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This paper presents a stochastic dynamic mathematical model, in which a Family Policy Index (XFPI) is included to measure and compare two different models of provision of resources to support families with children from 0 to 3 years old. The main variables in this model are the XFPI, fertility, mortality, emigration and immigration rates. This mathematical model was validated in two different countries, Spain and Norway, during the 2007–2015 period. A sensitivity analysis was applied to simulate the future trend (2016–2030), examining the influence of providing public pre-school services (0 to 3 years) on (XISF). The results obtained show that these services may indeed have an influence on fertility rates, as long as they are developed extensively. [ABSTRACT FROM AUTHOR]

Mathematical demography traditionally has been concerned with the dynamics of the growth and structure of a population that is undisturbed by migration. Recently, however, increasing attention has been directed at the relationships between interregional migration flows and the growth and structure of multiregional population systems that are open to internal migration. This paper contributes to that emerging body of knowledge by generalizing the notion of a life table to the multiregional case and showing how such a generalization leads to a mathematical theory of multiregional population growth that is consistent with the currently accepted single-region theory. [ABSTRACT FROM AUTHOR]

A stochastic model of migration, occupational and vertical mobility, based on the theory of Semis Markov processes, is presented and important features of these processes derived. The model is a generalization of the Markov process in which the probability of leaving a state can depend in any arbitrary way on the length of time the state has been occupied (duration-of-stay) and on the next state entered (pushes and pulls). For mobility processes it thus captures McGinnis' `axiom of cumulative inertia' Several distributions with cumulative inertia are presented and the relationship between the Semi-Markov model and the Mover-Stayer model explored. A method of including age effects is described. The model is shown to have applications to many other social processes, in addition to mobility, which have duration-of-stay effects. [ABSTRACT FROM AUTHOR]

We consider Schelling’s bounded neighborhood model (BNM) of unorganized segregation, from the perspective of modern dynamical systems theory. We carry out a complete quantitative analysis of the system for linear tolerance schedules. We derive a fully predictive model and associate each term with a social meaning. We recover and generalize Schelling’s qualitative results. For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur, and show how neighborhood tipping can be explained in terms of basins of attraction. When population movement is limited, we derive exact criteria for the occurrence of new population mixes. For nonlinear tolerance schedules, we illustrate our approach with numerical simulations. [ABSTRACT FROM AUTHOR]

Many social processes may be studied as collections of binary series. The processes which generate such series may be heterogeneous over the population, non-stationary over time and may exhibit a feedback effect, such as "cumulative inertia." Methods, using maximum likelihood estimation, are developed which model arbitrary heterogeneity and non-stationarity to provide an effective test of the presence of "true contagion" or feedback effects. Where absent, a parametric form of the heterogeneity mixing distribution may be empirically identified using moment derived criteria. Application to ten year migration histories for 10,000 residents of Wisconsin, U.S.A., identifies "true contagion" amongst the younger, but not the older, residents for both owners and renters. An Su type distribution is identified as appropriate for modelling the heterogeneity amongst the older renters whereas the older owners are shown to be homogeneous. [ABSTRACT FROM AUTHOR]

Several methods of analyzing the parameters of the Semi-Markov model and incorporating exogeneous information about its states are presented. Regression analysis of parameter estimates and doubly stochastic processes are discussed. Theoretical models for the structure of transition matrices, based on Luce's theory of choice behavior, are derived. Gravity models of varying specificity, useful in the study of migration, are special cases. Maximum likelihood procedures for estimating parameters, with fully operational numerical methods for solution of the likelihood equations, are given. Thus the integration of probabilistic models with theoretical and empirical analysis of causal structure, called for in the previous article, is carried out. [ABSTRACT FROM AUTHOR]