Todd; Milner, Fabio A. A finite difference method for a
two-sex model of population dynamics. SIAM Journal of Numerical
Analysis, Vol. 26, No. 6, Dec 1989. 1,474-86 pp. Philadelphia,
Pennsylvania. In Eng.
"An explicit finite difference algorithm is developed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations that models the dynamics of a two-sex population. The algorithm is unconditionally stable. The optimal rate of convergence of the algorithm is demonstrated for the maximum norm. Results from a numerical simulation of U.S. population growth from 1970 to 1980 are presented; these compare favorably with the actual data."
Correspondence: T. Arbogast, Purdue University, Department of Mathematics, West Lafayette, IN 47907. Location: Princeton University Library (SM).
Charles. Estimating the distribution of desired family
size and excess fertility. Journal of Human Resources, Vol. 24,
No. 4, Fall 1989. 709-24 pp. Madison, Wisconsin. In Eng.
"This paper proposes an econometric solution to the problem of censoring of desired family size (DFS) by the number of children ever born (CEB) in cross-sectional fertility and household surveys." The solution proposed is based on a bivariate ordered-probit model for both DFS and CEB. The model proposed also suggests an alternative solution to the problem of estimating the replacement effect of infant and child deaths on the number of children ever born.
Correspondence: C. Calhoun, International Institute for Applied Systems Analysis, Population Program, 2361 Laxenburg, Austria. Location: Princeton University Library (IR).
57:10746 Chan, W.
L.; Guo, Bao Zhu. Optimal birth control of population
dynamics. Journal of Mathematical Analysis and Applications, Vol.
144, No. 2, 1989. 532-52 pp. San Diego, California. In Eng.
"We study optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition [and] a fixed final horizon are developed, and the time optimal control problem, the problem with target sets, and the infinite planning horizon case are investigated."
Correspondence: W. L. Chan, Chinese University of Hong Kong, Department of Mathematics, Shatin, N.T., Hong Kong. Location: Princeton University Library (SM).
57:10747 Chan, W.
L.; Guo, Bao Zhu. Optimal birth control of population
dynamics. II: problems with free final time, phase constraints, and
mini-max costs. Journal of Mathematical Analysis and Applications,
Vol. 146, No. 2, 1990. 523-39 pp. San Diego, California. In Eng.
"We study optimal birth control of population systems of McKendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control. New results on problems with free final time, phase constraints, and mini-max costs are presented."
For Part 1, published in 1989, see elsewhere in this issue.
Correspondence: W. L. Chan, Chinese University of Hong Kong, Department of Mathematics, Shatin, N. T., Hong Kong. Location: Princeton University Library (SM).
Chin Long. A true rate of population growth: Lotka's
intrinsic rate of natural increase revisited. Mathematical
Biosciences, Vol. 103, No. 1, Feb 1991. 139-52 pp. New York, New York.
"In this paper, Lotka's intrinsic rate of current population growth is evaluated. A new method of computing the net reproduction rate and a new rate of population growth are proposed. The proposed rate is the rate of growth of the female population per woman per year. The rate is positive, equal to zero, or negative as a population is increasing, remaining stationary, or decreasing. The rate for the 1987 U.S. white female population was R = -0.0037. This means that the white population was decreasing in 1987 and was losing 3.7 females for every 1,000 women per year."
Correspondence: C. L. Chiang, University of California, School of Public Health, Berkeley, CA 94720. Location: Princeton University Library (SM).
Dimitrios S.; Sonis, Michael. Chaos and socio-spatial
dynamics. Applied Mathematical Sciences, Vol. 86, ISBN
0-387-97283-8. LC 90-9672. 1990. xvii, 184 pp. Springer-Verlag: New
York, New York/Berlin, Germany, Federal Republic of. In Eng.
"The main objective of this book is to present some key qualitative features of a universal discrete relative dynamics map (iterative process). It is argued that the form of this map can accommodate a wide range of dynamics found in social systems distributed in (discrete) space. Particular emphasis is placed on population dynamics. A gamut of models are included in the book, ranging from the one-stock, two-location case to multiple-stock, multiple-location examples." An example of how this universal map can be used in socio-spatial dynamics is provided. "Empirical evidence is presented, describing U.S. regional relative population distributions according to the universal map, covering approximately two centuries of observations and forecasts."
Correspondence: Springer-Verlag, 175 Fifth Avenue, New York, NY 10010. Location: Princeton University Library (SM).
David A.; Marsh, Lachlan M. Modeling AIDS as a function of
other sexually transmitted disease. Mathematical Biosciences, Vol.
103, No. 1, Feb 1991. 17-31 pp. New York, New York. In Eng.
"The spread of AIDS, as with any sexually transmitted disease, will depend on the pattern of sexual activity. Both the proportion of the population who have high partner exchange rates and the extent to which that proportion interacts with the remainder of the population are likely to be important determinants of the AIDS epidemic. However, it does not seem likely that surveys could obtain sufficiently reliable information of this nature for use in an accurate model of the AIDS epidemic. On the other hand, such information is implicitly contained in the epidemiology of other sexually transmitted diseases (STDs). Therefore a method is suggested of calculating the parameters of a model of the AIDS epidemic by comparing it with the epidemiology of another STD. The result is a model that predicts the likelihood of infection by the AIDS virus as a function of time and an individual's history of STD."
Correspondence: D. A. Kault, James Cook University of North Queensland, Townsville, Queensland 4811, Australia. Location: Princeton University Library (SM).
57:10751 Kim, Young
J.; Schoen, Robert; Sarma, P. Sankara. Momentum and the
growth-free segment of a population. Demography, Vol. 28, No. 1,
Feb 1991. 159-73 pp. Washington, D.C. In Eng.
"In the scenario of a sudden drop in fertility to replacement level, Preston (1986) argued that the population segment under age T, the length of generation, remained growth-free. Here we first present a new relationship for the momentum of any observed population as the ratio of 1) the proportion of the observed population under the mean age at childbearing to 2) the proportion of its life table population under that mean age. We then use that relationship to demonstrate Preston's approximation. Growth factors for other population segments are also presented. When the initial population is stable, momentum can be approximated as a function of the net reproduction rate alone....We selected 12 female populations...to span a broad range of age compositions and fertility and mortality rates."
Correspondence: Y. J. Kim, Johns Hopkins University, Department of Population Dynamics, Baltimore, MD 21205. Location: Princeton University Library (SPR).
Frank. Log-linear modelling and simultaneous
standardization of rates. Population Research Laboratory Research
Discussion Paper, No. 69, Nov 1990. 16 pp. University of Alberta,
Department of Sociology, Population Research Laboratory: Edmonton,
Canada. In Eng.
"This paper demonstrates how rates can be modelled and standardized for age and gender compositions simultaneously using log-linear rate models....Youth suicide in Canada for 1971 and 1981 is used as an empirical example to demonstrate the application of log-linear rate modelling with simultaneous standardization."
Correspondence: University of Alberta, Department of Sociology, Population Research Laboratory, Edmonton, Alberta T6G 2H4, Canada. Location: Princeton University Library (SPR).