A semigroup approach to the strong ergodic theorem of the multistate stable population process

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE)     

Asymptotic properties of the inhomogeneous Lotka‐Von Foerster system

In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution.     

Population growth with variable family size

The Sharpe‐Lotka continuous time deterministic model of population growth is developed to take account of some possible forms of mother‐daughter fertility association, characterised here by a bivariable measure, A. This leads to a linear double integral equation for which, subject to certain conditions, a finite time solution can be found by Laplace transform methods and thus also model specific results relating the intergenerational fertility effect to the long term population growth rate and magnitude are established. The quantitative implications of the theory are illustrated by a consideration of a general bilinear form of A and in this context numerical results illustrating the finite time growth and also the long term distribution of fertility levels in the stable female population are obtained. In particular, it is shown that different fertility specific subpopulations can coexist indefinitely.     

A dynamic multistate model of robustness and frailty

Dynamic multistate models can show realistic population dynamics over time, model complex cycles, and encompass the life history of a cohort. This paper uses a recently developed approach to obtain the analytic solution of a time‐dependent multidimensional differential equation. The illustrative robust/frail model presented shows that the assumption of fixed individual frailty can be abandoned in a two living state model that allows transitions between health statuses and nonproportional hazards of death.     

On the distribution of completed parities when fertility is heritable

Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two‐child families increases, the possible influence of mother‐daughter fertility associations on population growth decreases, though even now it could override otherwise significant changes in either or both of the birth and death intensities. In particular, it is shown that according as to how fertility is transmitted through generations, it is still possible to have zero growth rates consistently with a widely dispersed stable distribution of family size as well as a typical mortality regime.     

Life Tables with Covariates: Dynamic Model for Nonlinear Analysis of Longitudinal Data

ABSTRACT

Life table models based on nonlinear dynamics of risk factors are developed using stochastic differential Equations for individual changes and on the resulting Fokker-Planck equation to describe population changes. Central to the model is a microsimulation strategy developed as a numerical procedure to represent a mortality effect when analytic approaches are not applicable. The model is applied to the Framingham Heart Study 46-year follow-up data. Life table functions and projections of risk factors are calculated to demonstrate the nonlinear effects on observable quantities over time. A set of statistically significant nonlinear contributions to covariate dynamics is identified. Their synergistic effect on dynamics and use of them as “new” risk factors are discussed. An important advantage of this approach is the ability to study the effects of health interventions at the individual level. This is illustrated in several examples.     

Stable growth in native‐dependent multistate population dynamics

Users of multistate life tables and projections have recognized that the Markovian assumptions underlying such models are unduly restrictive and should be relaxed whenever data permit. Efforts to include the influences of previous occupancies have included the incorporation of place‐of‐birth dependence. This paper addresses the stable growth properties of such generalized multistate models. It shows how place‐of‐birth‐specific stable growth measures can be calculated without projection simply by solving the characteristic equation. An example using Canadian data illustrates the argument.     

Sex-Structured Dynamic of Multi-Group Herpes Simplex Virus 2

A 3(n + l)-dimensional ordinary differential equation for HSV-2 includes l groups of men and n groups of women with different risks of infection. Global Lyapunov functions based on graph theory and on LaSalle invariance principle show that the model dynamics are completely determined by the basic reproduction number ?₀. The disease-free equilibrium is globally asymptotically stable when ?₀ ≤ 1; a unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region when ?₀ > 1.     

On the use of the truncated Gompertz distribution and other models to represent the parity progression functions of high fertility populations

The Gompertz distribution, developed from the mortality “law”; long used by actuaries and demographers promises to be a useful distribution for many other demographic purposes as well. The continuous distribution can also be adapted to represent discrete data commonly encountered in demographic work, and maximum likelihood estimates of the two parameters are easily calculated using formulae developed in this paper, whether those data be continuous or discrete, truncated below or provided with observations in a final open‐ended interval.

The distribution is unimodel. The use of the truncated form of the distribution, however, allows the researcher to fit it to a wider range of observed distributions, including many for which the density function is monotonic decreasing.

Empirical studies using parity progression data of two high fertility populations indicate that the truncated Gompertz distribution in its discrete form provides a good overall picture of the parity distribution. Interestingly, the simple method of partial sums, commonly employed to fit the Gompertz function, appears to provide parameter estimates which are close to those estimated by maximum likelihood.     

A cost valuation model based on a stochastic representation of the IPAT equation

Within the framework of models for human-driven environmental impact based on the IPAT equation, we develop a model for the evolution of impact (expressed in terms of carbon dioxide emissions) and for the valuation of the economic cost associated to its reduction. We use a stochastic representation of the IPAT equation that is alternative to the STIRPAT model. This first step leads to a stochastic differential equations model that describes trends in carbon dioxide emissions on the basis of economic and demographic dynamics. As an example, we estimate the model parameters for the United States. We then use this framework to build a model for the assessment of the economic costs related to a reduction of carbon dioxide emissions for a country committed to respect an international agreement, such as the Kyoto protocol. In particular, we show that the adherence to an environmental treaty may be traced back to a problem of cost valuation and to a decision under risk. This allows us to use the mathematical tools that have been developed in quantitative finance, in the context of option pricing, to determine the expected investment that is required to reduce the emissions of a country by a certain amount and within a well-defined temporal frame.

Persistent age distributions for an age‐structured two‐sex population model*

In this paper we formulate an age‐structured two‐sex population model which takes into account a monogamous marriage rule and the duration of marriage. We are mainly concerned with the existence of exponential solutions with a persistent age distribution. First we provide a semigroup method to deal with the time‐evolution problem of our two‐sex population model. Next, by constructing a fixed point mapping, we prove the existence of exponential solutions under homogeneity conditions.     

Discrimination,Subjective Wellbeing,and the Role of Gender: A Mediation Model of LGB Minority Stress

ABSTRACT

The present study examined the link between discrimination and the three components of subjective wellbeing (positive and negative affect and life satisfaction) among a cisgender sample of lesbian, gay, and bisexual (LGB) adults. Specifically, we investigated internalized homonegativity and expectations of rejection as potential mediators of the links between discrimination and subjective wellbeing among a sample of 215 participants. Results from our structural equation model demonstrated a strong, positive direct link between discrimination and negative affect. Discrimination also had small, negative indirect effects on life satisfaction through our two mediators. Interestingly, neither discrimination nor our two mediators were related with positive affect, demonstrating the need for future research to uncover potential buffers of this link. Finally, our model evidenced configural, metric, and scalar invariance, suggesting that our model applies well for both women and men. Practical implications and future directions for research are discussed.     

Inventing the Pedophile in the Journal of Homosexuality

ABSTRACT

This article serves as one of the supplementary pieces of this special issue on “Mapping Queer Bioethics,” in which we take a solipsistic turn to “map” the Journal of Homosexuality itself. Here, the author examines one of the most controversial moments in the history of the journal, whereby a contributor was subject to governmental and popular rebuke for his scholarship on pederasty, pedophilia, and underage queer sexuality. In a chronological and intellectual appraisal of this pedophilia-themed text, the author asks us to recalibrate the disquietude we posit when same-sex affection, youthful sexuality, and sexual abuse are in close proximity.     

Macro‐demographic effects of the transition to adulthood: Multistate stable population theory and an application to Italy

We exploit a multistate generalisation of a classical, one‐sex, stable population model to evaluate structural and long‐term effects of changes in the attainment of adulthood. The demographic framework that inspired this paper is provided by Italy, where a strong delay in the transition to adulthood and union formation has been observed over the last several decades. Italy has also experienced very low fertility levels, and the subsequent ageing problems have become of primary concern. We first discuss a theoretical framework based on the model developed by Inaba (1995) and then include the process of transition to adulthood. We consider explicitly some specifications of the general model, and we present two distinct empirical applications, one using macrosimulation and the other one using a linear approximation. Our principal aim is to evaluate the impact of the delay in the attainment of adulthood on reproduction and on the age structure of the population.     

Buffon's needle and the estimation of migration distances

A procedure is suggested for estimating migration distances from data on the proportion of migrants crossing regional boundaries. The method makes use of Buffon's needle, a problem in geometrical probability from the eighteenth century that was originally used as an empirical means of estimating π. The procedure is described for various scenarios that differ in their assumptions about region shape, the spatial distribution of population, and the distribution of migration distances. An application to migration distances in the United States is given, and additional attention is given to the estimation of intraregional migration distances.     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.     

The association between mistreatment of women during childbirth and postnatal maternal and child health care: Findings from “Birth in Brazil”

BackgroundThe mistreatment of women during pregnancy, childbirth, and the puerperium is a global public health problem besides being a violation of human rights. However, research exploring the consequences of mistreatment of women and newborns is scarce.QuestionTo shed light on this issue, we investigated the association between the mistreatment of women during childbirth and the subsequent use of postnatal health services by women and their newborns.MethodsWe used data from the study “Birth in Brazil”, a national hospital-based survey of puerperal women and their newborns, carried out in 2011/2012. This analysis involved 19,644 women. Mistreatment was a latent variable composed of seven indicators. We assessed the attendance of women and newborns to a review consultation following birth, and the timing of this appointment. We applied multigroup structural equation modeling (based on childbirth payment source) and considered separate analysis for women (vaginal births and0 caesarean-sections) and newborns.FindingsWe found a causal association between mistreatment during childbirth and decreased and/or delayed use of postnatal health services, for both women and their newborns. These results also revealed that women who use the public sector are affected more than those who pay for private healthcare.ConclusionMistreatment during childbirth has broader implications than “maternal mental health”, and it would be useful to understand that experience of care has vast implications for families. In Brazil, the mistreatment must be mitigated via the implementation of public policy. This is part of the path to dignified and respectful childbirth care for all women.     

Linearity,symmetry, and equidistance in semantic differential scales for measuring images of self and images of others

ABSTRACT

Violations of linearity, symmetry, and equidistance of scale points in semantic differential scales may be due to respondents failing to figure out antonyms, to a positivity bias, or to respondents curtailing their reading the options. Multiple correspondence analysis on data provided by a randomized between-subjects experiment (split-ballot), using a web survey of 537 German residents, shows that bipolar semantic differential scales allow for linear measurement and conceal no positivity bias, and that using not suitable adjective pairs in semantic differential scales destroys symmetry.     

A nine‐parameter version of the Heligman‐Pollard formula

In this paper we outline and evaluate a nine‐parameter version of the Heligman‐Pollard formula. In our applications, using mortality data for five European countries we found that this version provides closer fits to empirical mortality data than the classical eight‐parameter formula, thus eliminating a source of systematic error in this latter formula.     

Can Pro-Marriage Policies Work? An Analysis of Marginal Marriages

Policies to promote marriage are controversial, and it is unclear whether they are successful. To analyze such policies, one must distinguish between a marriage that is created by a marriage-promoting policy (marginal marriage) and a marriage that would have been formed even in the absence of a state intervention (average marriage). We exploit the suspension of a cash-on-hand marriage subsidy in Austria to examine the differential behavior of marginal and average marriages. The announcement of an impending suspension of this subsidy led to an enormous marriage boom among eligible couples that allows us to locate marginal marriages. Applying a difference-in-differences approach, we show that marginal marriages are surprisingly as stable as average marriages but produce fewer children, children later in marriage, and children who are less healthy at birth.