A time-dependent McKendrick population model for logistic transition. (English) Zbl 0761.92029
Summary: We develop a time-dependent McKendrick population model for logistic transition between two birth-death equilibria. The case of age-specific fertility and mortality rates undergoing respective logistic transitions is considered. An example of nonlinear least squares estimation of the parameters of logistic transition is provided, using historical demographic rates of Sweden. The solution of a general time-dependent McKendrick population model is interpreted from the point of view of the evolution operators theory, and the stability of the system is derived. Finally, we apply these results to our newly established model.
MSC:
| 92D25 | Population dynamics (general) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35F10 | Initial value problems for linear first-order PDEs |
| 45J05 | Integro-ordinary differential equations |
| 45M10 | Stability theory for integral equations |
Keywords:
logistic transition; age-specific mortality rates; demographic transition; logistic equations; time-dependent McKendrick population model; birth-death equilibria; age-specific fertility; nonlinear least squares estimation; general time-dependent McKendrick population model; evolution operatorsReferences:
| [1] | Wrigley, E. A., Population and History (1974), McGraw-Hill: McGraw-Hill New York |
| [2] | Cowgill, D. O., The use of logistic curve and the transition model in the developing nations, (Bose, A.; Desai, P. B.; Jain, S. P., Studies in Demography (1970), The University of North Carolina Press: The University of North Carolina Press Chapel Hill, North Carolina), 157-165, and London, George Allen and Unwin |
| [3] | Keyfitz, N., Applied Mathematical Demography (1985), Springer-Verlag: Springer-Verlag New York · Zbl 0597.92018 |
| [4] | McKendrick, A. G., Application of mathematics to medical problems, Proc. Edin. Math. Soc., 44, 98-130 (1926) · JFM 52.0542.04 |
| [5] | Song, J.; Yu, J. Y., Population System Control (1987), Springer-Verlag |
| [6] | Yu, J. Y.; Guo, B. Z.; Zhu, G. T., Expansion in L \((0, r_m)\) for the population evolution and controllability of the population system, J. Sys. Sci. & Math. Scis, 7, 97-104 (1987) · Zbl 0633.92012 |
| [7] | Keyfitz, N.; Flieger, W., World Population — An Analysis of Vital Data (1968), University of Chicago Press: University of Chicago Press Chicago |
| [9] | Chen, R. Z., The stability of non-stationary population control systems and the critical fertility of females, KeXue TongBao, 26, 410-414 (1982), (No. 6) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
