In a previous preprint article, the author presented a conjecture on the trend of demographic mortality as the life span progresses. That article also provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work, we show the possibility that the demographic mortality at high ages would be given by the sum of four main components. The four components were derived by iteratively solving the Fredholm equation that can be associated with the model. These solutions are presented for three demographic cases based on statistical data available in the public databases and literature. These are: mortality data in the US from 1970 to 2017, in Italy from 1974 to 2019 and in Japan from 1974 to 2019. In all cases, similarities and invariant components are noted and presented in graphs and numerical data. The four aforementioned components appear on average equally spaced in the age peaks (in the case of females ~50, ~63, ~77, ~90 ages) and are always present for all sample years and in all three countries. These same components can be used to reconstruct the qx datum, at advanced ages, of the considered Life Tables. A correlation with a more recent study using a multi-omics approach is pointed out.
| Published in | Humanities and Social Sciences (Volume 14, Issue 1) |
| DOI | 10.11648/j.hss.20261401.13 |
| Page(s) | 20-31 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Demographic Mortality, S-System Distribution, Demographic Life Tables, Fredholm Equation
| [1] | G. Alberti “A conjecture on demographic mortality at high ages.” |
| [2] | G. Alberti "Fermi statistics method applied to model macroscopic demographic data” |
| [3] | S. Twomey “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature.” J. ACM 10 (1963), 79-101. |
| [4] |
Fredholm Integral Equations, web site: Available from:
https://inteq.readthedocs.io/en/latest/fredholm/index.html [Accessed 13 November 2025] |
| [5] | L. A. Gavrilov and N. S. Gavrilova, “Mortality Measurement at Advanced Ages: a Study of the Social Security Administration Death Master File”, North American Actuarial Journal. 15(3): 432-447. |
| [6] | Elizabeth Arias and Jiaquan Xu, “United States Life Tables, 2017”, NVSS, Volume 68, Number 7, June 24, 2019. |
| [7] |
Istituto Italiano di Statistica, “ISTAT Data”, Available from:
https://esploradati.istat.it/databrowser/#/en [Accessed 13 November 2025] |
| [8] |
National Institute of Population and Social Security, “The Japanese Mortality Database”, Available from:
https://www.ipss.go.jp/p-toukei/JMD/index-en.asp [Accessed 13 November 2025] |
| [9] | Jacques Demongeot, Pierre Magal, ‘ Population dynamics model for aging ‘, |
| [10] | F. Zane, C. MacMurray, C. Guillermain, C. Cansell, N.Todd and M. Rera, ‘Ageing as two-phases process: a theoretical framework’ |
| [11] | J. D. Zazueta-Borboa, J. M. Aburto, I. Permanyer, V. Zarulli & F. Janssen, ‘Contributions of age groups and causes of death to the sex gap in lifespan variation in Europe’, |
| [12] | A. Golubev, ‘A previously unrecognized peculiarity of late-life human mortality kinetics?’, |
| [13] | M. Tu˘grul and U. K. Steiner, ‘Demographic consequences of damage dynamics in single-cell aging’, |
| [14] | N. Shimoyama, M. Hosonuma, ‘Application of the first exit time stochastic model with self-repair mechanism to human mortality rates’, |
| [15] | P. Y. Nielsen, M. K Jensen, N. Mitarai, S. Bhatt, ‘A Systems Level Explanation for Gompertzian Mortality Patterns is provided by the "Multiple and Inter-dependent Component Cause Model”’, |
| [16] | J. Shi, Y. Shi, P. Wang and D. Zhu, ‘Multi-population mortality modelling: a Bayesian hierarchical approach’, |
| [17] | S. C. Patricio, F. Castellares, B. Queiroz, ‘Mortality modeling at old-age: an mixture model approach’, |
| [18] | S. C. Patricio, T. I. Missov,’ Makeham Mortality Models as Mixtures’, |
| [19] | X. Shen, C. Wang, X. Zhou, W.Zhou, D. Hornburg, S. Wu & M. P. Snyder “Nonlinear dynamics of multi-omics profiles during human aging”, Nature Aging, |
APA Style
Alberti, G. (2026). More on the Mortality Conjecture: The Components of Demographic Mortality. Humanities and Social Sciences, 14(1), 20-31. https://doi.org/10.11648/j.hss.20261401.13
ACS Style
Alberti, G. More on the Mortality Conjecture: The Components of Demographic Mortality. Humanit. Soc. Sci. 2026, 14(1), 20-31. doi: 10.11648/j.hss.20261401.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.hss.20261401.13,
author = {Giuseppe Alberti},
title = {More on the Mortality Conjecture: The Components of Demographic Mortality},
journal = {Humanities and Social Sciences},
volume = {14},
number = {1},
pages = {20-31},
doi = {10.11648/j.hss.20261401.13},
url = {https://doi.org/10.11648/j.hss.20261401.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.hss.20261401.13},
abstract = {In a previous preprint article, the author presented a conjecture on the trend of demographic mortality as the life span progresses. That article also provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work, we show the possibility that the demographic mortality at high ages would be given by the sum of four main components. The four components were derived by iteratively solving the Fredholm equation that can be associated with the model. These solutions are presented for three demographic cases based on statistical data available in the public databases and literature. These are: mortality data in the US from 1970 to 2017, in Italy from 1974 to 2019 and in Japan from 1974 to 2019. In all cases, similarities and invariant components are noted and presented in graphs and numerical data. The four aforementioned components appear on average equally spaced in the age peaks (in the case of females ~50, ~63, ~77, ~90 ages) and are always present for all sample years and in all three countries. These same components can be used to reconstruct the qx datum, at advanced ages, of the considered Life Tables. A correlation with a more recent study using a multi-omics approach is pointed out.},
year = {2026}
}
TY - JOUR T1 - More on the Mortality Conjecture: The Components of Demographic Mortality AU - Giuseppe Alberti Y1 - 2026/01/09 PY - 2026 N1 - https://doi.org/10.11648/j.hss.20261401.13 DO - 10.11648/j.hss.20261401.13 T2 - Humanities and Social Sciences JF - Humanities and Social Sciences JO - Humanities and Social Sciences SP - 20 EP - 31 PB - Science Publishing Group SN - 2330-8184 UR - https://doi.org/10.11648/j.hss.20261401.13 AB - In a previous preprint article, the author presented a conjecture on the trend of demographic mortality as the life span progresses. That article also provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work, we show the possibility that the demographic mortality at high ages would be given by the sum of four main components. The four components were derived by iteratively solving the Fredholm equation that can be associated with the model. These solutions are presented for three demographic cases based on statistical data available in the public databases and literature. These are: mortality data in the US from 1970 to 2017, in Italy from 1974 to 2019 and in Japan from 1974 to 2019. In all cases, similarities and invariant components are noted and presented in graphs and numerical data. The four aforementioned components appear on average equally spaced in the age peaks (in the case of females ~50, ~63, ~77, ~90 ages) and are always present for all sample years and in all three countries. These same components can be used to reconstruct the qx datum, at advanced ages, of the considered Life Tables. A correlation with a more recent study using a multi-omics approach is pointed out. VL - 14 IS - 1 ER -
Independent Researcher, Como, Italy
