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Modeling Human Mortality from All Diseases in the Five Most Populated Countries of the European Union

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Abstract

Age affects mortality from diseases differently than it affects mortality from external causes, such as accidents. Exclusion of the latter leads to the “all-diseases” category. The age trajectories of mortality from all diseases are studied in the five most populated countries of the EU, and the shape of these 156 age trajectories is investigated in detail. The arithmetic mean of ages where mortality reaches a minimal value is 8.47 years with a 95% confidence interval of [8.08, 8.85] years. Two simple deterministic models fit the age trajectories on the two sides of the mortality minimum. The inverse relationship is valid in all cases prior to this mortality minimum and death rates exactly decreased to three thousandths of its original size during the first 3000 days. After the mortality minimum, the standard Gompertz model fits the data in 63 cases, and the Gompertz model extended by a small quadratic element fits the remaining 93 cases. This analysis indicates that the exponential increase begins before the age of 15 years and that it is overshadowed by non-biological causes. Therefore, the existence of a mechanism switching that would explain the exponential increase in mortality after the age of 35 years is unlikely.

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Acknowledgements

This paper was supported by the research project Excellence 2017 and internal research SPEV—Investment in conditions of the concept Industry 4.0, Faculty of Informatics and Management, University of Hradec Kralove, Czech Republic.

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  1. University of Hradec Králové, Hradec Kralove, Czech Republic

    Josef Dolejs

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  1. Josef Dolejs
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Correspondence to Josef Dolejs.

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Appendix

Appendix

See Tables 3, 4, 5, 6 and Figs. 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23.

Table 3 Results of males in the linear model in the log–log scale in [0, A) years
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Table 4 Results of females in the linear model in the log–log scale in [0, A) years
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Table 5 Results of males in the two models in the semi-logarithmic scale in the second age interval [A, 95) years
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Table 6 Results of females in the two models in the semi-logarithmic scale in the second age interval [A, 95) years
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Fig. 6
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Age trajectory of all-diseases mortality fitted by the two models in Germany in the log–log scale in 2010

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Age trajectory of all-diseases mortality fitted by the two models in Germany in the semi-logarithmic scale in 2010

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Age trajectory of all-diseases mortality fitted by the two models in France in the log–log scale in 2000

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Age trajectory of all-diseases mortality fitted by the two models in France in the semi-logarithmic scale in 2000

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Fig. 10
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Age trajectory of all-diseases mortality fitted by the two models in France in the log–log scale in 2009

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Age trajectory of all-diseases mortality fitted by the two models in France in the semi-logarithmic scale in 2009

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Fig. 12
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Age trajectory of all-diseases mortality fitted by the two models in Italy in the log–log scale in 2003

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Age trajectory of all-diseases mortality fitted by the two models in Italy in the semi-logarithmic scale in 2003

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Fig. 14
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Age trajectory of all-diseases mortality fitted by the two models in Italy in the log–log scale in 2010

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Age trajectory of all-diseases mortality fitted by the two models in Italy in the semi-logarithmic scale in 2010

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Age trajectory of all-diseases mortality fitted by the two models in Spain in the log–log scale in 1999

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Fig. 17
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Age trajectory of all-diseases mortality fitted by the two models in Spain in the semi-logarithmic scale in 1999

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Fig. 18
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Age trajectory of all-diseases mortality fitted by the two models in Spain in the log–log scale in 2011

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figure 19

Age trajectory of all-diseases mortality fitted by the two models in Spain in the semi-logarithmic scale in 2011

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Fig. 20
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Age trajectory of all-diseases mortality fitted by the two models in the UK in the log–log scale in 2001

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Age trajectory of all-diseases mortality fitted by the two models in the UK in the semi-logarithmic scale in 2001

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Fig. 22
figure 22

Age trajectory of all-diseases mortality fitted by the two models in the UK in the log–log scale in 2010

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Fig. 23
figure 23

Age trajectory of all-diseases mortality fitted by the two models in the UK in the semi-logarithmic scale in 2010

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Dolejs, J. Modeling Human Mortality from All Diseases in the Five Most Populated Countries of the European Union. Bull Math Biol 79, 2558–2598 (2017). https://doi.org/10.1007/s11538-017-0341-y

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