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Age Trajectories of Mortality from All Diseases in the Six Most Populated Countries of the South America During the Last Decades

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Abstract

Age trajectories of total mortality represent an irreplaceable source of information about aging. In principle, age affects mortality from all diseases differently than it affects mortality from external causes. External causes (accidents) are excluded here from all causes, and the resultant category “all-diseases” is tested as a helpful tool to better understand the relationship between mortality and age. Age trajectories of all-diseases mortality are studied in the six most populated countries of the South America during 1996–2010. The numbers of deaths for specific causes of death are extracted from the database of WHO, where the ICD-10 revision is used. The all-diseases mortality shows a strong minimum, which is hidden in total mortality. Two simple deterministic models fit the age trajectories of all-diseases mortality. The inverse proportion between mortality and age fits the mortality decreases up to minimum value in all six countries. All previous models describing mortality decline after birth are discussed. Theoretical relationships are derived between the parameter in the first model and standard mortality indicators: Infant mortality, Neonatal mortality, and Postneonatal mortality. The Gompertz model extended with a small positive quadratic element fit the age trajectories of all-diseases mortality after the age of 10 years.

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Authors and Affiliations

  1. Department of Informatics and Quantitative Methods, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czech Republic

    Josef Dolejs

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  1. Josef Dolejs
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Correspondence to Josef Dolejs.

Appendix

Appendix

See Figs. 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 and 36.

Fig. 9
figure 9

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

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Fig. 10
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Age trajectory of all-diseases mortality fitted by the two models in Argentina in the semi-logarithmic scale in 2010

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Age trajectory of all-diseases mortality fitted by the two models in Brazil in the log-log scale in 2006

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Age trajectory of all-diseases mortality fitted by the two models in Brazil in the semi-logarithmic scale in 2006

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Age trajectory of all-diseases mortality fitted by the two models in Chile in the log-log scale in 1997

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Age trajectory of all-diseases mortality fitted by the two models in Chile in the semi-logarithmic scale in 1997

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Age trajectory of all-diseases mortality fitted by the two models in Chile in the log-log scale in 2009

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

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Fig. 17
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Age trajectory of all-diseases mortality fitted by the two models in Colombia in the log-log scale in 1997

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Age trajectory of all-diseases mortality fitted by the two models in Colombia in the semi-logarithmic scale in 1997

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Fig. 19
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Age trajectory of all-diseases mortality fitted by the two models in Colombia in the log-log scale in 1998

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Age trajectory of all-diseases mortality fitted by the two models in Colombia in the semi-logarithmic scale in 1998

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Fig. 21
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Age trajectory of all-diseases mortality fitted by the two models in Peru in the log-log scale in 1999

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Age trajectory of all-diseases mortality fitted by the two models in Peru in the semi-logarithmic scale in 1999

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Fig. 23
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Age trajectory of all-diseases mortality fitted by the two models in Peru in the log-log scale in 2007

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Fig. 24
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Age trajectory of all-diseases mortality fitted by the two models in Peru in the semi-logarithmic scale in 2007

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Fig. 25
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Age trajectory of all-diseases mortality fitted by the two models in Venezuela in the log-log scale in 1996

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Age trajectory of all-diseases mortality fitted by the two models in Venezuela in the semi-logarithmic scale in 1996

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Fig. 27
figure 27

Age trajectory of all-diseases mortality fitted by the two models in Venezuela in the log-log scale in 2007

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Age trajectory of all-diseases mortality fitted by the two models in Venezuela in the semi-logarithmic scale in 2007

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Fig. 29
figure 29

Residuals calculated in the quadratic model (1)

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Fig. 30
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Residuals calculated in the linear model (2)

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Fig. 31
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Residuals calculated in the model (3)

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Residuals calculated in the Gompertz model

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Residuals calculated in the quadratic Gompertz model

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Fig. 34
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Residuals calculated in the linear Gompertz model

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Residuals calculated in the logistic model with two parameters

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Fig. 36
figure 36

Residuals calculated in the Weibull model with two parameters

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Dolejs, J. Age Trajectories of Mortality from All Diseases in the Six Most Populated Countries of the South America During the Last Decades. Bull Math Biol 76, 2144–2174 (2014). https://doi.org/10.1007/s11538-014-0005-0

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