become extinct, despite experiencing growth in the short term. In chapter 5, we analysed the spatial-temporal model. More precisely, with the help of computer simulations we have considered different scenarios: the demographic invasion, needle-like perturbations, inhomogeneous perturbation of steady states. Interesting effects have been found such as a violation of the stability of the equilibrium in the needle perturbation of the initial state and the occurrence of chaos in the case of a space-inhomogeneous perturbation of the saddle point. In chapter 6, we have shown that Turing instability takes place in the economic-demographic model.