A modification of a continuous time model for first conception

The interval between marriage and the first conception leading to a live birth plays an important role in the determination of fertility components. Several probability models (Potter and Parker, 1964; Singh, 1961, 1964, 1967) based on varying sets of assumptions relating to this interval have been propounded in the recent past. All of them are based on the assumption that the females under study are susceptible to conception at the time of marriage. However, in certain situations, where some of the females already pregnant at the time of marriage report to have conceived within a short interval following marriage, this condition is not satisfied and these models become unsuitable. A probability distribution which is an inflated form of the continuous model proposed by Singh, for the time of the first conception leading to a live birth, is presented in this paper. It describes reasonably well the data on first conception times in the context of premarital conceptions. Simple expressions for the maximum likelihood estimators of the parameters involved in the model are obtained and a method for finding the asymptotic covariance matrix of the estimators is outlined. The model is applied to four sets of data.     

A mortality model based on a mixture distribution function

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman–Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman–Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture ‘accident humps’).     

Decomposing primary and secondary effects: A new decomposition method

One strand of educational inequality research aims at decomposing the effect of social class origin on educational choices into primary and secondary effects. We formalize this distinction and present a new and simple method that allows empirical assessment of the relative magnitudes of primary and secondary effects. Contrary to other decomposition methods, this new method is unbiased, is more intuitive, and decomposes effects of both discrete and continuous measures of social origin. The method also provides analytically derived statistical tests and is easily calculated with standard statistical software. We give examples using the Danish Longitudinal Survey of Youth.     

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.

Self-generated fertility waves in a non-linear continuous overlapping generations model

In this paper, Samuelson's simplified version of the Easterlin theory (Samuelson 1976) is extended to a continuous-time model with three age groups. This approach enables one to apply the qualitative theory of non-linear differential equations to show the existence of Easterlin-type cycles. In contrast to the discrete time model we obtain information about the period length of the cycle.This research was supported by the Austrian Science Foundation under grant P6601.     

A computer model of family building based on expected values

A computerized probability model of family building is described. Called FERMOD, the model is designed to follow the changing distribution of children ever born and birth intervals of a large homogeneous population as it moves through the reproductive period. Use of the model presupposes assumptions about such factors as risks of fetal wastage, lengths of pregnancy, and postdelivery amenorrhea conditional to outcome of pregnancy, length of reproductive period, fecundability, desired family size, preferred birth spacing!, and effectiveness of contraception. Use of FERMOD is illustrated in a limited application to United States fertility. Relations to other models are briefly discussed.     

The species-area relation II. A second model for continuous sampling

Summary A second mathematical model describing the species-area relation was proposed for continuous expanding of sample area. This model is expressed asS=λ ln(1+x/E) whereS is the number of species occurring in an areax, and λ andE are the constants termedspecific diversity andelemental area respectively. As a result of testing the validity of the model for several sets of data, it was shown that the above equation would provide an adequate fit to a group of species belonging to a single synusia which exists in an open habitat. The ecological implications of parameters involved were discussed and the characteristic area presented previously (Kobayashi, 1974) was defined in terms ofE. The relation between results obtained by discrete sampling and continuous sampling was examined and the possibility of converting one to another was suggested. Contribution from the Laboratory of Applied Zoology, Yamagata University, No. 79.     

A magical model to predict individual differences in mood change

We tested a mathematical model of psychological well-being (PWB) with data from a paradigm that included a negative mood induction followed by a positive induction. The propositions from the model encompass the hypothesis that the relative mood prior to either induction has implications for the magnitude of subsequent induction effects, such that relative mood is defined by current mood as a ratio of the prevailing mood that is predicted by the model. The findings confirm the hypothesis that the relative mood at baseline predicts mood change in a nonoverlapping time period, even after control for potentially mediating variables.     

从人力资本运营谈促进就业的一种方式

本文从人力资本运营理论出发,对影响人力资本流动的就业歧视进行了解释,同时对劳动力的迁移进行了成本收益分析,指出当前促进就业可以通过建立统一的可自由流动的城乡劳动力市场来解决,并对城乡劳动力市场的互动提出了一些建议。     

Maximum likelihood estimates for the parameters of a continuous time model for first conception

The duration of time between two successive births or between marriage and first birth is an indicator of the level of fertility of a couple. Potter and Parker (1964) and Singh (1961, 1967) have suggested the Type I Geometric as a distribution appropriate for representing the length of interval to first conception leading to a live birth. Potter and Parker estimated the parameters of this distribution with the help of the first two moments. Majumdar and Sheps (1970) pointed out the limitations of these moment estimates and gave a method to obtain maximum likelihood estimates, based on formulas which are too involved for solution without the help of a computer. Singh proposed a continuous probability distribution based on another set of assumptions for the above situation. He outlined a method to obtain best asymptotically normal estimates of the parameters. These estimates are obtained after several iterations starting from any set of consistent estimates. The objective of this paper is to show that it is relatively easier to obtain maximum likelihood estimates of the parameters of the continuous model, which describes the data on duration to first conception as well as does the discrete model. Simple expressions for the moment and maximum likelihood estimates with the corresponding covariance matrices are obtained. Application is made to three sets of data.     

A model of the determinants in married women of sterilization method choice

A model for predicting sterilization method selection is constructed on the basis of hypotheses about 1. the relationship between the fertility termination, sterilization, and method selection decisions and 2. the influence of substantive, processual, and contextual factors in those decisions. The model is found to have an acceptably good fit to data from almost five hundred women in married couples selecting either tubal ligation or vasectomy. A number of interesting dynamic pathways leading to method selection are observed. Some weaknesses in the model are discussed. It is desirable that further confirmation and elaboration of the model using longitudinal and husband-wife data be undertaken.This paper is based on a study funded by the National Institutes of Child Health and Human Development, Center for Population Research, Grant Number 13459.     

A method for assessing the global spread of HIV-1 infection based on air travel

"The paper presents a methodology aimed at quantifying the impact of regular air traffic on the global spread of AIDS. A compartmental approach is used to represent the fluxes of infective passengers between 52 major cities. The impact of these fluxes on the pandemic is assessed by using a methodology which has been applied in the past for studying the dynamic of an influenza pandemic. In its present version, under simplified assumptions, the model reproduces qualitatively the three world patterns of HIV-1 infection in 1988. The methodology developed in this paper does not provide a detailed past history of the virus, and does not take into account the possibility of multifoci sporadic cases in the past. However it provides evidence that the significant start of the pandemic...was by the end of the 60's in Central Africa." (SUMMARY IN FRE)     

A decomposition of immigrant divorce rates in Australia

Crude divorce rates of overseas-born Australians by birthplace are not comparable because different birthplace groups have different age structures and marriage patterns that affect the rates. This paper decomposes the crude rates into components due to the effects of age structrue, marriage patterns and the divorce rate of married men and women. This allows for a better comparison of the level of divorce by birthplace. The range in the standardized divorce rates by birthplace is smaller than that indicated by the crude rates. Nonetheless, there remains considerable variation in immigrant divorce rates in Australia.     

Prey capture tactics of spiders: An analysis based on a simulation model for spider's growth

Summary The prey capture tactics of spiders was analyzed, considering the energy gained by the capture of prey and that required for it. For the purpose of it, a growth model of spiders was constructed, expressing the flow rate of prey biomass to the spider's body by differential equations. Solving these equations under the differing values of three parameters, growth curves of spiders was obtained. These three parameters are the amount of prey biomass supplied daily to spiders,x ₀, the rate of prey capture of spiders, α, and a coefficient of the respiration rate required for the capture of prey,k. When the value ofk increased, spiders could grow only at high value ofx ₀. These results suggest that habitats with small prey biomass are preferred by spiders adopting a sit-and-wait tactics for prey capture, which requires small values ofk. Wolf spiders are one of these spiders showing that tactics. On the other hand, web-builders which require large amount of energy for spinning webs (namely, take large value ofk), are able to grow only in the habitats with large prey biomass. Each species of spiders are considered to locate in a certain point between both extremes of these tactics for the capture of prey.     

On the dependence of age structure on asequence of mortality and fertility schedules: An exposition of a cyclical model of population change

In this paper a method to investigate the dependence of age structure and growth rate on a given sequence of fertility and mortality schedules under the conditions of unchanging mortality and absence of migration is discussed. The method consists in projecting an arbitrary population classified by age to the ends of successive periods assuming that a given age pattern of mortality will remain without change and that a given sequence of fertility schedules will repeatedly operate on the population in a cyclical fashion. It is shown that after a sufficiently large number of repetitions of the cycle, the shifts in age structure between the ends of successive periods and the changes in the growth of the different age groups from one period to the next show a cyclical pattern. Formulas are derived expressing the above changes in terms of a sequence of k growth multipliers, k being the number of schedules in the fertility sequence, and the survival rates in the mortality schedule. A numerical illustration of the theory is given using fertility data from Finland.     

A formula for determining social worker positions based upon the Pardes method

An alternative approach to traditionalad hoc methods of determining social worker positions is presented. It is based upon the collection of objective data and their inclusion in a mathematical formula. This apprach assures the employment of identical criteria and administrative procedures for the assignment of social workers' positions. It guarantees that for a given number of social work bureaux the assignment is equitable. The particular example presented is that of regional councils in Israel. The formula includes the variables: number of residents within each council's jurisdiction, and of community distress and distance travelled by social workers between the settlements of a council.     

A mathematical model of a theoretical sleeping sickness vaccine

ABSTRACT

Human African sleeping sickness is found throughout sub-Saharan Africa. It affects up to 70,000 individuals per year, primarily the poor. Existing treatments are limited, costly, and often toxic. Recent evidence suggests that a vaccine may be viable. Potential vaccines against Rhodesian sleeping sickness may be imperfect, may only be delivered to some proportion of the population, may wane over time, and may not always mount an immunogenic response in the individual receiving it. The potential effects of such a vaccine are addressed and compared to vector control. The basic reproductive ratio for both unvaccinated and vaccinated individuals is derived. The fitness ratio is used to show that vaccines that grant longer life must be accompanied by a corresponding reduction in transmissibility. A sensitivity analysis shows that control of tsetse flies through insecticide is superior to an idealized vaccine. Such a vaccine is unlikely to eradicate the disease, even if delivered to 100% of the population. Consequently, efforts to control sleeping sickness that do not incorporate vector control may be flawed.     

A model for culturally adapting a learning system

The Cross-Cultural Adaption Model (XCAM) is designed to help identify cultural values contained in the text, narration, or visual components of a learning instrument and enables the adapter to evaluate his adapted model so that he can modify or revise it, and allows him to assess the modified version by actually measuring the amount of cultural conflict still present in it. Such a model would permit world-wide adaption of learning materials in population regulation. A random sample of the target group is selected. The adapter develops a measurin g instrument, the cross-cultural adaption scale (XCA), a number of statements about the cultural affinity of the object evaluated. The pretest portion of the sample tests the clarity and understandability of the rating scale to be used for evaluating the instructional materials; the pilot group analyzes the original version of the instructional mater ials, determines the criteria for change, and analyzes the adapted version in terms of these criteria; the control group is administered the original version of the learning materials; and the experimental group is administered the adapted version. Finally, the responses obtained from the XRA rating scale and discussions of both the experimental and control groups are studied and group differences are ev aluated according to cultural conflicts met with each version. With this data, the preferred combination of elements is constructed.     

A components method for measuring the impact of a family planning program on birth rates

One of the major goals of family planning programs worldwide has been to reduce the level of fertility in hopes of slowing the rate of natural increase and promoting social and economic development. Such programs have now been in existence for sufficient lengths of time to have had an impact on fertility levels. In general countries with organized family planning programs, marked declines in fertility levels have been observed. The extent to which such declines may be credited to organized programs has not been rigorously measured because an appropriate research methodology has been lacking. This paper describes one method of directly linking declines in fertility levels to the contraceptive protection experienced by a population. The contribution of organized family planning programs is estimated by decomposing the amount of total contraceptive protection into within-program and outside-program sources.